11 EQUATIONS

PRACTICE SHEET-1
1. A train started from a station with a certain
number of passengers. At the first halt, 7. Let there be three simultaneous linear
1/3rd of its passengers got down and 120 equations in two unknowns, which are non-
passengers got in. At the second halt, half of parallel and non-collinear them. What can
the passengers got down and 100 persons be the number of solutions (if they do exist)?
got in. Then, the train left for its destination (a) One or infinite (b) Only one
with 240 passengers. How many passengers (c) Exactly two (d) exactly three
were there in the train when it started?
(a) 540 (b) 480 8. If 1 is added to the denominator of a
(c) 360 (d) 240 fraction, it becomes 1/2 and if 1 is added to
the numerator, the fraction becomes 1. What
2. A person bought a certain number of books is the fraction?
for Rs 80. If he had bought 4 more books for (a) 5/9 (b) 2/3
the same sum, each book would have cost (c) 4/7 (d) 10/11
Rs 1 less. What is the price of each book?
(a) Rs 10 (b) Rs 8 2 3 9 and 4 9 21 , where x ≠ 0
9. If    
(c) Rs 5 (d) Rs 4 x y xy x y xy
and y ≠ 0, then what is the value of x + y?
3. A person bought 5 tickets from a station P to
(a) 2 (b) 3
a station Q and 10 tickets from the station P
(c) 4 (d) 8
to a station R. He paid Rs 350. If the sum of
a ticket from P to Q and a ticket from P to R
10. The sum of two numbers is 80. If the larger
is Rs 42, then what is the fare from P to Q?
number exceeds four times the smaller by 5,
(a) Rs 12 (b) Rs 14
what is the smaller number?
(c) Rs 16 (d) Rs 18
(a) 5 (b) 15
(c) 20 (d) 25
4. Pooja started her job with certain monthly
salary and gets a fixed increment every year.
11. If 2a + 3b = 17 and 2a+2 − 3b+1 = 5, then,
If her salary was Rs 4200 after 3 years and `
(a) a = 2, b = 3 (b) a = -2, b = 3
6800 after 8 years of service, then what are
(c) a = 2, b = –3 (d) a = 3, b = 2
her initial salary and the annual increment,
respectively?
2 x  3 y  1 x  4 y  8 4 x  7 y  2 then what is
(a) Rs 2640, Rs 320 (b) Rs 2460, Rs 320 12. If  
2 3 5
(c) Rs 2460, Rs 520 (d) Rs 2640, Rs 520
(x + y) equal to?
(a) 3 (b) 2
5. A number consists of two digits, whose sum
(c) 0 (d) –2
is 10. If 18 is subtracted from the number,
digits of the number are reversed. What is
13. Sum of two numbers is 21 and their
the product?
difference is 11, then the greatest number is
(a) 15 (b) 18
(a) 5 (b) 16
(c) 24 (d) 32
(c) 9 (d) 10
6. A railway ticket for a child costs half the full
14. The area of a rectangle remains the same if
fare but the reservation charge is the same
the length is increased by 7 m and the
on half tickets as much as on full ticket. One
breadth is decreased by 3 m. The area
reserved first class ticket for a journey
remains unaffected if the length is decreased
between two stations is Rs 362, one full and
by 7 m and the breadth is increased by 5 m ,
one half reserved first class tickets cost Rs
then area of rectangle is
554. What is the reservation charge?
(a) 280 m2 (b) 320 m2
(a) Rs 18 (b) Rs 22
(c) 420 m 2 (d) 400 m2
(c) Rs 38 (d) Rs 46

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 161 -

15. A and B each have a certain number of combined. How many of each item should
mangoes. A says to B: "If you give 30 of your they order?
mangoes, I will have twice as many as left (a) (40, 60, 100) (b) (20, 30, 80)
with you" B replies "If you give me 10, I will (c) (50, 100, 60) (d) (40, 80, 25)
have thrice as many as left with you". How
many mangoes did A has? 22. A student was asked to find 5 of a number.
(a) 41 (b) 62 16
(c) 34 (d) 32 By mistake he found 5 of that number. His
6
16. There are two examination rooms A and B. If answer was 250 more than the correct
10 candidates are sent from room A to room answer. Find the given number.
B the number of students in each room is (1) 300 (2) 480
the same. If 20 candidates are sent from B (3) 450 (4) 500
to A, the number of students in A is double
the number in of students in B. Then,
number of students room B is 23. A tin of oil was 4 full. When 6 bottles of oil
5
(a) 40 (b) 100
was taken out and 4 bottles of oil was
(c) 80 (d) 60
3
poured into it, it was full. How many
17. The numerator of a fraction is 2 less than 4
the denominator. If one is added to its bottles of oil can the tin contain?
denominator, it becomes 1/2, the fraction is (1) 10 (2) 20
(a) 2/3 (b) 3/5 (3) 30 (4) 40
(c) 3/4 (d) 5/7
24. A candidate in an examination was asked to
18. The sum of digits of a two-digit number is 8 find
5 of a certain number. By mistake he
and the difference between the number and 14
that formed by reversing the digits is 18.
What is three difference between the digits of found 5 of it. Thus, his answer was 25 more
4
the number?
than the correct answer. The number was:
(a) 1 (b) 2
(1) 28 (2) 56
(c) 3 (d) 4
(3) 84 (4) 140
19. A length of rectangle is 5 cm less than twice
its width. if the length is decreased by 5 cm, 25. A man read 2 th of a book on the first day.
and width is decreased by 2 cm. the 5
perimeter of resulting rectangle will be 18 1
He read rd more on second day than he
cm, Find the length of original rectangle ? 3
(a) 9 (b) 7 read on the first day. 15 pages were left for
(c) 6 (d) 5 the third day. The number of pages in the
book is
20. The present of Sita's father is three times the (1) 100 (2) 105
present age of Sita. After six years sum of (3) 225 (4) 250
their ages will be 72 years. Find the present
age of Sita ?
(a) 12 yrs (b) 15 yrs 26. A girl was asked to multiply a number by 7 ,
8
(c) 16 yrs (d) 10 yrs
instead she divided the number by
7 and
21. The Community Relief fund receives a large 8
donation of $ 2800. The foundation agrees to got the result 15 more than the correct
spend the money on $ 20 school bags, $ 25 result. The sum of the digits of the number
sweaters, $ 5 b0oks. They want to buy 200 was:
items and send them to schools in (1) 4 (2) 8
earthquake-hit areas. They must order as (3) 6 (4) 11
many books as school bages and sweaters

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 162 -

27. A, B, C and D purchase a gift worth Rs 60. A (1) 40 (2) 16
1 1 (3) 20 (4) 100
pays of what others are paying, B pays
2 3
1 29. Thrice the square of a natural number
of what others are paying and C pays of decreased by four times the number is equal
4
to 50 more than the number. The number is:
what others are paying. What is the amount
(1) 4 (2) 5
paid by D?
(3) 10 (4) 6
(1) 16 (2) 13
(3) 14 (4) 15
30. A farmer divides his herd of n cows among
his four sons so that the first son gets one –
28. A number of boys raised 400 for a famine half the herd, the second son gets one –
relief fund, each boy giving as many 25 paise fourth, the third son gets one – fifth and the
coins as there were boys. The number of fourth son gets 7 cows. The value of n is
boys was: (1) 80 (2) 100
(3) 140 (4) 180

ANSWER KEY
1. (d) 2. (c) 3. (b) 4. (d) 5. (c) 6. (b) 7. (b) 8. (b) 9. (c) 10. (b)
11. (d) 12. (d) 13. (b) 14. (c) 15. (c) 16. (c) 17. (b) 18. (b) 19. (a) 20. (b)
21. (a) 22. (b) 23. (d) 24. (a) 25. (c) 26. (d) 27. (b) 28. (a) 29. (b) 30. (c)

PRACTICE SHEET-2
1. A men has some hens and cows. If the (1) 6 (2) 10
number of heads be 48 and the number of (3) 12 (4) 14
feet equals 140, then the number of hens 5. A fraction becomes 1 when 1 is subtracted
will be 3
(1) 23 (2) 22 from both the numerator and the
(3) 24 (4) 26 1
denominator. The same fraction becomes
2. Slope of the line 2x − y + 4 = 0 is 2
(1) 2 (2) 1 when 1 is added to both the numerator and
the denominator. The sum of numerator and
(3) 0 (4) 1/2
denominator of the fraction is
(1) 10 (2) 18
3. A number consists of two digits. If the (3) 7 (4) 16
number formed by interchanging the digits
is added to the original number, the 6. If 1 is added to both the numerator and the
resulting number (i.e. the sum) must be 1 . If 2
divisible by denominator of a fraction, it becomes
4
(1) 11 (2)9
is added to both the numerator and the
(3) 5 (4)3
denominator of that fraction, it becomes 1 .
3
4. If 1 is added to the denominator of a fraction The sum of numerator and denominator of
it becomes 1 . If 1 is added to the numerator the fraction is:
2 (1) 8 (2) 13
it becomes 1. The product of numerator and (3) 22 (4) 27
denominator of the fraction is

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 163 -

7. In a two digit number if it is known that its
units digit exceeds its tens digit by 2 and 15. The product of two numbers is 24 times the
that the product of the given number and difference of these two numbers. If the sum
the sum of its digits is equal to 144, then the of these numbers is 14, the larger number is
number is (1) 9 (2) 8
(1) 46 (2) 42 (3) 7 (4) 10
(3) 26 (4) 24
16. If a and b are negative real numbers and c is
8. In a test, 1 mark is awarded for each correct a positive real number, then which of the
answer and one mark is deducted for each following is/are correct?
wrong answer. If a boy answers all 20 items 1. a – b < a – c
of the test and gets 8 marks, the number of a b
questions answered correct by him was 2. If a < b then 
(1) 16 (2) 14
c c
(3) 12 (4) 8 1 1
3. 
b c
9. The difference between two positive numbers Select the correct answer using the code
is 3. If the sum of their squares is 369, then given below:
the sum of the numbers is: (1) 1 (2) 2 only
(1) 81 (2) 33 (3) 3 only (4) 2 and 3
(3) 27 (4) 25
17. Equation x + 3y − 6 = 0 will cut the Y axis
10. A number consists of two digits such that (1) 6 unit above the origin
the digit in the ten’s place is less by 2 than (2) 2 unit above the origin
the digit in the unit’s place. Three times the (3) 6 unit below the origin
6 (4) 2 unit below the origin
number added to times the number
7
obtained by reversing the digits equals 108. 18. The graph of equation y = 5 is parallel to
The sum of digits in the number is: (1) Y axis (2) X axis
(1) 8 (2) 9 (3) Both axis (4) None of these
(3) 6 (4) 7
19. Which of the following is not a method to
11. Of the three numbers, the second is twice solving linear equation of two variables?
the first and it is also thrice the third. If the (1) Elimination method
average of three numbers is 44, the (2) Substitution method
difference of the first number and the third (3) Cross multiplication method
number is: (4) Division method
(1) 24 (2) 18
(3) 12 (4) 6 20. Which of the following is not a linear
equation?
12. A two digit number is five times the sum of (1) ax + by + c = 0
its digits. If 9 is added to the number, the (2) ax + c = 0
digits interchange their positions. The sum (3) ax + by + cz + d = 0
of digits of the number is: (4) (ax + b)x + c = 0
(1) 11 (2) 9
(3) 7 (4) 6 21. In an examination, a student scores 4 marks
for every correct answer and loses 1 mark
13. Solution of equation x + y = 5 and 2x + y − 6 for every wrong answer. A student attempted
=0 is all the 200 questions and scored in all 200
(1) x = 1 , y = 2 (2) ) x = 1 , y = 4 marks. The number of questions, he
(c) ) x = 2 , y = 3 (4) ) x = 4 , y = 2 answered correctly was
14. Straight line 2x − 3y − 6 = 0 will cut the line
4x + ky = 15 if (1) 82 (2) 80
(1) k = 1 (2) k = 2 (3) 68 (4) 60
(3) k = 3 (4) All of above

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 164 -

22. What is/are the solutions of the set of 3x  y  1 2 x  y  2 3x  2 y  1
homogeneous equations (4x + 2y = 0) and   is given by
3 5 6
(6x + 3y = 0) ?
which one of the following?
(a) Only x = 0, y = 0
(a) x = 2, y = 1
(b) Only x = 0, y = 0 and x = 1, y = 2
(b) x = 1, y = 1
(c) An infinite number of solutions
(c) x = –1, y = –1
(d) No solution
(d) x = 1, y = 2
23. The cost of 4 books and 3 pencils is same as
27. What is the solution of the equations x – y =
that of 8 books and 1 pencil. This cost will
0.9 and 11(x + y)–1 = 2?
be same as that of which one of the
(a) x = 3.2 and y = 2.3
following?
(b) x = 1 and y = 0.1
(a) 2 books and 6 pencils
(c) x = 2 and y = 1.1
(b) 5 books and 5 pencils
(d) x = 1.2 and y = 0.3
(c) 6 books and 2 pencils
(d) 12 books and 4 pencils
28. What is the value of k for which the system
of equations x + 2y – 3 = 0 and 5x + ky + 7 =
24. If one-third of a two-digit number exceeds its
0 has no solution?
one-fourth by 8, then what is the sum of the
(a) – 3/14 (b) – 14/3
digits of the number?
(c) 1/10 (d) 10
(a) 6 (b) 13
(c) 15 (d) 17
29. Under what condition do the equations kx –
y = 2 and 6x – 2y = 3 have a unique
25. What is the sum of two numbers whose
solution?
difference is 45 and the quotient of the
(a) k = 3 (b) k ≠ 3
greater number by the lesser number is 4?
(c) k = 0 (d) k ≠ 0
(a) 100 (b) 90
30. For what value of k , the following equation
(c) 80 (d) 75
will be inconsistent? 2x − ky = 4 and 3x + 2y
=6?
26. The solution of the equations
(a) 4/3 (b) −4/3
(c) 2/3 (d) 3/2

ANSWER KEY
1. (4) 2. (1) 3. (1) 4. (1) 5. (1) 6. (1) 7. (4) 8. (2) 9. (3) 10. (3)
11. (3) 12. (2) 13. (2) 14. (4) 15. (2) 16. (4) 17. (2) 18. (2) 19. (4) 20. (4)
21. (2) 22. (3) 23. (3) 24. (3) 25. (4) 26. (2) 27. (1) 28. (4) 29. (2) 30. (2)

PRACTICE SHEET-3
1. Every quadratic equation ax2 + bx + c = 0, 1b q 1 b q
where a, b, c  R, a ≠ 0 has: (c)    (d)   
2p a  2 a a 
(a) Exactly one real root
(b) At least one real root
3. If  and  are the roots the equation ax2 + bx
(c) At least two real roots
(d) At most two real roots + c = 0, where a ≠ 0, then (a + b) (a + b) is
equal to:
(a) ab (b) bc
2. If ,  are roots of ax2 + bx + c = 0 and  + h,
(c) ca (d) abc
 + h are the roots of px2 + qx + r = 0, then
what is h equal to?
4. The roots of the equation 2a2 x2  2abx + b2
1b q 1 b q = 0, when a < 0 and b > 0 are:
(a)    (b)    
2a p 2 a p (a) Sometimes complex (b) Always irrational

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 165 -

 (c) Always complex (d) Always real (a) 1  r (b) q  r
(c) 1 + r (d) q + r
5. The quadratic equation x2 + bx + 4 = 0 will
have real roots, if: 14. The solution of the simultaneous linear
(a) Only b  4 (b) Only b  4 equations 2x + y = 6 and 3y = 8 + 4x will
(c) 4 < b < 4 (d) b   4, b  4 also be satisfied by which one of the
following linear equation?
6. If  and  are the roots of the equation x2 + x (a) x + y = 5 (b) 2x + y = 5
10  10 (c) 2x−3y = 10 (d) 2x + 3y = 6
+ 2 = 0, then what is 10 equal to?
  10
15. If the difference between the roots of ax2 +
(a) 4096 (b) 2048 bx + c = 0 is 1, then which one of the
(c) 1024 (d) 512 following is correct?
(a) b2 = a (a+4c) (b) a2 = b (b+4c)
7. What is the difference in the roots of the (c) a2 = c (a+4c) (d) b2 = a (b+4c)
equation x2  10x + 9 = 0.
(a) 2 (b) 3 Direction (for next two): The equation
(c) 5 (d) 8 formed by multiplying each root of ax2 + bx +
c = 0 by 2 is x2 + 36x + 24 = 0.
8. If  and  are the roots of the equation ax2 + 16. What is the value of b:c?
bx + b = 0, then what is the value of (a) 3:1 (b) 1:2
  b (c) 1:3 (d) 3:2
  ?
  a
(a) 10 (b) 0 17. Which one of the following correct?
(c) 1 (d) 2 (a) bc = a2 (b) bc = 36a2
(c) bc = 72a2 (d) bc = 108a2
9. The roots of the equation x2  8x + 16 = 0:
18. The sum of the reciprocals of two alternate
(a) Are imaginary
(b) Are distinct and real 7
natural numbers is . What is the sum of
(c) Are equal and real 24
(d) Cannot be determined the numbers?
(a) 12 (b) 13
10. If a and b are rational and b is not perfect (c) 14 (d) 16
square, then the quadratic equation with
rational coefficients whose one root is 3a + 19. What is the value of y =
b is:
82 82 82 8
(a) x2  6ax + 9a2  b = 0
(b) 3ax2 + x  b  0 (a) 10 (b) 8
(c) 6 (d) 4
(c) x2 + 3ax + b  0
(d) b x2 + x  3a = 0 20. If  and  be the roots of the equation (xa)
(xb) = c, c ≠ 0. Then, the roots of the
11. What is the sum of the squares of the roots equation (x) (x) + c = 0 are:
of the equation x2 + 2x  143 = 0? (a) a,c (b) b,c
(a) 170 (b) 180 (c) a, b (d) a+b, a+c
(c) 190 (d) 290
21. What is the sum of the roots of the equation
12. If one of the roots of the equation + ax  b
x2 (2 3 )x2  (74 3 ) x + (2+ 3 ) = 0?
= 0 is, 1, then what is the value of (ab)? (a) 2 3 (b) 2+ 3
(a) 1 (b) 1
(c) 74 3 (d) 4
(c) 2 (d) 2
22. If one root of the equation ax2 + bx + c = 0,
a≠0 is reciprocal of the other root, then
13. If  and  are the roots of the equation. x2 
which one of the following is correct?
q(1+x)  r = 0 then what is the value of (1+)
(a) a = c (b) b = c
(1+)?

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 166 -

 (c) a = c (d) b = 0 27. If p, q, r are rational numbers, then the
roots of the equation x2  2px + p2  q2 + 2qr
23. If sum of squares of the roots of the equation  r2 = 0 are:
x2 + kx  b = 0 is 2b, then what is k equal (a) Complex (b) Pure imaginary
to? (c) Irrational (d) Rational
(a) 1 (b) b
(c) b (d) 0 28. If x  y  4, then the how many non-zero
positive integer ordered pair (x,y) ?
24. If 3 is the root of the equation x2  8x + k = (a) 4 (b) 5
0, then what is the value of k? (c) 6 (d) 8
(a) 15 (b) 9
(c) 15 (d) 24 29. What is the set of points (x,y) satisfying the
equations x2 + y2 = 4 and x + y = 2 ?
25. What is the condition that one root of the (a) {(2,0),(−2,0),(0,2)}
equation ax2 + bx + c = 0, a ≠ 0 should be (b) {(0,−2),(0,2)}
double the other? (c) {(2,0),(0,2)}
(a) 2a2 = 9bc (b) 2b2 = 9ac (d) {(2,0),(−2,0),(0,2),(0,−2)}
(c) 2c2 = 9ab (d) None of these
30. If α and β are the roots of equation 4x2 + 3x
26. What is the solution set for the equation x4  + 7 = 0, then what is the value of α−2 + β−2 ?
26x2 + 25 = 0? (a) 47/49 (b) 49/47
(a) {5, 1, 1, 5} (b) {5, 1} (c) −47/49 (d) −49/47
(c) {1,5} (d) {5,0,1,5}

ANSWER KEY
1. (c) 2. (a) 3. (c) 4. (c) 5. (d) 6. (c) 7. (d) 8. (b) 9. (c) 10. (a)
11. (d) 12. (a) 13. (a) 14. (a) 15. (a) 16. (a) 17. (d) 18. (c) 19. (d) 20. (c)
21. (a) 22. (a) 23. (d) 24. (c) 25. (b) 26. (a) 27. (d) 28. (c) 29. (c) 30. (c)

PRACTICE SHEET-4
1. If the product of the roots of x 2 – 3kx + 2k2 – 0 may be found by solving which one of the
1 = 0 is 7 for a fixed k, then what is the following equations?
nature of roots? (a) y2 + 14y – 7 = 0 (b) y2 + 8y + 1 = 0
(a) Integral and positive (c) y2 + 10y – 7 = 0 (d) y2 – 8y + 7 = 0
(b) Integral and negative
(c) Irrational 4. If a polynomial equation has rational co-
(d) Rational but not integral efficient and has exactly three real roots,
then what is the degree of the polynomial?
2. Which one of the following is the quadratic (a) Equal to 3
equation whose roots are reciprocal to the (b) Greater than or equal to 3
roots of the quadratic equation 2x2 – 3x – 4 = (c) Strictly greater than 3
0? (d) Less than 3
(a) 3x2 – 2x – 4 = 0 (b) 4x2 + 3x – 2 = 0
(c) 3x – 4x – 2 = 0
2 (d) 4x2 – 2x – 3 = 0 5. If α and β are the roots of ax2 + bx + c = 0,
2
then what is the value of  1  1 
3. The value of y which will satisfy the  2
  2 
equations 2x2 + 6x + 5y + 1 and 2x + y + 3 =

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 167 -

 (a) b (b  4ac) (b) b(b  4ac)
2 2 2

c4 c2 14. If one of the roots of the equation ax 2 + x – 3

= 0 is −1.5, then what is the value of a?
(c) (b  4ac) (d) (b  4ac)
2 2
(a) 4 (b) 3
c2 c4 (c) 2 (d) –2

6. Which one of the following is one of the two 15. r is a non-zero real number such that r75 >
consecutive positive integers, the sum of r90. This is possible only when
whose squares is 761? (a) –1 < r < 0 (b) 0 < r < 1
(a) 15 (b) 20 (c) 1 < r (d) –1 < r < 1
(c) 24 (d) 25
16. When the roots of the quadratic equation ax 2
7. If 3x + 27(3–x) = 12, then what is the value of + bx + c = 0 are negative of reciprocals of
x? each other, then which one of the following
(a) Only 1 (b) Only 2 is correct?
(c) 1 or 2 (d) 0 or 1 (a) b = 0 (b) c = 0
(c) a = c (d) a = –c
8. What is the magnitude of difference of the
roots of x2 – ax + b = 0? 17. What are the roots of the equation log10(x2 –
(a) a  4b
2
(b) b  4a
2 6x + 45) = 2?
(a) 9, –5 (b) –9, 5
(c) 2 a 2  4b (d) b 2  4ab (c) 11, –5 (d) –11, 5

9. If a + b = 2m2, b + c = 6m, a + c = 2, where 18. The sum of the roots of the equation
m is a real number and a ≤ b ≤ c, then which 1 1 1
one of the following is correct?   is zero. What is the product
(a) 0 ≤ m ≤ 1/2 (b) −1 ≤ m ≤ 0
x  a x  b c
of the roots of the equation?
(c) 1/3 ≤ m 1 d) 1 < m ≤ 2
( a  b) ( a  b)
(a)  (b)
10. Students of a class are made to stand in 2 2
rows. If one student is extra in a row, there (a  b )
2 2
(a  b 2 )
2

would be two rows less. If one student is less (c)  (d)

2 2
in a row, there would be three rows more.
Then, what is the number of students in the
19. For what value of k, will the roots of the
class?
equation kx2 – 5x + 6 = 0 be in the ratio of 2
(a) 65 (b) 55
: 3?
(c) 60 (d) 50
(a) 0 (b) 1
(c) –1 (d) 2
11. What is the ratio of sum of squares of roots
to the product of the roots of the equation
20. If α and β are the roots of the equation x2 +
7x2 + 12x + 18 = 0?
px + q = 0, then –α–1, –β–1 are the roots of
(a) 6 : 1 (b) 1 : 6
which one of the following equations?
(c) – 6 : 1 (d) –6 : 7
(a) qx2 – px + 1 = 0 (b) q2 + px + 1 = 0
(c) x + px – q = 0
2 (d) x2 – px + q = 0
12. If the roots of the equation
x( x  1)  (m  1) x are equal, then what is
 21. If one root of the equation ax2 + x – 3 = 0 is –
( x  1)(m  1) m 1, then what is the other root?
the value of m? (a) 1/4 (b) 1/2
(a) 1 (b) 1/2 (c) 3/4 (d) 1
(c) 0 (d) – 1/ 2
22. If the equation (a2 + b2) x2 – 2 (ac + bd)
13. What is the least integral value of k for x + (c2 + d2) = 0 has equal roots, then which
which equation x2 – 2(k – 1)x + (2k + 1) = 0 one of the following is correct?
has both the roots positive? (a) ab = cd (b) ad = bc
(a) 1 (b) −1/2 (c) a2 + c2 = b2 + d2 (d) ac = bd
(c) 4 (d) 0

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 168 -

 27. If one root of the equation 2x2 + 3x + c = 0 is
23. What is the solution of the equation 0.5, then what is the value of c?
x x3 3 (a) –1 (b) –2
  (c) –3 (d) –4
x3 x 2
(a) 1 (b) 2
28. What is the condition that the equation ax2 +
(c) 4 (d) None of these
bx + c = 0, where a ≠ 0 has both the roots
positive?
24. What are the roots of the equation 4x – 3.2x +
2 + 32 = 0?
(a)a, b and c are of same sign.
(b)a and b are of same sign.
(a) 1, 2 (b) 3, 4
(c)b and c have the same sign opposite to
(c) 2, 3 (d) 1, 3
that of a.
(d)a and c have the same sign opposite to
25. If α and β are the roots of the equation x2 – x
that of b.
– 1 = 0, then what is the value of (α4 + β4)?
(a) 7 (b) 0
29. The equation (1 + n2)x2 + 2ncx + (c2 – a2) = 0
(c) 2 (d) None of these
will have equal roots, if
(a) c2 = 1 + a2 (b) c2 = 1 – a2
26. If sum as well as product of roots of a
(c) c = 1 + n + a
2 2 2 (d) c2 = (1 + n2)a2
quadratic equation is 9, then what is the
equation?
30. The equation whose roots are twice the roots
(a) x2 + 9x – 18 = 0 (b) x2 – 18x + 9 = 0
of the equation x2 – 2x + 4 = 0 is
(c) x2 + 9x + 9 = 0 (d) x2 – 9x + 9 = 0
(a) x2 – 2x + 4 = 0 (b) x2 – 2x + 16 = 0
(c) x2 – 4x + 8 = 0 (d) x2 – 4x + 16 = 0

ANSWER KEY
1. (c) 2. (b) 3. (c) 4. (a) 5. (a) 6. (b) 7. (c) 8. (a) 9. (c) 10. (c)
11. (d) 12. (d) 13. (c) 14. (c) 15. (b) 16. (d) 17. (c) 18. (c) 19. (b) 20. (a)
21. (c) 22. (b) 23. (a) 24. (c) 25. (a) 26. (d) 27. (b) 28. (d) 29. (d) 30. (d)

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 169 -

 CDS PYQ
1. X, Y and Z had taken a dinner together. The [CDS 2013 (1)]
cost of the meal of Z was 20% more than (a) Rs 3000 (b) Rs 3300
that of Y and the cost of the meal of X was (c) Rs 3500 (d) Rs 3800
5/6 as much as the cost of the meal of Z. If
Y paid Rs 100, then what was the total 6. The difference in the root of the equation 2x2
amount that all the three of them had paid? –11x + 5 = 0 is
[CDS 2013 (1)] [CDS 2013 (1)]
(a) Rs 285 (a) 4.5 (b) 4
(b) Rs 300 (c) 3.5 (d) 3
(c) Rs 355
(d) None of the above 7. If one of the roots of the equation x2–bx + c =
0 is the square of the other, then which of
2. The system of equations 3x + y – 4 = 0 and the following option is correct?
6x + 2y – 8 = 0 has: [CDS 2013 (1)]
[CDS 2013 (1)] (a) b3 = 3bc + c2 + c (b) c3 = 3bc + b2 + b
(a) A unique solution x = 1, y =1 (c) 3bc = c3 + b2 + b (c) 3bc = c3 + b3 + b2
(b) A unique solution x = 0, y = 4
(c) No solution 8. If x + y – 7 = 0 and 3x + y – 13 = 0, then
(d) Infinite solution what is 4x2 + y2 + 4xy equal to?
[CDS 2013 (2)]
3. For what value of k, (x + 5) is a factor of 6x2 (a) 75 (b) 85
+ kx + 10? (c) 91 (d) 100
[CDS 2013 (1)]
(a) 5 (b) 32 9. A bus starts with some passengers. At the
(c) 36 (d) 40 first stop, one-fifth of the passengers gets
down and 40 passengers get in. At the
4. A number consists of two digit whose sum is second stop, half of the passengers gets
10. If the digit of the number are reversed, down and 30 get in. The number of
then the number decreased by 36. Which of passengers now in 70. The number of
the following is/are correct? passengers with which the bus started was:
I.The number is divisible by a composite [CDS 2013 (2)]
number (a) 40 (b) 50
II.The number is a multiple of a prime (c) 60 (d) 70
number
Select the correct answer using the codes 10. Consider the following statements in respect
given below: of the quadratic equation ax2 + bx + b = 0,
[CDS 2013 (1)] where a  0.
I.The product of roots is equal to the sum of
(a) Only 1 (b) Only II the roots
(c) Both I and II (d) Neither I nor II II.The roots of the equation are always
unequal and real
5. Ten chairs and six tables together cost Rs Which of the statements given above is/are
6200, three chairs and two tables together correct?
cost Rs 1900. The cost of 4 chairs and 5 [CDS 2013 (2)]
tables is: (a) Only I (b) Only II

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 170 -

 (c) Both I and II (d) Neither I nor II (c) 35 years and 29 years
(d) 35 years and 33 years
11. If  and  are the roots of the equation x2 –
 2  2 16. Two chairs and one table cost Rs 700 and 1
x – 1 = 0, then what is equal
      
2 2
 chair and 2 tables costs Rs 800. If the cost
m tables and m chairs is Rs 30,000, then
to? what is m equal to?
[CDS 2013 (2)] [CDS 2014 (1)]
2 3 (a) 60 (b) 55
(a) (b)
5 5 (c) 50 (d) 45
4
(c) (d) 4 17. In solving a problem, one student makes a
5
mistake in the coefficient of the first degree
12. Which one is one of the factors of: term and obtain–9 and –1 for the roots.
Another student makes a mistake in the
1  1
x2+ 2  8  x    14 ? constant term of the equation and obtains 8
x  x
and 2 for the roots. The correct equation
[CDS 2013 (2)] was:
1 1 [CDS 2014 (1)]
(a) x+  1 (b) x +  3
x x (a) x + 10x + 9 = 0
2 (b) x –10x+16 = 0
2

1 1 (c) x2–10x + 9 = 0 (d) None of these

(c) x+  6 (d) x+  7
x x
18. If m and n are the roots of the equation ax2 +
13. A positive number, when increased by 10 bx + c = 0, then the equation whose roots
equals 200 times its reciprocal. What is
number? are

m2  1and
n2 1 is:
m n
[CDS 2014 (1)]
[CDS 2014 (1)]
(a) 100 (b) 10
(a) acx2 + (ab + bc) x + b2 + (a–c)2 = 0
(c) 20 (d) 200
(b) acx2 + (ab – bc) x + b2 + (a–c)2 = 0
(c) acx2 – (ab – bc) x + b2 –(a–c)2 = 0
14. The sum of two positive numbers x and y is
(d) acx2 – (ab + bc) x + b2 –(a–c)2 = 0
2.5 times their difference. If the product of
numbers is 84, then what is the sum of
19. The value of x2 – 4x + 11 can never be less
those two numbers?
than:
[CDS 2014 (1)]
[CDS 2014 (1)]
(a) 7 (b) 8
(a) 26 (b) 24
(c) 11 (d) 22
(c) 22 (d) 20

20. If the roots of the equation

15. Ravi’s brother is 3 years elder to him. His
(a2 – bc) x2 + 2 (b2 – ac) x + (c2 – ab) = 0 are
father was 28 years of age when his sister
equal, where a, b, c  0, then which one of
was born while his mother was 26 years of
the following is correct?
age when he was born. If his sister was 4
[CDS 2014 (1)]
years of age when his brother was born, the
(a) a+b+c=abc (b) a2+b2+c2=0
ages of Ravi’s father and mother,
(c) a3+b3+c3=0 (d) a3+b3+c3=abc
respectively, when his brother was born
were:
21. If the roots of the equation Ax2 + Bx + C = 0
[CDS 2014 (1)]
are –1 and 1, then which one of the following
(a) 32 years and 23 years
is correct?
(b) 32 years and 29 years

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 171 -

 [CDS 2014 (1)] Which of the above statements is/are
(a) A and C are both zero correct?
(b) A and B are both positive [CDS 2015 (1)]
(c) A and C are both negative (a) 1 only (b) 2 only
(d) A and C are of opposite sign (c) Both 1 and 2 (d) Neither 1 nor 2

22. If m and n (m > n) are the roots of the 28. For which value of k does the pair of
equation 7(x + 2a)2 + 3a2 = 5a (7x + 23a), equations x2 – y2 = 0 and (x – k)2 + y2 = 1
where a > 0, then what is 3m–n equal to? yield a unique positive solution of x?
[CDS 2014 (2)] [CDS 2015 (1)]
(a) 12a (b) 14a (a) 2 (b) 0
(c) 15a (d) 18a (c) 2 (d) – 2

23. If one the roots of the equation px2 + qx + r = 29. The sign of the quadratic polynomial ax2 +
0 is three times the other, then which one of bx + c is always positive if:
the following relations is correct? [CDS 2015 (1)]
[CDS 2014 (2)] (a) a is positive and b2–4ac  0
(a) 3q2 = 16 pr (b) a2 = 24 pr (b) a is positive and b2–4ac  0
(c) p = q + r (d) p + q + r = 1 (c) a can be any real number and b2–4ac  0
(d) a can be any real number and b2–4ac  0
24. If m and n are the roots of the equation x2 +
30. If k = x – y + 2z where –2 ≤ x ≤ 1, –1≤ y ≤ 2
ax + b = 0 and m2, n2 are the roots of the and 3 ≤ z ≤ 6, then which one of the
equation x2 – cx + d = 0, then which of the following is correct?
following is/are correct? [CDS 2015 (2)]
1. 2b – a2 = c (a) 0 ≤ k ≤ 9 (b) 5 ≤ k ≤ 11
2. b2 = d (c) 2 ≤ k ≤ 14 (d) 2 ≤ k ≤ 11
Select the correct answer using the codes
31. The number of pairs (x, y) where x, y are
given below: integers satisfying the equation 21x+48y=5
[CDS 2014 (2)] is:
(a) Only 1 (b) Only 2 [CDS 2015 (2)]
(c) Both 1 and 2 (d) Neither 1 nor 2 (a) Zero (b) One
(c) Two (d) Infinity
25. If (x+k) is the common factor of x2 + ax + b
32. Let x and y be positive integers such that x
and x2 + cx + d of and then what is k equal
is prime and y is composite. Which of the
to? following statements are correct?
[CDS 2014 (2)] 1. (y–x) can be an even integer
(a) (d–b)/(c–a) (b) (d–b)/(a–c) 2. xy can be an even integer
(c) (d+b)/(c+a) (d) (d–b)/(c+a) 3. 0.5 (x+ y) can be an even integer
Select the correct answer using the code
26. If the equation x + 2(1+k) x+k = 0 has
2 2 given below:
[CDS 2015 (2)]
equal roots, then what is the value of k?
(a) 1 and 2 only (b) 2 and 3 only
[CDS 2014 (2)] (c) 1 and 3 only (d) 1, 2 and 3
(a) 1/2 (b) –1/2
(c) 1 (d) –1 33. If the roots of the quadratic equations x2 – 4
– log10 N = 0 are all real, then the minimum
27. Consider the following statements: value of N is:
[CDS 2015 (2)]
1.The equation 1990x – 173y = 11 has no
1 1
solution in integers for x and y. (a) (b)
2.The equation 3x –12y = 7 has no solution 100 1000
in integers for x and y.

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 172 -

 5x 2y=10
1
(c) (d) 10000 4

10000
3

34. The difference of maximum values of the

..
2 2x 6y=21
expressions (6 + 5x – x2) and (y – 6 – y2) for 1
any real values of x and y is: 0 1 2
[CDS 2015 (2)] 3 4
The linear in equations, for which the
(a) 16 (b) 17
shaded area in the figure given above is the
(c) 18 (d) 19
solution set, are:
[CDS 2016 (1)]
35. What is 4  4  4  4  ............... equal to? (a) 2x+6y ≤ 21, 5x – 2y ≤ 10
(b) 2x+6y ≤ 21, 5x – 2y  10
[CDS 2015 (2)] (c) 2x+6y  21, 5x – 2y ≤ 10
13  1 (d) 2x+6y  21, 5x – 2y  10
(a) 3 (b)
2
41. If a and b are negative real numbers and c is
13  1
(c) (d) 0 a positive real number, then which of the
2 following is/are correct?
4
1. a – b < a – c
36. A tin of oil was full. When 6 bottles of oil a b
5
were taken out from this tin and 4 bottles of 2. If a < b then 
3
c c
oil were poured into it, it was full. Oil of 1 1
4
how many bottles can the tin contain? (All 3. 
b c
bottles are of equal volume)
Select the correct answer using the code
[CDS 2015 (2)]
given below:
(a) 35 (b) 40
[CDS 2016 (1)]
(c) 45 (d) 50
(a) 1 (b) 2 only
(c) 3 only (d) 2 and 3
37. If the equations x2 – px + q = 0 and x2 + qx –
p = 0 have a common root, then which one 42. If the roots of the equation lx2 + mx + m = 0
of the following is correct? are in the ratio p : q, then:
[CDS 2016 (1)] p q m
(a) p–q=0 (b) p+q–2=0   is equal to:
q p l
(c) p+q–1=0 (d) p–q–1=0
[CDS 2016 (1)]
38. The value of k, for which the system of (a) 0 (b) 1
equation 3x – ky – 20 = 0 and 6x –10y + 40 = (c) 2 (d) 3
0 has no solution, is:
[CDS 2016 (1)] 43. If 3x 2  7x  30  2x 2  7x  5  x  5 has 
and  as its roots, then the value of  is:
(a) 10 (b) 6 [CDS 2016 (1)]
(c) 5 (d) 3
(a) –15 (b) –5
39. There are three brothers. The sums of ages (c) 0 (d) 5
of two of them at a time are 4 years, 6 years
and 8 years. The age difference between the 44. Let p and q be non-zero integers. Consider
eldest and the youngest is: the polynomial A(x) = x2 + px + q.
[CDS 2016 (1)] It is given that (x – m) and (x –km) are linear
(a) 3 years (b) 4 years factors of A (x), where m is a non-zero
(c) 5 years (d) 6 years integer and k is a positive integer, k  2.
Which one of the following is correct?
40. [CDS 2016 (1)]
(a) (k +1)2 p2 = kg (b) (k +1)2 q = kp2
(c) k2 q =(k +1) p2 (d) k2p2 =(k +1)2q

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 173 -

45. If the linear factors of ax2 – (a2 + 1) x + a are 52. If  and  are the two zeros of the polynomial
p and q them p + q is equal to: 25x2 –15x + 2, then what is a quadratic
[CDS 2016 (1)] polynomial whose zeros are (2)–1 and (2)–1?
(a) (x – 1) (a + 1) (b) (x + 1) (a + 1) [CDS 2016 (2)]
(c) (x – 1) (a – 1) (d) (x + 1) (a – 1) (a) x2 + 30x + 2 (b) 8x2 – 30x + 25
(c) 8x2 – 30x (d) x2 + 30x
46. If the sum of the roots of ax2 + bx + c = 0 is
equal to the sum of the squares of their 53. If p and q are the roots of x2 + px + q = 0,
reciprocals, then which one of the following then which of the following is correct?
relations is correct? [CDS 2016 (2)]
[CDS 2016 (1)] (a) p = 0 or 1 (b) p = 1 only
(a) ab2 + bc2 = 2a2 c (b) ac2 + bc2 = 2b2 a (c) p = – 2 or 0 (d) p = – 2 only
(c) ab + bc = a c
2 2 2 (d) a2 + b2 + c2 =1
54. The pair of linear equations kx + 3y + 1 = 0
47. Under what condition on p and q, one of the and 2x + y + 3 = 0 intersect each other, if:
roots of the equation x2 + px + q = 0 is the [CDS 2017 (1)]
square of the other? (a) k=6 (b) k6
[CDS 2016 (1)] (c) k=0 (d) k0
(a) 1 + q + q2 = 3pq (b) 1 + q + p2 = 3pq
(c) p3 + q + q2 = 3pq (d) q3 + p + p2 = 3pq 55. The system of equations 2x + 4y = 6 and 4x
+ 8y = 8 is:
48. The solution of the in-equation: [CDS 2017 (1)]
1 1 (a) Consistent with a unique solution
1+  2  0 is (given that x  0)
x x (b) Consistent with infinitely many solution
[CDS 2016 (1)] (c) Inconsistent
(a) x > 0 (d) None of the above
(b) x < 0
56. If  and  are the roots of the quadratic
1  5 1  5
(c) x equation 2x2 + 6x + k = 0, where k < 0, then
2 2  
1  5 1  5 what is the maximum value of    ?
(d) x  or x   
2 2 [CDS 2017 (1)]
(a) 2 (b) –2
49. If 4x2y = 128 and 33  32y –9xy = 0, then the (c) 9 (d) –9
value of x + y can be equal to:
[CDS 2016 (1)] 57. If one root of (a2–5a+3) x2 + (3a–1) x + 2 = 0
(a) 7 (b) 5 is twice the other, then what is the value of
(c) 3 (d) 1 ‘a’?
[CDS 2017 (1)]
2 2
50. Which of the points P(5,–1), Q(3,–2) and R(1, (a) (b) –
1) lie in the solution of the system of in- 3 3
equations x + y ≤ 4 and x–y  2 ? 1 1
(c) (d) –
[CDS 2016 (1)] 3 3
(a) Q and R only (b) P and R only
(c) P and Q only (d) P, Q and R 58. (x+4) is a factor of which one of the following
expressions?
51. If  it is an integer and   are the roots of [CDS 2017 (1)]
 (a) x2 – 7x + 44 (b) x 2 – 7x – 44
4x2 – 16x +  0 such that 1 <  < 2 and 2
4 (c) x2 – 7x – 44 (d) x2 + 7x + 44
<  < 3, then how many values can  take?
[CDS 2016 (2)] 59. If  and  are the roots of the equation x2 +
(a) 3 (b) 9 px + q = 0, then what is 2 + 2 equal to?
(c) 14 (d) 15 [CDS 2017 (1)]

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 174 -

 (a) p2–2q (b) a2–2p [CDS 2017 (2)]
(c) p2 + 2q (d) q2–q (a) 2b = a + c (b) b2 = ac
2 1 1 1 1 1
60. Aman and Alok attempted to solve a (c)   (d)  
b a c b a c
quadratic equation. Aman made a mistake
in writing down the constant term and
ended up in roots (4,3). Alok made a mistake 67. If k is an integer, then x2 + 7x – 14  k 2  7 
 8 
in writing down the coefficient of x to get 
roots (3,2). The correct roots of the equation =0 has:
are: [CDS 2017 (2)]
[CDS 2017 (1)] (a) Both integral roots
(a) –4, –3 (b) 6, 1 (b) At least one integral root
(c) 4, 3 (d) –1,–1 (c) No integral root
(d) Both positive integral roots
61. What number must be subtracted from both
the numerator and the denominator of the 68. What is the value of  (  0) for which x2–5x
fraction
27
so that it becomes ?
2 + , and x2 – 7x + 2 have a common factor?
35 3 [CDS 2017 (2)]
[CDS 2017 (1)] (a) 6 (b) 4
(a) 6 (b) 8 (c) 3 (d) 2
(c) 9 (d) 11
69. The value of 1  1  1  .......... :
62. The value of x which satisfy the equation
51+x + 51–x = 26 are: [CDS 2017 (2)]
[CDS 2017 (1)] (a) Equals to 1
(a) –1, 1 (b) 0, 1 (b) Lies between 0 and 1
(c) 1, 2 (d) –1, 0 (c) Lies between 1 and 2
(d) Is greater than 2
63. Sunil wants to spend Rs200 on two types of
sweets, costing Rs 7 and Rs 10 respectively. 70. If 65x – 33y = 97 and 33x – 65y = 1, then
What is the maximum number of sweet he what is xy equal to?
can get so that no money is left over? [CDS 2018 (1)]
[CDS 2017 (1)] (a) 2 (b) 3
(a) 25 (b) 26 (c) –2 (d) –3
(c) 27 (d) 28
71. If the roots of the equation px2 + x + r = 0
64. What is the value of u in the system of are reciprocal to each other, then which one
equations 3(2u + v) = 7uv, 3 (u + 3v) =11uv? of the following is correct?
[CDS 2017 (2)] [CDS 2018 (1)]
1 (a) p=2r (b) p=r
(a) 0 (b) (c) 2p=r (d) p=4r
4
1
(c) (d) 1 72. If  and  are the roots of the equation ax2 +
2 bx + c = 0, then what is the value of
65. What is the positive value of m for which the expression (+1) (+1)?
roots of the equation 12x2 + mx + 5 = 0 are [CDS 2018 (1)]
in the ratio 3:2?
abc bca
[CDS 2017 (2)] (a) (b)
a a
5 10
(a) 5 10 (b) abc a bc
12 (c) (d)
5 12 a a
(c) (d)
12 5
73. A quadratic polynomial ax2 + bx + c is such
that when it is divided by x, (x–1) and (x + 1),
66. If the roots of the equation a (b–c) x2 + b (c– the remainders are 3, 6 and 4 respectively.
a) x + c(a – b) = 0 are equal, then which one What is the value of (a + b)?
of the following is correct? [CDS 2018 (1)]

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 175 -

 (a) 3 (b) 2 and Raj. Some years later, Ravi dies and
(c) 1 (d) –1 leaves half of his property to his widow and
rest to his brother Raj. When Raj dies he
1 leaves half of his property to his widow and
74. of the students who registered did not remaining to his mother, who is still alive.
25
The mother now owns Rs 88,000 worth of
11
appear for the examination, of those who the property. The total worth of the property
20 of Mr. Sharma was :
appeared passed. If the number of registered [CDS 2018 (2)]
students is 2000, the number who passed (a) Rs 1,00,000 (b) Rs 1,24,000
is: (c) Rs 1,28,000 (d) Rs 1,32,000
[CDS 2018 (1)]
(a) 1920 (b) 1056 81. X bought 4 bottles of lemon juice and Y
(c) 1020 (d) 864 bought one bottle of orange juice. Orange
juice per bottle costs twice the cost of lemon
75. The age of a woman is a two-digit integer. juice per bottle. Z bought nothing but
On reversing this integer, the new integer is contributed Rs 50 for his share of the drink
the age of her husband who is elder to her. which they mixed together and shared the
The difference between their ages is one- cost equally. If Z’s Rs 50 is covered from his
eleventh of their sum. What is the difference share, then what is the cost of one bottle of
between their ages? orange juice?
[CDS 2018 (1)] [CDS 2018 (2)]
(a) 8 yrs (b) 9 yrs (a) Rs 75 (b) Rs 50
(c) 10 yrs (d) 11 yrs (c) Rs 46 (d) Rs 30
76. If x2 – 6x – 27 > 0, then which one of the 82. The solution of linear inequalities x + y  5
following is correct? and x – y ≤ 3 lies:
[CDS 2018 (2)] [CDS 2018 (2)]
(a) –3 < x < 9 (b) x < 9 or x > – 3 (a) Only in the first quadrant
(c) x > 9 or x < – 3 (d) x < – 3 (b) In the first and second quadrants
(c) In the second and third quadrants
77. If the sum of the square of three consecutive (d) In the third and fourth quadrants
natural numbers is 110, then the sum of
their cubes is: 83. It is given that the equations x2–y2 = 0 and
[CDS 2018 (2)] (x–a)2 + y2 = 1 have single positive solution.
(a) 625 (b) 654 For this, the value of ‘a’ is:
(c) 684 (d) 725 [CDS 2018 (2)]
(a) 2 (b) 2
78. If  and  are the roots of the equation ax2 +
1 1 (c) – 2 (d) 1
bx + c = 0, then the value of  is:
a  b a  b
84. Which of the following pair of numbers is the
[CDS 2018 (2)] solution of the equation 3x+2 + 3-x = 10?
a b [CDS 2019 (1)]
(a) (b)
bc ac (a) 0, 2 (b) 0, –2
c 1 (c) 1,–1 (d) 1, 2
(c) (d)
ab abc 85. The inequality 3N > N3 holds when:
[CDS 2019 (1)]
79. The minimum value of the expression 2x2 + (a) N is any natural number
5x + 5 is: (b) N is a natural number greater than 2
[CDS 2018 (2)] (c) N is a natural number greater than 3
(a) 5 (b) 15/8 (d) N is a natural number except 3
(c) –15/8 (d) 0
86. A man who recently died left a sum of Rs
80. According to Mr. Sharma’s will, half of his 3,90,000 to be divided among his wife, five
property goes to his wife and the rest is sons and four daughters. He directed that
equally divided between his two sons, Ravi

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 176 -

 each son should receive 3 times as much as 93. A real number x is such that (x – x2) is
each daughter receives and that each maximum. What is x equal to?
daughter should receive twice as much as [CDS 2019 (2)]
their mother receives. What was the wife’s (a) –1.5 (b) –0.5
share? (c) 0.5 (d) 1.5
[CDS 2019 (1)]
(a) Rs 14,000 (b) Rs 12,000 94. The sum of the squares of four consecutive
(c) Rs 10,000 (d) Rs 9,000 natural numbers is 294. What is the sum of
the numbers?
87. If p and q are the roots of the equation x2– [CDS 2019 (2)]
15x + r = 0 and p – q = 1, then what is the (a) 38 (b) 34
value of r? (c) 30 (d) 26
[CDS 2019 (1)]
(a) 55 (b) 56 95. The equation x2 + px + q = 0 has roots
(c) 60 (d) 64 equal to p and q where q  0. What are the
values of p and q respectively?
88. For the in-equality x2–7x + 12 > 0, which [CDS 2019 (2)]
one of the following is correct? (a) 1, –2 (b) 1, 2
[CDS 2019 (1)] (c) –1, 2 (d) –1, –2
(a) 3 < x < 4
(b) – < x < 3 only 96. If (b–6) is one root of the quadratic equation
(c) 4 < x <  only x2 – 6x + b = 0, where b is an integer, then
(d)– < x < 3 or 4 < x <  what is the maximum value of b2?
[CDS 2019 (2)]
89. If the sum of a real number and its (a) 36 (b) 49
reciprocal is
26
, then how many such (c) 64 (d) 81
5
numbers are possible?
97. What is the
maximum value of the
[CDS 2019 (2)]
1
(a) None (b) one expression 2 ?
(c) Two (d) Four x  5x  10
[CDS 2019 (2)]
90. If the equations x2 + 5x + 6 = 0 and x2 + kx 15 15
(a) (b)
+ 1 = 0 have a common root, then what is 4 2
the value of k? 4
[CDS 2019 (2)] (c) 1 (d)
15
5 10 5 10
(a)  or  (b) or
2 3 2 3 98. Two numbers p and q are such that the
5 10 5 10 quadratic equation px2 + 3x + 2q = 0 has –6
(c) or  (d)  or
2 3 2 3 as the sum and the product of the roots.
91. What is (x – a) (x – b) (x – c) equal to? What is the value of (p–q)?
[CDS 2019 (2)] [CDS 2019 (2)]
(a) x3 – (a + b + c) x2 + (bc + ca + ab) x – abc (a) –1 (b) 1
(b) x3 – (a + b + c) x2 + (bc + ca + ab) x + abc (c) 2 (d) 3
(c) x3 – (bc + ca + ab) x2 + (a + b + c) x – abc
(d) x3 + (bc + ca + ab) x2 - (a + b + c) x – abc 99. If  and  are the roots of the quadratic
equation x2 + kx –15 = 0 such that  –  =
92. A person carries Rs500 and wants to buy 8, then what is the positive value of k?
apples and oranges out of it. If the cost of [CDS 2020 (1)]
one apple is Rs5 and the cost of one orange (a) 2 (b) 3
is Rs7, then what is the number of ways in (c) 4 (d) 5
which a person can buy both apples and
oranges using total amount? 100. Students of a class are made to sit in rows
[CDS 2019 (2)] of equal number of chairs. If number of
(a) 10 (b) 14 students in increased by 2 in each row,
(c) 15 (d) 17 then the number of rows decreases by 3. If
number of students in increased by 4 in

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 177 -

 each row, then the number of rows 4 5
decreases by 5. What is the number of (c) (d)
5 6
students in the class?
[CDS 2020 (1)] 108. The sum of the reciprocals of two alternate
(a) 100 (b) 105
7
(c) 110 (d) 120 natural numbers is . What is the sum of
24
101. How many integral values of x and y satisfy the numbers?
the equation 5x + 9y = 7, where –500 < x < [CDS 2021 (1)]
500 and –500 < y < 500? (a) 12 (b) 13
[CDS 2020 (1)] (c) 14 (d) 16
(a) 110 (b) 111
(c) 112 (d) None 109. Which one of the following equations does
not have real roots?
102. If x + 9y = 6xy, then what is y : x equal to?
2 2 [CDS 2021 (2)]
[CDS 2020 (1)] (a) 2x2 + 16x + 3 = 0 (b) 2x2 + 10x –1 = 0
(a) 1 : 3 (b) 1 : 2 (c) x2 – 8x + 1 = 0 (d) 4x2 + 9x + 6 = 0
(c) 2 : 1 (d) 3 : 1
110. The sum and the product of the roots of a
103. The number of different solutions of the quadratic equation are 7 and 12
equations x + y + z = 12, where each of x , y respectively. If the bigger root is halved and
and z is a positive integer, is: the smaller root is doubled, then what is
[CDS 2020 (2)] the resulting quadratic equation?
(a) 53 (b) 54 [CDS 2021 (2)]
(c) 55 (d) 56 (a) x2 – 6x + 12 = 0 (b) x 2 – 8x + 12 = 0

(c) x2 + 8x + 12 = 0 (d) x2 –10x +12 = 0

104. A 60 page book has n lines per page. If the
number of lines were reduced by 3 in each 111. For which values of k, does the equation x
2

page, the number of pages would have to be – kx + 2 = 0 have real and distinct
increased by 10 to give the same writing solutions?
space. What is the value of n? [CDS 2021 (2)]
[CDS 2020 (2)] (a) –2√2 < k < 2√2
(a) 18 (b) 21 (b) k <–2√2 only
(c) 24 (d) 30 (c) k > 2√2 only
(d) k < –2√2 or k > 2√2
105. If the equation 4x2 – 2kx + 3k = 0 has equal
roots, then what are the values of k? 112. 5 pencils, 6 notebooks and 7 erasers Cost
[CDS 2021 (1)] Rs250; whereas 6 pencils, 4 notebooks and
2 erasers cost Rs180. What is the cost of 2
(a) 4, 12 (b) 4, 8 notebooks and 4 erasers?
(c) 0, 12 (d) 0, 8 [CDS 2021 (2)]

106. If the sum as well as the product of the (a) Rs 90 (b) Rs 75

roots of the equation px2 – 6x + q = 0 is 6, (c) Rs 60 (d) Rs 40
then what is (p +q) equal to?
[CDS 2021 (1)] 113. If p and q (p > q) are the roots of the
(a) 8 (b) 7 equation x2 – 60x + 899 = 0, then which
(c) 6 (d) 5 one of the following is correct?
[CDS 2021 (2)]
107. Which one of the following fractions will (a) p – q – 1 = 0 (b) p – 2q + 27 = 0
have minimum change in its value if 3 is (c) 2p – q – 30 = 0 (d) 3p – 2q – 43 = 0
added to both the numerator and the
denominator of all the fractions? 114. If one of the roots of the equation ax2 – 4ax
[CDS 2021 (1)] 3
+ 15 = 0 is , then what is the sum of the
2 3 2
(a) (b) squares of the roots?
3 4 [CDS 2021 (2)]

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 178 -

 15 17
(a) (b)
2 2
120. Consider a question and two statements:
19 21 Question:
(c) (d) Does the equation ax2 + bx + c2 = 0
2 2
Have real roots of opposite sign
115. The present age of a father is equal to sum Statement-I: The discriminates D > 0
of the ages of his 4 children. After ten years Statement-II: c/a > 0
the sum of the ages of the children will be Which one of the following is correct in
1.6 times the age of their father. What is respect of the question and the statements?
the present age of father? [CDS-2022-1]
[CDS 2021 (2)] (a)Statement-I alone is sufficient to answer
(a) 36 years (b) 40 years the question
(c) 42 years (d) 45 years (b)Statement-II alone sufficient to answer
the question
116. The sum of numerator and denominator of (c)Both Statements-I & II are together
a fraction is 10. If the numerator is sufficient to answer the question.
increased by 3 and denominator is (d)Both Statement-I & II are not sufficient
decreased by 1, the fraction becomes 1. to answer the question.
What is the difference between numerator
and denominator of the fraction? 121. How many quadratic equations have the
[CDS 2021 (2)] sum of their roots equal to the product of
(a) 2 (b) 3 their roots?
(c) 4 (d) 5 [CDS-2022-1]
(a) Zero (b) One
117. If the system of equation 7x + ky = 27 and (c) Two (d) Infinitely many
kx + 7y = 19 have unique solution, then
which one of the following is correct? 122. If  and  are the roots of the quadratic
[CDS 2021 (2)] equation x2 + x +  = 0, where   0, then
(a) k7 (b) k13 what is the value of  – ?
(c) k=7 (d) k=13 [CDS-2022-1]
(a) 4 (b) 3
118. A person agrees to work for 30 days, on a (c) –1 (d) –3
condition for every day’s work he should
receive Rs500, and that for every day’s 123. If the sum of the roots of the equation x 2 –
absence from work he should forfeit Rs100. k2x + 30kx – 161x – 64 = 0 is zero, then
At the end of the time he received Rs what is the difference of the roots?
11,400. How many days did he work? [CDS-2022-1]
[CDS 2021 (2)] (a) 15 (b) 16
(a) 20 (b) 21 (c) 17 (d) 18
(c) 24 (d) 25
124. A piece of cloth costs `10,000. If a 2 m
119. Consider a question and two statements: longer piece of the same cloth is purchased
Question: for the same amount, it would cost `250
Is 3x + 2y positive less per meter. What is the original length
Statement-I: x3 = – 29.8 of the piece of cloth?
Statement-II: y3 = 3x [CDS-2022-1]
Which one of the following is correct in (a) 8m (b) 10m
respect of the question and the statements? (c) 12m (d) 16m
[CDS-2022-1]
(a)Statement-I alone is sufficient to answer 125. What is the condition that the roots of the
the question equation ax2+bx+c=0 are in the ratio c : 1?
(b)Statement-II alone sufficient to answer [CDS-2022-1]
the question (a) b2 = a(c + 1)2 (b) a = bc (c + 1)
2 2
(c)Both Statements-I & II are together (c) b2 = a(c – 1)2 (d) ab2 = (c + 1)2
sufficient to answer the question.
(d)Both Statement-I & II are not sufficient 126. Two sides of a triangle forming a right angle
to answer the question. are 6x2 and (2x2 –1). If the area of the

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 179 -

 triangle is 84 square units, then what is the 134. If  and  are the roots of the equation x2 –
perimeter of the triangle? 7x + 1 = 0, then what is the value of 4 + 4
[CDS-2022-1] ?
(a) 51 units (b) 53 units [CDS – 2023 (1)]
(c) 56 units (d) 59 units (a) 2207 (b) 2247
(c) 2317 (d) 2337
127. If squaring a positive real number x is same
as adding 12, then what is x equal to? 135. The age of Q exceeds the age of P by 3
[CDS-2022-1] years. The age of R is twice the age of P and
(a) 2 (b) 3 age of Q is twice the age of S. Further, the
(c) 4 (d) 5 age difference of R and S is 30 years. What
is the sum of the ages of P and Q?
128. How many minutes are there in x weeks [CDS – 2023 (1)]
and x days? (a) 35 years (b) 38 years
[CDS-2022-1] (c) 39 years (d) 45 years
(a) 11520x (b) 5760x
(c) 480x (d) 192x 136. If a, b, c are non-zero real numbers such
that a + b + c = 0, then what are the roots
129. What are the values of k for which the of the equation ax2 + bx + c = 0?
polynomial (k –3) x2 – kx – 1 has no real [CDS – 2023 (1)]
linear factors? (a) 2, 1 + (c/a) (b) 1, a/c
[CDS 2022 (II)] (c) 1, c/a (d) 2, (c/a)–1
(a) k < – 6 (b) –6 < k < 2
(c) 2 < k < 6 (d) k > 6 137. If the roots of the equation x2 – bx + c = 5
differ by 5, then which one of the following
130. The value of a 2-digit number is 5 times the is correct?
sum of the digits. What is the product of [CDS – 2023 (1)]
the digits? (a) b2 = 4c + 5 (b) c2 = 4b – 5
[CDS 2022 (II)] (c) b2 + c2 = 5 (d) b2 – c2 = 5
(a) 15 (b) 18
(c) 20 (d) 27 138. The sum of digits of a 2-digit number is 12.
When the digits are reversed, the number
131. If the sum of the squares of the roots of the becomes greater by eighteen. What is the
equation x2 – 14x + k = 0 is 100, then what difference between the digits in the
is the value of k? number?
[CDS 2022 (II)] [CDS – 2023 (1)]
(a) 42 (b) 48 (a) 1 (b) 2
(c) 52 (d) 56` (c) 3 (d) 4

132. Consider the following statements in 139. Question: What are the unique values of a,
respect of the polynomial a(b – c) (x – b) (x – b and c if 2 is a root of the equation ax 2 +
c) + b (c – a) (x – c) (x – a) + c(a – b)(x – a) (x bx + c = 0?
– b): Statement I: Ratio of c to a is 1
1.the coefficient of x2 is 0 Statement II: Ratio of b to a is (–5/2)
2.The coefficient of x is (a – b) (b – c) (c – a) [CDS – 2023 (1)]
Which of the statements given above is/are (a) Choose this option if the question can be
correct? answered by one of the statements alone
[CDS – 2023 (1)] but not by the other.
(a) 1 only (b) 2 only (b) Choose this option if the question can be
(c) both 1 and 2 (d) neither 1 nor 2 answered by either statement alone.
(c) Choose this option if the question can be
133. For what values of m, is mx2 + mx + 8x + 9 answered by using both the statements
a perfect square? together, but cannot be answered by using
[CDS – 2023 (1)] either statement alone
(a) 1, 4 (b) 4, 9 (d)Choose this option if the question cannot
(c) 9, 16 (d) 4, 16 be answered even by using both statements
together

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 180 -

 (a) 201/7 (b) 197/7
140. Let  and  be the roots of the equation (c) 30 (d) 32
1 1 1 1
   ; a  0, b  0, x  0. Which
xab x a b 146. Consider the following statements:
one of the following is a quadratic equation 1.The age of F cannot be determined due to
whose roots are 2 and 2? insufficient data
[CDS-2023 (2)] 2.The average weight of D and F is equal to
(a) x2 + (a2 + b2) x + a2b2 = 0 weight of E
(b) x2 – (a2 + b2) x + a2b2 = 0 3.The weight difference is maximum for D
(c) x2 – (a2 + b2) x – a2b2 = 0 and A
(d) x2 + (a2 + b2) x – a2b2 = 0 Which of the statements given above are
correct?
6 [CDS-2023 (2)]
141. If x = the value of x –3x+2
2
7
6 (a) 1 and 2 only (b) 2 and 3 only
7
6 (c) 1 and 3 only (d) 1, 2 and 3
6
7
7x Consider the following for the next two
equal to? items that follow:
[CDS-2023 (2)] Mark option (a) if the question can be
(a) 0 (b) 1 answered by using one of the statements
(c) 18 (d) 20 alone, but cannot be answered using the
other statement alone.
Consider the following the next (05) Mark option (b) if the question can be
items that follow: answered by using either statements alone.
A, B, C, D, E, F and G are cousins. D is Mark option (c) if the question can be
thrice as old as A. Further, C is as many answered by using both the statements
years younger to B, as G to E and E to D. together, but cannot be answered using
The average age of D and G is 16 years; the either statement alone.
average age of A and E is 11 years; the Mark option (d) if the question cannot be
average of B and C is also 11 years. B and answered even by using both the
C have equal weight. A’s weight is 10 kg statements together.
less than that of B; D is 4 kg heavier than 147. Question: What is the other root of the
E; E is 4 kg heavier than F; F is 4 kg quadratic equation with real coefficients if
heavier than G. Further, D has age-weight
 4  10
ratio of 9:20, where age is in years and one of the roots is ?
2
weight in kg; A has age-weight ratio of 2:5.
Statement I:
Moreover, none of them is more than 40kg.
The product of the roots is –3/2 (3+10)
142. What is D’s age (in years)?
Statement II:
[CDS-2023 (2)]
The sum of roots of quadratic equation is –
(a) 15 (b) 16
1.
(c) 17 (d) 18
148. Question: What is the cost of 15 pens, 21
143. What is the average age (in years) of B, C,
pencils and 18 note books?
D, E and G?
Statement I:
[CDS-2023 (2)]
The cost of 7 pens, 6 pencils and 5 note
(a) 12 (b) 13
books is Rs.200
(c) 14 (d) 15
Statement II:
The of 3 pens, 8 pencils and 7 note books is
144. What is the difference between the weights
Rs.210
(in kg) of G and C?
[CDS-2023 (2)]
149. The combined age of a man and his wife is
(a) 4 (b) 3
6 times the combined age of their children.
(c) 2 (d) 1
Two years ago their combined age is 10
times the combined age of their children;
145. What is the average weight (in kg) of A, B,
and six years later their combined age will
C, D, E, F and G?
be 3 times the combined age of their
[CDS-2023 (2)]

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 181 -

 children. How many children do they have 155. What is the monthly electricity bill for a
if each child is at least 2 years old? house with 7 rooms consuming 300 units?
[CDS-2023 (2)] [CDS-2023 (2)]
(a) 2 (b) 3 (a) Rs.500 (b) Rs.440
(c) 4 (d) 5 (c) Rs.340 (d) Rs.300

150. How many real roots does the equation Consider the following for the next two
x  9 = x–3 have? (02) items that follow:
[CDS-2023 (2)] A quadratic equation is given by (a + b +
(a) only one (b) only two c)x2 – (2a + 2b)x + (a + b – c) = 0; where a, b
(c) only three (d) none and c are real and distinct.

151. If 3x–1 + 33–x = 6, then what is 2x–1 + 23–x 156. What are the roots of the equation?
equal to? [CDS-2023 (2)]
[CDS-2023 (2)] (a) 1, a  b  c
(b) 1, a  b  c

(a) 4 (b) 3 a  b  c  a  b  c 
(c) 2 (d) 1 (c) –1, a  c  c 
(d) –1, a  b  c 
a  b  c  a  b  c 
Consider the following for the next two
(02) items that follow: 157. Consider the following statements:
1.One of the roots of the equation is always
Let x  a x  b   x  a x  b  ; m, a, b > 0. less than 1 if a, b and c are all positive
x  ma x  mb  x  ma x  mb 
2.One of two roots of the equation is always
2 negative if a, b and c are all negative.
152. What is 2x  ab equal to? Which of the statements given above is/are
x  m 2ab
correct?
[CDS-2023 (2)] [CDS-2023 (2)]
(a) – 12 (b) 12 (a) 1 only (b) 2 only
m m
(c) both 1 and 2 (d) neither 1 nor 2
2 1
(c) (d)
m m
158. If the equation x cos  = x2 + p has a real
153. What is x equal to? 
solution for every , where 0    , then
[CDS-2023 (2)] 4
(a) ± mab (b) ± ab which one of the following is correct?
[CDS-2024 (1)]
(c) ± 2mab (d) ± 2ab (a) p = 1/8 (b) p  1/8
(c) p  1/8 (d) p  1/4
Consider the following for the next two
(02) items that follow: 159. What is the greatest value of k for which
The total monthly electricity bill for a house 2x2  4x + k = 0 has real roots?
consists of the sum of two parts, one part is [CDS-2024 (1)]
proportional to number of rooms and the (a) 1 (b) 2
other part is proportional to number of (c) 3 (d) 4
units consumed. Rs.400 is the monthly
electricity bill for the a house with 8 rooms 160. If the sum and product of the roots of n
and consuming 240 units and Rs.320 is the
quadratic equation are 2 and 100
monthly electricity bill for a house with 6
respectively, then which one of the following
rooms and consuming 200 units.
is correct?
[CDS-2024 (1)]
154. What is the monthly electricity bill for a
(a) There are infinitely many such equations
house with m rooms and consuming n
having differing roots
units?
(b) There is only one such equation which is
[CDS-2023 (2)]
x2 + 2x  100 = 0
(a) Rs.(40m + n) (b) Rs.(20m + n)
(c) There is only one such equation which is
40m  n  30m  n  x2  2x  100 = 0
(c) Rs. (d) Rs.
2 2 (d) There is no such equation

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 182 -

 Statement 1 : x2 – 26x + 133 = 0
161. A real number x is such that the sum of the Statement 2 : x2 – 44x + 475 = 0
number and four times its square is the Which of the following is correct in respect
least. What is that number? of the above Question and the statements?
[CDS-2024 (2)] [CDS – 2024 (2)]
(a) – 0.625 (b) – 0.125 (a) The question can be answered by using
(c) 0.125 (d) 1 one of the statements alone, but cannot be
answered using the other statement alone.
162. Let p, q be the roots of the equation x2 + mx (b) The question can be answered by using
– n = 0 and m, n be the roots of the either statement alone.
equation x2 + px – q = 0 (m, n, p, q are non (c) The question can be answered by using
zero numbers). Which of the following both the statements together, but cannot be
statements is/are correct? answered using either statement alone.
I. m(m + n) = - 1 (d) The question cannot be answered even
II. p + q = 1 by using both the statements together.
Select the answer using the code given
below 166. If two quadratic equations px2 + px + 4 = 0
[CDS-2024 (2)] and x2 + qx + q = 0 have a common root 2,
(a) I only (b) II only then what is p + q equal to?
(c) Both I and II (d) Neither I nor II [CDS-2025 (1)]
(a) – 3 (b) – 2
163. If the roots of the equation x2 – (k – 2)x + (k (c) 0 (d) 3
+ 1) = 0 are equal, then what are the values
of k ? 167. If p(≠0) and q(≠0)are the roots of the
[CDS-2024 (2)] equation x2 + px + q = 0, then what is p2 +
(a) 0, 4 (b) 0, 8 q2 equal to?
(c) 4, 4 (d) 2, 6 [CDS-2025 (1)]
(a) 2 (b) 3
164. Consider the question and the statements (c) 4 (d) 5
and mark the correct option.
Question: What is the integral value of k 168. The equations x2 + px + q = 0 and x2 + qx +
for which the expression 4x2 – kx + 1 is p = 0 (p ≠ q) have a common root. What is
positive ? the value of (p + q) ?
Statement 1 : k < – 2 [CDS-2025 (1)]
Statement 2 : k > – 4 (a) – 1 (b) 0
Which of the following is correct in respect (c) 1 (d) 2
of the above Question and the statements?
[CDS – 2024 (2)] 169. A real number M is squared to give the
(a) The question can be answered by using value N. What is the minimum value of (M +
one of the statements alone, but cannot be N)?
answered using the other statement alone. [CDS-2025 (1)]
(b) The question can be answered by using (a) – 0.25 (b) – 0.50
either statement alone. (c) 0 (d) 0.25
(c) The question can be answered by using
both the statements together, but cannot be 170. If α and β are the roots of the equation
answered using either statement alone. abx
(d) The question cannot be answered even xab  , then what is
ab  ax  bx
by using both the statements together.
      equal to ?
165. Consider the question and the statements [CDS-2025 (1)]
and mark the correct option. (a) ab + a + b (b) ab – a – b
Question: Can we have a common solution (c) a + b – ab (d) –(ab + a + b)
which is prime?

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 183 -

 ANSWER KEY
1. d 2. d 3. b 4. d 5. a 6. a 7. a 8. d 9. b 10. d
11. b 12. c 13. b 14. d 15. a 16. a 17. c 18. a 19. a 20. d
21. d 22. c 23. a 24. b 25. a 26. b 27. b 28. c 29. a 30. c
31. a 32. d 33. c 34. c 35. c 36. b 37. d 38. c 39. b 40. c
41. b 42. a 43. a 44. b 45. a 46. a 47. c 48. d 49. b 50. c
51. d 52. b 53. b 54. b 55. c 56. a 57. a 58. c 59. a 60. b
61. d 62. a 63. b 64. d 65. a 66. c 67. c 68. c 69. c 70. a
71. b 72. c 73. a 74. b 75. b 76. c 77. c 78. b 79. b 80. c
81. b 82. b 83. a 84. b 85. d 86. c 87. b 88. d 89. c 90. b
91. a 92. b 93. c 94. b 95. a 96. d 97. d 98. c 99. a 100. d
101. b 102. a 103. c 104. b 105. c 106. b 107. d 108. c 109. d 110. b
111. d 112. b 113. b 114. b 115. b 116. c 117. a 118. c 119. c 120. c
121. d 122. b 123. b 124. a 125. b 126. c 127. c 128. a 129. b 130. c
131. b 132. a 133. d 134. a 135. a 136. c 137. a 138. b 139. d 140. b
a,d d
141. 142. 143. c 144. b 145. a 146. d 147. b 148. c 149. a 150. b
151. a 152. d 153. a 154. b 155. b 156. a 157. a 158. b 159. b 160. c
161. b 162. c 163. b 164. a 165. c 166. b 167. d 168. a 169. a 170. b
CLICK HERE FOR YOUTUBE SOLUTIONS OF CDS PYQs

or Scan QR code given on marks distribution page of this book

CAPF PYQ

1. In an exam , a candidate attempts 20 3. A test consists of 25 MCQs. Each correct

questions and scores 72 marks, If 5 marks answer gives +4 marks and incorrect answer
are awarded for each correct answer and 2 gives –1 mark. If a candidate scores 74
marks are deducted for each wrong answer, marks, then how many questions were left
then how many questions were answered un-attempted?
correctly by him? [CAPF 2022]
[CAPF 2020] (a) 4 (b) 3
(a) 18 (b) 17 (c) 5 (d) 9
(c) 16 (d) 15
4. A person has a total of 100 coins consisting
2. A number is 124 more than its one-third. of Rs 2 and Rs 5 coins. If the total value of
What is that number? the cons is Rs 320, then the number of Rs 2
[CAPF 2022] coins is:
(a) 194 (b) 180 [CAPF 2022]
(c) 189 (d) 186 (a) 40 (b) 50
(c) 60 (d) 70

ANSWER KEY

1. c 2. d 3. a 4. c

SANDEEP SINGH BRAR Ph:- +91 9700900034 - 184 -