UPSC sample papers

SCRA Maths Sample Paper SCRA Maths Sample Paper consist 100 objective type questions based on class 11th and 12th syllabus.

Question: The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line, is
(a) 8C3
(b) 8C35C3
(c) 8C35C3 – 1
(d) none of these
Ans: (c)

Question: In a certain town 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard
(i) 10% families own both a car and a phone
(ii) 35% families own either a car or a phone
(iii) 40000 families live in the town
Which of the above statements are correct?
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (i), (ii) and (iii)
Ans: (c)

Question: The distance s meters covered by a body in t seconds, is given by s = 3t2 – 8t + 5, the body will stop after
(a) 1 second
(b) 3/4 seconds
(c) 4/3 seconds
(d) 4 seconds
Ans: (c)

Question: The sum of the series 1.32 + 2.52 + 3.72 + … upto 20 terms is
(a) 188090
(b) 189080
(c) 199080
(d) none of these
Ans: (a)

Question: The number of critical points of f (x) = |x| (x – 1) (x – 2) (x – 3) is
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (d)

Relaated: Quantitative Aptitude Sample Paper

Question: Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set
A = {3, 6, 9, 12}. The relation is
(a) reflexive and symmetric only
(b) an equivalence relation
(c) reflexive only
(d) reflexive and transitive only
Ans: (c)

Question: The equation of sphere, which passes through the intersection of the sphere  x2 + y2 + z2 = 9 and the plane 2x + 3y + 4z = 5 and through the point (1, 2, 3) is
(a) 3(x2 + y2 + z2) – 2x – 3y – 4z – 22 = 0
(b) (x2 + y2 + z2) – 2x – 3y – 4z – 22 = 0
(c) 3(x2 + y2 + z2) + 2x + 3y + 4z – 22 = 0
(d) 3(x2 + y2 + z2) – 2x – 3y – 4z + 22 = 0
Ans: (a)

Question: If z is a complex number, then  |3z – 1| = 3|z – 2| represents
(a) y-axis
(b) a circle
(c) x-axis
(d) a line parallel to y-axis
Ans: (d)

Question: Ranks of 10 students of a class in two subjects are (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is
(a) 0
(b) – 1
(c) 1
(d) 0.5
Ans: (b)

Question: If a, b, c are the pth , qth and rth terms respectively of a G.P., then (qr) log a + (rp) log b + (pq) log c is equal to
(a) 0
(b) 1
(c) – 1
(d) abc
Ans: (a)

Question: If 4a2 + 9b2 + 16c2 = 2(3ab + 6bc + 4ca) where a, b, c are nonzero numbers, then a, b, c are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) none of these
Ans: (c)

Question: The sum 1 (1!) + 2(2!) + 3(3!) + ….. + n(n!) equals to
(a) 2(n!) + n – 3
(b) (n + 1)! – (n – 1)!
(c) (n + 1)! – 1
(d) 2 (n!) – 2n – 1
Ans: (c)

Question: If (x – 1)4 – 16 = 0 then the sum of non real complex values of x is
(a) 2
(b) 0
(c) 4
(d) none of these
Ans: (a)

Question: Which of the following planes intersects the planes x – y + 2z = 3 and 4x + 3y – z = 1 along the same line ?
(a) 11x + 10y – 5z = 0
(b) 7x + 7y – 4z  = 0
(c) 5x + 2y + z = 2
(d) none of these
Ans: (a)

Question: If the coefficients of the (m + 1)th term and the (m + 3)th term in the expansion of (1 + x)20 are equal then the value of m is
(a) 10
(b) 8
(c) 9
(d) none of these
Ans: (c)

Related: General Awareness questions

Question: In a polygon the number of diagonals is 54. The number of sides of the polygon is
(a) 10
(b) 12
(c) 9
(d) none of these
Ans: (b)

Question: The coefficient of x6 in {(1 + x)6 + (1 + x)7 + … + (1 + x)15} is
(a) 16C9
(b) 16C56C5
(c) 16C6 – 1
(d) none of these
Ans: (a)

Question: A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to
(a) 2
(b) 3
(c) 4
(d) 5
Ans: (c)

Question: The number of solutions of log2 (x + 5) = 6 – x is
(a) 2
(b) 0
(c) 3
(d) none of these
Ans: (d)

Question: In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together?
(a) 1540
(b) 1450
(c) 1504
(d) 1405
Ans: (a)

Question: The combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by 2x2 – xy – y2 = 0 is
a) 2x2 – xy – 2y2 + 4x – y = 6
(b) 2x2 – xy – y2 – 4x – y + 2 = 0
(c) 2x2 – xy – y2 – 4x + y + 2 = 0
(d) none of these
Ans: (c)

Related: UPSC English Practice Paper

Question: The order of differential equation of all parabolas having directrix parallel to x-axis is
(a) 3
(b) 1
(c) 4
(d) 2
Ans: (a)

Question: A ray of light incident at the point (–2, –1) gets reflected from the tangent at (0, –1) to the circle x2 + y2 = 1. The reflected ray touches the circle. The equation of the line along which the incident ray moved is
(a) 4x – 3y + 11 = 0
(b) 4x + 3y + 11 = 0
(c) 3x + 4y + 11 = 0
(d) none of these
Ans: (b)

Question: Two finite sets A and B having m and n elements. The total number of relations A to B is 64, then possible values of m and n are :
(a) 2 and 4
(b) 2 and 3
(c) 2 and 1
(d) 64 and 1
Ans: (b)

Question: The length of the latus rectum of the parabola x = ay2 + by + c is
(a) a/4
(b) a/3
(c) 1/a
(d) 1/4a
Ans: (c)

Related: important Antonyms

Question: A parachute weighing 1 kg falling with uniform acceleration from rest describes 16 m in first 4 secs. The resultant pressure of air on the parachute is
(a) 8.7 N
(b) 7.8 N
(c) 9.8 N
(d) none of these
Ans: (b)

Question: The H.M. of the segments of a focal chord of the parabola y2 = 4ax is
(a) 4a
(b) 2a
(c) a
(d) a2
Ans: (b)

Question: Let a, b be two positive numbers, where a > b and 4 × G.M. = 5 × H.M. for the numbers. Then a is
(a) 4b
(b) 1/4 b
(c) 2b
(d) b
Ans: (a)

Question: The centre of the conic section 14x2 – 4xy + 11y2 – 44x – 58y + 71 = 0 is
(a) (2, 3)
(b) (2, –3)
(c) (–2, 3)
(d) (–2, –3)
Ans: (a)

Question: The total number of words that can be made by writing the letters of the word PARAMETER so that no vowel is between two consonants is
(a) 1440
(b) 1800
(c) 2160
(d) none of these
Ans: (b)

Question: Three dice are thrown simultaneously. The probability of getting a sum of 15 is
(a) 1/72
(b) 5/36
(c) 5/72
(d) none of these
Ans: (d)