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) ^{6}C_{3} x ^{4}C_{2}

(b) ^{4}C_{2} x ^{4}P_{3}

(c) ^{4}C_{2} x ^{4}P_{3}

(d) None of these

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

(a) 0

(b) 1

(c) –1

(d) 2

**Ques. **Let the determinant of a 3 ´ 3 matrix A be 6, then B is a matrix defined by B = 5A^{2}. Then determinant of B is

(a) 180

(b) 100

(c) 80

(d) none of these

**Ques:** If | a x b | = 4 and | a.b |= 2, then |a|^{2} |b|^{2} =

(a) 2

(b) 6

(c) 8

(d) 20

**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

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**Ques. **If the equation x^{2} + y^{2} + 2gx + 2fy + 1 = 0 represents a pair of lines, then

(a) g^{2} – f^{2} = 1

(b) f^{2} – g^{2} = 1

(c) g^{2} + f^{2} = 1

(d) f^{2} + g^{2} = 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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**Ques:** If the lines of regression are 3x + 12y = 19 and 3y + 9x = 46 then r_{xy} will be

(a) 0.289

(b) – 0.289

(c) 0.209

(d) None of these

**Ques. **The length intercepted by the curve y^{2} = 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

**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

**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

**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

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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

**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

**Ques. **The number of points with integral coordinates (2*a*, *a* – 1) that fall in the interior of the larger segment of the circle *x*^{2} + *y*^{2} = 25 cut of by the parabola *x*^{2} + 4*y* = 0, is

(a) one

(b) two

(c) three

(d) none of these

**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 *h*^{2
}(a) is greater than 3

(b) is greater than 9

(c) equals 7

(d) is grater than 7

**Ques. **The number of real roots of the equation e^{sin x} – e^{–sin x} – 4 = 0 are

(a) 1

(b) 2

(c) infinite

(d) none of these

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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)

**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)

**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

**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)

**Ques. **If the *r*th, (r + 1)th and (r + 2) th coefficients of (1 + x)^{n} are in AP, then *n* is a root of the equation

(a) x^{2} – x(4r + 1) + 4r^{2} – 2 = 0

(b) x^{2} + x(4r + 1) + 4r^{2} – 2 = 0

(c) x^{2} + x(4r + 1) + 4r^{2} + 2 = 0

(d) none of these

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**Ques.** In a certain test a_{i} 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) a_{1} + 2a_{2} + 3a_{3} + … ka_{k}

(b) a_{1} + a_{2} + a_{3} + …, + a_{k}

(c) Zero

(d) None of these

**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

**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

**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

**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

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**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)

**Ques:** If y = 2x is a chord of the circle x^{2} + y^{2} – 10x = 0, then the equation of the circle of which this chord is a diameter, is

(a) x^{2} + y^{2} – 2x + 4y = 0

(b) x^{2} + y^{2} + 2x + 4y = 0

(c) x^{2} + y^{2} – 2x + 4y = 0

(c) x^{2} + y^{2} – 2x – 4y = 0

**Ques. **In the process of finding the root of the equation x^{3} – 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

**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)

**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

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**Ques.** If the straight line y = mx is outside the circle x^{2} + y^{2} – 20y + 90 = 0, then

(a) m > 3

(b) m < 3

(c) |m| > 3

(d) |m| < 3

**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
}

**Ques. **The vertex of the parabola y^{2} = 4(a’ – a)(x – a) is

(a) (*a*‘, *a*)

(b) (*a*, *a’*)

(c) (*a*, 0)

(d) (*a’*, 0)

**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

**Ques. **The equation x^{2} + 4xy + 4y^{2} – 3x – 6y – 4 = 0 represents

(a) circle

(b) pair of lines

(c) parabola

(d) none of these

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**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) ^{5}*C*_{2} × 4! × 6!

**Ques. **3x – 4y – 24 = 0 and 3x – 4y -12 = 0 are two parallel lines. If L_{1} makes an intercept of 3 units with these parallel lines then the equation of L_{1} may be given as

(a) x = 1

(b) y = 1

(c) x = 2y + 3

(d) none of these

**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) ^{6}C_{3} x ^{4}C_{2}

(b) ^{4}C_{3} x ^{4}C_{3}

(c) ^{4}P_{2} x ^{4}P_{3}

(d) none of these

**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

**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

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**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) *x*^{2} + *y*^{2} = 2*a*^{2}

(b) 3*x*^{2} + 3*y*^{2} = 2*a*^{2
}(c) 5*x*^{2} + 5*y*^{2} = 3*a*^{2}

(d) none of these

**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

**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

**Ques:** ^{n – 1}C_{3} + ^{n – 1}C_{4} > ^{n}C_{3} then the value of n is

(a) 7

(b) < 7

(c) > 7

(d) None of these

**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

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**Ques:** The value of the nearest root of the equation x^{3} + 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

**Ques:** 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 4A^{3} + 2A^{2} + 7A + I = O, then A^{–1} equals

(a) (4A^{2} + 2A + 7I)

(b) –(4A^{2} + 2A + 7I)

(c) –(4A^{2} – 2A + 7I)

(d) (4A^{2} + 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

**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

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**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

**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