DELHI PUBLIC SCHOOL, VIJAYAWADA
SUMMER VACATIONS ASSIGNMENT
CLASS: X DATE OF ISSUE: 26-04-2025
SUBJECT: MATHEMATICS PREPARED BY: Mr.BTR
Solve the following:
1. The LCM of smallest prime and smallest odd composite number is
A) 6 B) 12 C) 17 D) 24
2. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number
is completely divided by 2 the quotient is 33. The other number is
A) 162 B) 32 C) 66 D) 132
3. If n is any natural number, then 9n 5n ends with
A) 3 B) 6 C) 5 D) 8
4. If the LCM of 24 and 60 is 13m+3 then m=__________
A) 2 B) 3 C) 4 D) 5
5. The HCF of two numbers is 29 and other two factors of their LCM are 16 and 16,, then
larger of two numbers is
A) 464 B) 304 C) 551 D) 8816
6. The smallest number which when divided by 17, 23 and 29 leaves a remainder 11 is
each case is _____
A) 493 B) 11350 C) 11339 D) 667
7. If p x ax 2 bx c and a+b+c=0 then one zero is _____
b c b
A) B) C) D) None
a a c
8. If α and β are zeroes of the polynomial ax 2 5 x c and α + β = α β = 10 then
1 5 5 1
A) a 5 c B) a 1 c C) a , c 1 D) a , c 5
2 2 2 2
9. If α and β are zeroes of the polynomial x 2 6 x k and 3 4 20 then the value of k
is
A) –8 B) 16 C) –16 D) 8
1 1
10. If α, β are zeroes of the polynomial f x ax 2 bx c then 2
2 _____
b 2 2ac b 2 2ac b 2 2ac b 2 2ac
A) B) C) D)
a2 c2 a2 c2
11. The parabola representing the quadratic polynomial p x ax 2 bx c intersecting x-
axis in two different points (–4, 0) and (2, 0) then the quadratic polynomial is
A) x 2 4 x 8 B) x 2 2 x 8 C) x 2 2 x 8 D) x 2 2 x 8
12. If zeroes of QP ax 2 bx c c 0 are equal then
A) c and a have opposite signs B) c and b have opposite signs
C) c and a have same sign D) c and b have same sign
13. Two digit number is divisible by 9. Number when multiplied by sum of digits is equal
to 486, then the number is _____
A) 18 B) 54 C) 27 D) 45
14. The ratio of a two digit – number and sum of its digits is 7:1 then no. of two digit
numbers are
A) 1 B) 4 C) 9 D) infinite
b
15. y a where a, b are real numbers, y=1 when x=–1 and y=5 when x=–5 the a+b=
x
_____
A) –1 B) 0 C) 11 D) 10
16. The pair of linear equations y= –5 has
A) one solution B) two solutions C) infinitely many D) no solution
17. The area of the triangle formed by 2 x 3 y 18 with coordinate axes is _____
A) 27 sq. units B) 6 units C) 54 sq. units D) 36 squares
18. If x=a, y=b is solution of pair of linear equations 37 x 43 y 123, 43 x 37 y 117 then
a3 b3 ____
A) –7 B) 7 C) 9 D) –9
19. The number of real roots of the equation x 12 x 2 2 x 3 2 0 is
A) 2 B) 1 C) 0 D) 1
20. The Quadratic equation px x 3 9 0 has equal roots then p=_____
A) –4 B) 3 C) –3 D) 4
21. If the difference of the roots of the equation x 2 bx c 0 be 1 then
A) b 2 4c 1 0 B) b 2 4c 0 C) b 2 4c 1 0 D) b 2 4c 0
22. If the price of a book is reduced by `5, person can buy 5 more books for `300, then
original price of book is _____
A) 15 B) 20 C) 25 D) 30
23. The roots of Quadratic equation x 2 5 x 1 6 0 (where α is constant) are
A) α+1, α+6 B) α+1, –(α+6) C) –(α+1), α+6 D) –(α+1), –(α+6)
24. If arithmetic mean of two numbers α and β is A and α . β =G2 then the Quadratic
equation is
A) x 2 2 Ax G 2 0 B) x 2 2 Ax G 2 0 C) x 2 2 Ax G 2 0 D) x 2 2 Ax G 2 0
25. The Points A(-1, 1) B(5, 7) C(8, 10) are –
A) vertices of equilateral triangle B) vertices of Isosceles triangle
C) collinear D) None
26. If A(3, 0) B(4, 5) C(-1, 4) and (-2,-1) area vertices of Rhombus then its area is
__________ sq units .
A) 48 B) 72 C) 24 D) 36
27. If the distance of the point p(x, y) from A(a, 0) is a+x then y2= _________
A) ax B) 2ax C) 3ax D) 4ax
28. The distance of the point P(-6, 8) from the origin is
A) 8 B) 2√7 C) 10 D) 6
29. It P(x,-3) and Q(3, y) are the points of tri section of the line segment A(7, -2) and
B (1, -5) then x=________ and y=____________
5
A) x=5, y=2 B) x=-5, y = 4 C) x=5, y=–4 D) x=–5, y
2
30. ABCD is rectangle whose vertices are B(4, 0) C(4, 3) and D(0, 3) then length of
diagonal AC =________
A) 5 B) 4 C) 3 D) 25
