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.
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
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
If | a x b | = 4 and | a.b |= 2, then |a|2 |b|2 =
(a) 2
(b) 6
(c) 8
(d) 20
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
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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
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
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
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
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)
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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
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
Function f : R – – R, f(x) = [x] is
(a) One-one onto
(b) One-one into
(c) Many-one onto
(d) Many-one into
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)}
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
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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
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
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
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
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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)
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)
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
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)
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
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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
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
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
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
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
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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)
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
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
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)
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
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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
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
The vertex of the parabola y2 = 4(a’ – a)(x – a) is
(a) (a‘, a)
(b) (a, a’)
(c) (a, 0)
(d) (a’, 0)
In the expansion of (1 + x)5, the sum of the coefficients of the terms is
(a) 80
(b) 16
(c) 32
(d) 64
The equation x2 + 4xy + 4y2 – 3x – 6y – 4 = 0 represents
(a) circle
(b) pair of lines
(c) parabola
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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!
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
The number of ways that 8 beads of different colours be string as a necklace is
(a) 2520
(b) 2880
(c) 5040
(d) 4320
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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
If A is a non–singular matrix of order 3, then |adj(adj A)| equals
(a) | A|4
(b) | A |6
(c) | A |3
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
n – 1C3 + n – 1C4 > nC3 then the value of n is
(a) 7
(b) < 7
(c) > 7
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
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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
If mean = (3 median – mode) k, then the value of k is
(a) 1
(b) 2
(c) 1/2
(d) 3/2
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)
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
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
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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
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
