Engineering Entrance Sample Papers

KEE Sample Paper for Mathematics 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 + sin2 x = 1, then the value of expression cos12 x + 3cos10 x + 3 cos8 x + cos6 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) 29
(b) 92
(c) 32
(d) 29 – 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)

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) 22C10
(b) 18C3
(c) 12C4
(d) 18C4
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) x2 + y2 + 8x + 8y + 16 = 0
(b) x2 + y2 + 8x – 8y + 16 = 0
(c) x2 + y2 – 8x + 8y + 16 = 0
(d) x2 + y2 – 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 60o 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 l1 and l2 are said to be related by the relation R if l1 is parallel to l2. 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 x64 + x27 + 1 is divided by (x + 1) is
(a) 1
(b) – 1
(c) 2
(d) – 2
Ans:- (a)

Ques. If x = et sin t, y = et cos t, t is a parameter, then d2y / dx2 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 z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex. Further, assume that origin, z1 and z2 form an equilateral triangle. Then
(a) a2 = b
(b) a2 = 2b
(c) a2 = 3b
(d) a2 = 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 x2 – 3x + p = 0 and let c and d be the roots of x2 – 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)

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 x2 + 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) (e2 – 2)/e
(b) (e – 1)2/2e
(c) (e2 – 1)/2e
(d) (e2 – 1)/2
Ans:- (b)