# COMEDK Mathematics Practice Questions This Maths Practice sample paper is based on EAMCET syllabus and consist 34 questions, you can download all 34 questions in PDF format using link below last question.

Ques. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then men select the chairs from amongst the remaining. The number of possible arrangements is
(a) 6C3 x 4C2
(b) 4C2 x 4P3
(c) 4C2 x 4P3
(d) None of these

Ans. (d)

Ques: If sin x + sin2 x = 1, then the value of expression cos12 x + 3 cos10 x + 3 cos8 x + cos6 x – 1 is equal to
(a) 0
(b) 1
(c) –1
(d) 2

Ans. (a)

Ques. Let the determinant of a 3 ´ 3 matrix A be 6, then B is a matrix defined by B = 5A2. Then determinant of B is
(a) 180
(b) 100
(c) 80
(d) none of these

Ans. (a)

Ques: If | a x b | = 4 and | a.b |= 2, then |a|2 |b|2 =
(a) 2
(b) 6
(c) 8
(d) 20

Ans. (d)

Ques: If there are n harmonic means between 1 and 1/31 and the ratio of 7th and (n – 1)th harmonic means is 9 : 5 then the and value of n will be
(a) 12
(b) 13
(c) 14
(d) 15

Ans. (c)

Related: quiz on d and f block elements

Ques. If the equation x2 + y2 + 2gx + 2fy + 1 = 0 represents a pair of lines, then
(a) g2 – f2 = 1
(b) f2 – g2 = 1
(c) g2 + f2 = 1
(d) f2 + g2 = ½

Ans. (c)

Ques: Let G denote the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication
(a) G is a subgroup
(b) G is a finite abelian group
(c) G is an infinite, non-abelian group
(d) G is infinite, abelian

Ans. (c)

Ques. A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
(a) (y – q)2 = 4px
(b) (x – q)2 = 4py
(c) (y – p)2 = 4qx
(d) (x – p)2 = 4qy

Ans. (d)

Ques. A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its  asymptotes.  Then the equations of its transverse and conjugate axis are
(a) x – y – 5 = 0 and x + y + 1 = 0
(b) x – y = 0 and x + y + 5 = 0
(c) x + y – 5 = 0 and x – y – 1 = 0
(d) x + y – 1 and x – y – 5 = 0

Ans. (c)

Ques. The coordinates of the centre of the sphere (x + 1) (x + 3) + (y – 2) (y – 4) + (z + 1) (z + 3) = 0 are
(a) (1, – 1, 1)
(b) (– 1, 1, – 1)
(c) (2, – 3, 2)
(d) (– 2, 3, – 2)

Ans. (d)

Ques: If the lines of regression are 3x + 12y = 19 and 3y + 9x = 46 then rxy will be
(a) 0.289
(b) – 0.289
(c) 0.209
(d) None of these

Ans. (b)

Ques. The length intercepted by the curve y2 = 4x on the line satisfying dy/dx = 1 and passing through point (0, 1), is given by :
(a) 1
(b) 2
(c) 0
(d) none of these

Ans. (c)

Ques. Function f : R – – R, f(x) = [x] is
(a) One-one onto
(b) One-one into
(c) Many-one onto
(d) Many-one into

Ans. (d)

Ques. Let f  = {(1, 5), (2, 6), (3, 4)}, g = {(4, 7), (5, 8), (6, 9)}. Then gof is
(a) {(4, 7), (5, 8), (6, 9), (1, 5), (2, 6), (3, 4)}
(b) null set
(c) {(1, 8), (2, 9), (3, 7)}
(d) none of these

Ans. (c)

Ques: A box contains 100 tickets numbered 1, 2 …… 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability
(a) 1/8
(b) 13/15
(c) 1/7
(d) None of these

Ans. (b)

Ques: Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
(a) Reflexive
(b) Transitive
(c) Not symmetric
(d) A function

Ans. (c)

Ques. A hockey stick pushes a ball at rest for 0.01 second with an average force of 50 N. If the ball weighs 0.2 kg, then the velocity of the ball just after being pushed is
(a) 3.5 m/sec
(b) 2.5 m/sec
(c) 1.5 m/sec
(d) 4.5 m/sec

Ans. (b)

Ques. The number of points with integral coordinates (2a, a – 1) that fall in the interior of the larger segment of the circle x2 + y2 = 25 cut of by the parabola x2 + 4y = 0, is
(a) one
(b) two
(c) three
(d) none of these

Ans. (c)

Ques. The equation 3(x – 1)2 + 2h (x – 1) (y – 2) + 3(y – 2)2 = 0 represents a pair of straight lines passing through the point (1, 2). The two lines are real and distinct if h2
(a) is greater than 3
(b) is greater than 9
(c) equals 7
(d) is grater than 7

Ans. (b)

Ques. The number of real roots of the equation esin x – e–sin x – 4 = 0 are
(a) 1
(b) 2
(c) infinite
(d) none of these

Ans. (d)

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Ques. If a party of n persons sit at a round table, then the odds against two specified individuals sitting next to each other are
(a) 2 : (n – 3)
(b) (n – 3) : 2
(c) (n – 2) : 2
(d) 2 : (n – 2)

Ans. (b)

Ques. If a, b, c are in A.P., then the straight line ax + by + c = 0 will always pass through the point
(a) (–1, –2)
(b) (1, –2)
(c) (–1, 2)
(d) (1, 2)

Ans. (b)

Ques. The number of ways in which five identical balls can be distributed among ten different boxes such that no box contains more than one ball, is
(a) 10 !
(b) 10!/5!
(c) 10!/(5!)2
(d) none of these

Ans. (c)

Ques. The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
(a) cos–1 (2/3)
(b) cos-1 (3/4)
(c) cos-1 (4/5)
(d) cos-1 (5/6)

Ans. (c)

Ques. If the rth, (r + 1)th and (r + 2) th coefficients of (1 + x)n are in AP, then n is a root of the equation
(a) x2 – x(4r + 1) + 4r2 – 2 = 0
(b) x2 + x(4r + 1) + 4r2 – 2 = 0
(c) x2 + x(4r + 1) + 4r2 + 2 = 0
(d) none of these

Ans. (a)

Ques. In a certain test ai students gave wrong answers to at least i questions where i = 1, 2, 3, …, k. No student gave more than k wrong answers. The total numbers of wrong answers given is
(a) a1 + 2a2 + 3a3 + … kak
(b) a1 + a2 + a3 + …, + ak
(c) Zero
(d) None of these

Ans. (b)

Ques. The number of ways in which five identical balls can be distributed among ten different boxes such that no box contains more than one ball, is
(a) 10 !
(b) 10!/5!
(c) 10!/(5!)2
(d) none of these

Ans. (c)

Ques. If the letters of the word ‘DATE’ be permuted and the words so formed be arranged as in a dictionary.  Then the rank of ‘DATE’ is
(a) 12
(b) 13
(c) 14
(d) 8

Ans. (d)

Ques. When the correlation between two variables is perfect, then the value of coefficient of correlation r is
(a) – 1
(b) + 1
(c) 0
(d) +1

Ans. (d)

Ques. The value of k, for which (cos x + sin x)2 + k sin x cos x – 1 = 0, is an identity, is
(a) – 1
(b) – 2
(c) 1
(d) 0

Ans. (b)

Related: square root cube root questions

Ques. The vertices of a feasible region of the above question are
(a) (0, 18), (36, 0)
(b) (0, 18), (10, 13)
(c) (10, 13), (8, 14)
(d) (10, 13), (8, 14), (12, 12)

Ans. (c)

Ques: If y = 2x is a chord of the circle x2 + y2 – 10x = 0, then the equation of the circle of which this chord is a diameter, is
(a) x2 + y2 – 2x + 4y = 0
(b) x2 + y2 + 2x + 4y = 0
(c) x2 + y2 – 2x + 4y = 0
(c) x2 + y2 – 2x – 4y = 0

Ans. (d)

Ques. In the process of finding the root of the equation x3 – x – 1 = 0 in the interval [1, 2] by bisection method, the first aproximation after the initial approximation is
(a) 1.5
(b) 1.75
(c) 1.25
(d) 1.375

Ans. (c)

Ques. Two circles, each of radius 5, have a common tangent at (1, 1) whose equation is 4x + 3y – 7 = 0, then the centres are
(a) (–5, 4), (3, –2)
(b) (–3, 4), (5, –2)
(c) (5, 4), (–3, –2)
(d) (4, 2), (–2, 0)

Ans. (c)

Ques. In the group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 7 is
(a) 7
(b) 3
(c) 9
(d) 1

Ans. (b)

Ques. If the straight line y = mx is outside the circle x2 + y2 – 20y + 90 = 0, then
(a) m > 3
(b) m < 3
(c) |m| > 3
(d) |m| < 3

Ans. (d)

Ques. The binary equivalent of decimal number (0.65625)10 is
(a) (0.10101)2
(b) (0.110101)2
(c) (0.10011)2
(d) (0.10110)2

Ans. (a)

Ques. The vertex of the parabola y2 = 4(a’ – a)(x – a) is
(a) (a‘, a)
(b) (a, a’)
(c) (a, 0)
(d) (a’, 0)

Ans. (c)

Ques. In the expansion of (1 + x)5, the sum of the coefficients of the terms is
(a) 80
(b) 16
(c) 32
(d) 64

Ans. (c)

Ques. The equation x2 + 4xy + 4y2 – 3x – 6y – 4 = 0 represents
(a) circle
(b) pair of lines
(c) parabola
(d) none of these

Ans. (b)

Ques. There are 10 seats in a double decker bus, 6 in the lower deck and 4 on the upper deck. Ten passengers board the bus, of them 3 refuse to go to the upper deck and 2 insist on going up. The number of ways all the passengers can be seated is
(a) 60
(b) 10
(c) 100
(d) 5C2 × 4! × 6!

Ans. (d)

Ques. 3x – 4y – 24 = 0 and 3x – 4y -12 = 0 are two parallel lines. If L1 makes an intercept of 3 units with these parallel lines then the equation of  L1 may be given as
(a) x = 1
(b) y = 1
(c) x = 2y + 3
(d) none of these

Ans. (a)

Ques. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then men select the chairs from amongst the remaining. The number of possible arrangements is
(a) 6C3 x 4C2
(b) 4C3 x 4C3
(c) 4P2 x 4P3
(d) none of these

Ans. (d)

Ques. The number of ways that 8 beads of different colours be string as a necklace is
(a) 2520
(b) 2880
(c) 5040
(d) 4320

Ans. (a)

Ques: x + y + z + 2 = 0 together with x + y + z + 3 = 0 represents in space
(a) A line
(b) A point
(c) A plane
(d) None of these

Ans. (d)

Ques. A circle circumscribing an equilateral triangle with centroid at (0, 0)  of side a is drawn and a square is drawn whose four sides touch the circle. The equation of the circle circumscribing the square is
(a) x2 + y2 = 2a2
(b) 3x2 + 3y2 = 2a2
(c) 5x2 + 5y2 = 3a2
(d) none of these

Ans. (b)

Ques. If A is a non–singular matrix of order 3, then |adj(adj A)| equals
(a) | A|4
(b) | A |6
(c) | A |3
(d) none of these

Ans. (a)

Ques. A die is formed in such a way that the probability of occurrence of an even face is twice of the probability of occurrence of an odd face. The probability of occurrence of a prime number is
(a) 1/3
(b) 4/9
(c) 5/9
(d) ½

Ans. (b)

Ques: n – 1C3 + n – 1C4 > nC3 then the value of n is
(a) 7
(b) < 7
(c) > 7
(d) None of these

Ans. (c)

Ques: A particle possess two velocities simultaneously at an angle of tan–1 12/5 to each other. Their resultant is 15 m/s. If one velocity is 13m/s, then the other will be
(a) 5 m/s
(b) 4 m/s
(c) 12 m/s
(d) 13m/s

Ans. (b)

Related: Ohm law question

Ques: The value of the nearest root of the equation x3 + x – 1 = 0 after third iteration by Newton-Raphson method near x = 1 is
(a) 0.51
(b) 0.42
(c) 0.67
(d) 0.55

Ans. (c)

Ques: If mean = (3 median – mode) k, then the value of k is
(a) 1
(b) 2
(c) 1/2
(d)  3/2

Ans. (c)

Ques: If a matrix A is such that 4A3 + 2A2 + 7A + I = O, then A–1 equals
(a) (4A2 + 2A + 7I)
(b) –(4A2 + 2A + 7I)
(c) –(4A2 – 2A + 7I)
(d) (4A2 + 2A – 7I)

Ans. (b)

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. 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. 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. 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)