### Karunya University (KITS) Entrance Exam Maths Practice Questions:

**Ques. **If value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be

(a) 11

(b) 121

(c) 1331

(d) 14641

Ans:- (d)

**Ques. **If sin x + sin^{2} x = 1, then the value of expression cos^{12} x + 3cos^{10} x + 3 cos^{8} x + cos^{6} x – 1 is equal to

(a) 0

(b) 1

(c) –1

(d) 2

Ans:- (a)

**Ques. **The number of integral values of *k*, for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution, is

(a) 4

(b) 8

(c) 10

(d) 12

Ans:- (b)

**Ques. **sin (2 sin^{–1} 0.8) =

(a) 0.96

(b) 0.48

(c) 0.64

(d) None of these

Ans:- (a)

**Ques. **If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is

(a) 2^{9}

(b) 9^{2}

(c) 3^{2}

(d) 2^{9 – 1}

Ans:-(a)

**Ques. **Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2), will be

(a) x – 7y + 12 = 0

(b) 7x + y – 12 = 0

(c) x – 7y + 16 = 0

(d) 7x + y + 16 = 0

Ans:- (a)

**Related:** JEE Sequences and Series (Maths) Practice Exercise

**Ques. **In how many ways a team of 10 players out of 22 players can be made if 6 particular players are always to be included and 4 particular players are always excluded

(a) ^{22}C_{10}

(b) ^{18}C_{3}

(c) ^{12}C_{4}

(d) ^{18}C_{4}

Ans:- (c)

**Ques. **If the pair of straight lines xy – x – y + 1 = 0 and the line ax + 2y – 3 = 0 are concurrent, then *a* =

(a) – 1

(b) 0

(c) 3

(d) 1

Ans:- (d)

**Ques. **Solution of the differential equation y’ = y tan x – 2 sin x, is

(a) y = tan x + 2c cos x

(b) y = tan x + c cos x

(c) y = tan – 2c cos x

(d) None of these

Ans:- (d)

**Ques. **A circle lies in the second quadrant and touches both the axes. If the radius of the circle be 4, then its equation is

(a) x^{2} + y^{2} + 8x + 8y + 16 = 0

(b) x^{2} + y^{2} + 8x – 8y + 16 = 0

(c) x^{2} + y^{2} – 8x + 8y + 16 = 0

(d) x^{2} + y^{2} – 8x – 8y + 16 = 0

Ans:- (b)

**Ques. **A heavy rod ACDB, where AC = a and DB = b rests horizontally upon two smooth pegs C and D. If a load P were applied at A, it would just disturb the equilibrium. Similar would do the load Q applied to B. If CD = c, then the weight of the rod is

(a) Pa+Qb / c

(b) Pa–Qb/c

(c) Pa+Qb/2c

(d) None of these

Ans:- (a)

**Ques. **The length of the latus rectum of the parabola whose focus is (3, 3) and directrix is 3x – 4y – 2 = 0 is

(a) 2

(b) 1

(c) 4

(d) None of these

Ans:- (a)

**Related:** Bihar CET Maths Sample Paper

**Ques. **A train is running at 5 m/s and a man jumps out of it with a velocity 10 m/s in a direction making an angle of 60° with the direction of the train. The velocity of the man relative to the ground is equal to

(a) 12.24 m/s

(b) 11.25 m/s

(c) 14.23 m/s

(d) 13.23 m/s

Ans:- (b)

**Ques. **Vectors a, b, c are inclined to each other at an angle of 60^{o} and |a| = |b| = 2 and |c| = 2, then (2a + 3b – 5c) . (4a – 6b + 10c) = (a) 167

(b) – 167

(c) 120

(d) – 120

Ans:- (d)

**Ques. **Let *L* be the set of all straight lines in the Euclidean plane. Two lines l_{1} and l_{2} are said to be related by the relation *R* if l_{1} is parallel to l_{2}. Then the relation *R* is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) Equivalence

Ans:- (a,b,c,d)

**Ques. **The lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are perpendicular to each other, if

(a) aa’ + cc’ = 1

(b) aa’ + cc’ = –1

(c) ac + a’c’ = 1

(d) ac + a’c’ = –1

Ans:- (b)

**Ques. **If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is

(a) 13/32

(b) 1/4

(c) 1/32

(d) 3/16

Ans:- (a)

**Ques. **Let E = {1, 2, 3, 4} and F = {1, 2}.Then the number of onto functions from *E* to *F* is

(a) 14

(b) 16

(c) 12

(d) 8

Ans:- (a)

**Ques. **The remainder obtained when the polynomial x^{64} + x^{27} + 1 is divided by (x + 1) is

(a) 1

(b) – 1

(c) 2

(d) – 2

Ans:- (a)

**Ques. **If x = e^{t} sin t, y = e^{t} cos t, t is a parameter, then d^{2}y / dx^{2} at (1, 1) is equal to

(a) – ½

(b) – ¼

(c) 0

(d) ½

Ans:- (a)

**Related:** BITSAT Maths Important Questions

**Ques. **Which of the following is not a measure of central tendency

(a) Mean

(b) Median

(c) Mode

(d) Range

Ans:- (d)

**Ques. **Three forces *P*, *Q* and *R* act along the sides *BC*, *AC* and *BA* of an equilateral triangle *ABC*. If their resultant is a force parallel to *BC* through the centroid of the triangle *ABC*, then

(a) P = Q = R

(b) P = 2Q = 2R

(c) 2P = Q + 2R

(d) 2P = 2Q = R

Ans:- (b)

**Ques. **Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, *z* being complex. Further, assume that origin, z_{1} and z_{2 }form an equilateral triangle. Then

(a) a^{2} = b

(b) a^{2} = 2b

(c) a^{2} = 3b

(d) a^{2} = 4b

Ans:- (c)

**Ques. **The set of fourth roots of unity forms a group

(a) Of order 4 under addition

(b) Of order 4 under division

(c) Of order 4 under multiplication

(d) None of these

Ans:- (c)

**Ques. **Let a and b be roots of x^{2} – 3x + p = 0 and let c and d be the roots of x^{2} – 12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to

(a) 8 : 7

(b) 11 : 10

(c) 17 : 15

(d) None of these

Ans:- (c)

**Related:** Trigonometry (Maths) Sample Paper

**Ques. **Define * is defined on the set of real numbers by a * b = 1 + ab. Then the operation * is

(a) Commutative but not associative

(b) Associative but not commutative

(c) Neither commutative nor associative

(d) Both commutative and associative

Ans:- (a)

**Ques. **Two candidates attempt to solve the equation x^{2} + px + q = 0. One starts with a wrong value of *p* and finds the roots to be 2 and 6 and the other starts with a wrong value of *q* and find the roots to be 2 and – 9. The roots of the original equation are

(a) 2, 3

(b) 3, 4

(c) –2, – 3

(d) – 3, – 4

Ans:- (d)

**Ques. **If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is

(a) 324

(b) 341

(c) 359

(d) None of these

Ans:- (a)

**Ques. **If the sum of the coefficients in the expansion of (x + y)^{n} is 1024, then the value of the greatest coefficient in the expansion is

(a) 356

(b) 252

(c) 210

(d) 120

Ans:- (b)

**Ques. **The sum of series ½! + ¼! + 1/6! + … is

(a) (e^{2} – 2)/e

(b) (e – 1)^{2}/2e

(c) (e^{2} – 1)/2e

(d) (e^{2} – 1)/2

Ans:- (b)

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https://www.examsegg.com/downloads/karunya-mathematics-questions-for-practice.pdf

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