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Quantitative Aptitude for SSC CGL - Algebra
Q1. F(x)F(x) is a fourth order polynomial with integer coefficients and with no common factor. The
roots of F(x)F(x) are –2, –1, 1, 2. If p is a prime number greater than 97, then the largest integer that
divides F(p)F(p) for all values of pp is
A.72
B.120
C.240
D.360
Q2. Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of
400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of
diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate
optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800
kms?
A.49 km per hour
B.55 km per hour
C.50 km per hour
D.53 km per hour
Q3. In a cricket match, Team AA scored 232 runs without losing a wicket. The score consisted of
byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by the two
batsmen are 26 times wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram
and Shyam is 6:76:7, then the runs scored by Ram is:
A.88
B.96
C.102
D.112
Q4.
Three business entities XX Ltd, YY Ltd. and ZZ Ltd, with 4, 3 and 5 employees respectively, merged into
XYZXYZ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur.
After two years, on the question of management decisions on the new venture at Jaipur, the employees
started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there
is no quarrel among the employees of the erstwhile (i.e. former) XX Ltd, YY Ltd and ZZ Ltd, what could
be the maximum number of quarrels that can take place within XYZXYZ Ltd?
A.31
B.53
C.47
D.41
Q5.
PQRSTUPQRSTU is a regular hexagon drawn on the ground. Prashant stands at PP and he starts jumping
from vertex to vertex beginning from PP. From any vertex of the hexagon except SS, which is opposite to
AA, he may jump to any adjacent vertices. When he reaches SS, he stops. Let Sn be the number of
distinct paths of exactly nn jumps ending at SS. What is the value of S2kS2k, where kk is an integer?
A.00
B.44
C.2k2k
D.Depends on the value of k
Q6. Firoz has a certain amount of money in only Re 1 and Rs 10 notes. The number of Re 1 notes
multiplied by the number of Rs 10 notes is equal to the total money (in Rs) that he has. The number of
Rs 10 notes is less than ten. Which of the following is a possible figure for the total number of notes he
can have?
A.18
B.14
C.16
D.20
Q7. A shop sells two kinds of rolls- egg roll and mutton roll. Onion, tomato, carrot, chili sauce and
tomato sauce are the additional ingredients. You can have any combination of additional ingredients, or
have standard rolls without any additional ingredients subject to the following constraints:
(a) You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.
(b) If you have onion or tomato or both you can have chilli sauce, but not otherwise.
How many different rolls can be ordered according to these rules?
A.21
B.33
C.40
D.42
Q8. A lock has a code consisting of five distinct letters, from among the first eleven words of English
alphabet. The lock opens, if any three letters of the code match occurring not in the same position.
What is the least number of five-letter codes, one should try to be sure that the lock is opened?
A.7
B.4
C.6
D.5
Q9. A total of 15 teams participated in a tournament. Each team plays with every other team exactly
once. A team gets 3 points for a win, 2 points for a draw and 1 point for a loss. The team which scored
the least got 21 points. The scores of all the teams were distinct and at least one match played by
winning team was drawn. Which of the following is always true for the winning team?
A.It had at least two draws
B.It had maximum of four loss
C.It had a maximum of 9 wins
D.All of the above
Q10. Because of the economic slowdown, a multinational company curtailed some of the allowances
of its employees. Rashid, the marketing manager of the company whose monthly salary has been
reduced to Rs 42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs 2,000
between his earning and expenses in the first month. This deficit, because of inflationary pressure, will
keep on increasing by Rs 500 every month. Rashid has a saving of Rs 60,000 which will be used to fill the
deficit. After his savings get exhausted, Rashid would start borrowing from his friends. How soon will he
start borrowing?
A.10th10th months
B.11th11th months
C.12th12th months
D.13th13th months
Q11. The number of gift pack bought by Dexter is one more than the price, in rupees, of each gift
pack. The amount of Rs 380 which Dexter had, fell short of the required amount. What is the amount by
which he might have fallen short.
A.20
B.40
C.21
D.10
Q12. In a group, each person has at most two AA. No person has less than three CC. Considering all
the persons in the group there are more AA than GG, more GG than BB and more BB than persons. Find
the minimum number of persons in the groups?
A.4
B.5
C.3
D.2
Q13. Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him
the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins. Kartik first goes to the grocery
shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the
same number of 1 Rupee coins. Next he goes to the dairy shop to buy milk and butter and gives all 2
Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by
7575 more than the original number. If the number of 1 rupee coins now is 50, the number of 1 rupee
and 5 rupee coins originally were:
A.10, 60
B.10, 70
C.10, 80
D.None of these
Q14. If f(x) = 3x
3 − 7x + 5, then f(−1) =
A. 1 B. −1 C. 9 D. 8
Q 15.Which of these values of x satisfies the inequality −2x + 4 ≤ −6
A. 5 B. 0 C. −2 D. −6
Q 16.The domain of the function f(x) = √
x + 2 is given by
A. x > 2 B. x > −2 C. x ≥ 2 D. x ≥ −2
Q 17.The lines x = 3 and y = −2 are
A. Parallel B. Perpendicular
C. Neither parallel nor perpendicular D. none of these
Q 18.The equation |3x + 1| = k has no solutions if k =
A. 0 B. 3 C. 1 D. −1
Q 19. Which of the following statements is ALWAYS true?
A. A function is not a relation B. Every function is a relation
C. Every relation is a function D. A relation is not a function
Q 20.Which of these inequalities has NO solutions?
A. 2x + 4 > 1 B. |x| > −5 C. |x| < −10 D. −x + 3 ≥ 5
Q 21.A system of two linear equations with two variables is independent if it has
A. Two solutions B. One solution
C. No solutions D. Many solutions
Q 22. The lines y = (a + 1)x + 3 and y = −3x + 2 are parallel if a =
A. −4 B. 4 C. −3 D. 3
Q 23.Which of these points is on the graph of the equation 2x + 3y = 7?
A. (2, 3) B. (0, 3) C. (−1, 3) D. (3, 0)
Q 24.Choose the correct answer.
(a) If x = −2 and y = −1, then x^3-2y=
A. 6 B. −10 C. −6 D. 10
