Maths EAMCET Sample paper has 80 objective type questions with answers. Correct answer is bold marked.

**Ques.** If 2z_{1} – 3z_{2 }+ z_{3} = 0 then z_{1}, z_{2}, z_{3} are represented by

(a) three vertices of a triangle

(b) three collinear points

(c) three vertices of a rhombus

(d) none of these

**Ques.** The octal number 473 in the decimal representation is equal to

(a) (312)_{10}

(b) (308)_{10}

(c) (315)_{10}

(d) None of these

**Ques.** How many numbers can be made with the help of the digits 0, 1, 2, 3, 4, 5 which are greater than 3000 (repetition is not allowed)

(a) 180

(b) 360

(c) 1380

(d) 1500

**Ques.** A chord of the circle x^{2} + y^{2} = a^{2} cuts it at two points A and B such that angle AOB is a right angle where O is the centre of the circle. If there is a moving point P on this circle then the locus of orthocentre of △PAB will be a

(a) parabola

(b) circle

(c) straight line

(d) none of these

**Ques.** If one root of the equation x^{2} + px + 12 = 0 is 4, while the equation x^{2} + px + q = 0 has equal roots, then the value of q is

(a) 49/4

(b) 4/49

(c) 4

(d) none of these

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**Ques.** If 7x – y + 3 = 0, x + y – 3 = 0 are the equations of two equal sides of an isosceles triangle and (1, 0) is on the base, then the equation of the third side is

(a) x + 3y – 1 = 0

(b) 3x + y – 3 = 0

(c) 7x – y – 7 = 0

(d) x – 7y = 1

**Ques.** Two tangents are drawn from a point *P* on radical axis to the two circles touching at *Q* and *R* respectively then triangle formed by joining *PQR* is

(a) Isosceles

(b) Equilateral

(c) Right angled

(d) None of these

**Ques.** If x–coordinate of a point P on the join of Q (2, 2, 1) and R(5, 1, –2) is 4, then its z–coordinate is

(a) –2

(b) –1

(c) 1

(d) 2

**Ques. **The tangent to y^{2} = 4x at the points (1, 2) and (4, 4) meet on the line

(a) x = 3

(b)* *y = 3

(c) x + y = 4

(d) y – 2 = 0

**Ques.** If for positive integers r > 1, n > 2 the coefficient of the (3r)^{th }and (r + 2)^{th} powers of *x *in the expansion of (1 + x)^{2n }are equal, then

(a) n = 2r

(b) n = 3r

(c) n = 2r + 1

(d) None of these

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**Ques.** From an urn containing 3 white and 5 black balls, 4 balls are transferred into an empty urn. From this urn a ball is drawn and found to be white. The probability that out of four balls transferred, 3 are white and 1 is black, is

(a) 1/3

(b) 1/7

(c) 2/3

(d) none of these

**Ques.** The radical axis of the two circles having centres at C_{1} and C_{2} and radii r_{1} and r_{2} is neither intersecting nor touching any of the circles, if

(a) C_{1}C_{2} = 0

(b) 0 < C_{1}C_{2} < |r_{1 }– r_{2}|

(c) C_{1}C_{2} = |r_{1} – r_{2}|

(d) |r_{1} – r_{2}| < C_{1}C_{2} < r_{1} + r_{2
}

**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

**Ques.** In a test an examine either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it is 1/8. the probability that he know the answer to the question given that he correctly answered it.

(a) 24/29

(b) 8/29

(c) 13/29

(d) none of these

**Ques. **The locus of an end of latus-rectum of all ellipses having a given major axis is

(a) straight line

(b)* *parabola

(c) ellipse

(d) circle

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**Ques.** In a polygon the number of diagonals is 54. The number of sides of the polygon is

(a) 10

(b) 12

(c) 9

(d) none of these

**Ques.** The image of the pair of lines represented by ax^{2} + 2hxy + by^{2} = 0 by the line mirror y = 0 is

(a) ax^{2} – 2hxy – b^{2}y = 0

(b) bx^{2} – 2hxy + ay^{2} = 0

(c) bx^{2} + 2hxy + ay^{2} = 0

(d) ax^{2} – 2hxy + by^{2} = 0

**Ques. **A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to

(a) 2

(b) 3

(c) 4

(d) 5

**Ques.** Let f(x) = x^{3} + 3x^{2} + 33x + 2 for x > 0 and ‘g’ be its inverse, then the value of ‘K’ such that Kg’ (2) = 1, is

(a) 33

(b) 42

(c) 12

(d) all of the above

**Ques. **In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together?

(a) 1540

(b) 1450

(c) 1504

(d) 1405

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**Ques. **Numbers of zeros at the end of 300 ! is equal to

(a) 75

(b) 89

(c) 74

(d) 98

**Ques.** A gun projects a ball at an angle of 45 degree with the horizontal. If the horizontal range is 39.2 *m*, then the ball will rise to

(a) 9.8 *m*

(b) 4.9 *m*

(c) 2.45 *m*

(d) 19.6* m*

**Ques.** If f(x) = max {|16 – x^{2} |, |x|}, the minimum value of f(x) in the interval [–3, 3] is

(a) 2

(b) 6

(c) 4

(d) none of these

**Ques.** What will be the equation of that chord of ellipse x^{2} / 36 + y^{2} / 9 = 1 which passes from the point (2, 1) and bisected on the point

(a) x + y = 2

(b) x + y = 3

(c) x + 2y = 1

(d) x + 2y = 4

**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

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**Ques.** Let f(x) = a – (x – 3)^{8/9}, then greatest value of f(x) is

(a) 3

(b) a

(c) no maximum value

(d) none of these

**Ques.** The central value of the set of observations is called

(a) Mean

(b) Median

(c) Mode

(d) G.M.

**Ques.** If y = a log |x| + bx^{2} + x has its extremum values at x = –1 and x = 2, then

(a) a = 2, b = –1

(b) a = 2, b = – ½

(c) a = –2, b = ½

(d) None of these

**Ques. **The largest value of a third order determinant whose elements are equal to 1 or 0 is

(a) 1

(b) 2

(c) 3

(d) none of these

**Ques.** The differential equation corresponding to the family of curves y = e^{x} (a cos x + b sin x), a and b being arbitrary constant is

(a) 2y_{2} + y_{1} – 2y = 0

(b) y_{2} – 2y_{1} + 2y = 0

(c) 2y_{2} – y_{1} + 2y = 0

(d) none of these

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**Ques. **Two finite sets *A* and *B* having *m* and *n* elements. The total number of relations *A* to *B* is 64, then possible values of *m* and *n* are :

(a) 2 and 4

(b) 2 and 3

(c) 2 and 1

(d) 64 and 1

**Ques. **Which one is True?

(a) sin 1 > sin 2 > sin 3

(b) sin 1 < sin 2 < sin 3

(c) sin 1 < sin 3 < sin 2

(d) sin 3 < sin 1 < sin 2

**Ques. **A parachute weighing 1 kg falling with uniform acceleration from rest describes 16 m in first 4 secs. The resultant pressure of air on the parachute is

(a) 8.7 N

(b) 7.8 N

(c) 9.8 N

(d) none of these

**Ques.** If the vertex is (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2), then the parabola is

(a) y^{2} = 2x – 4

(b) x^{2} = 4y – 8

(c) y^{2} = 4x – 8

(d) none of these

**Ques.** Let a, b be two positive numbers, where a > b and 4 × G.M. = 5 × H.M. for the numbers. Then a is

(a) 4b

(b) 1/4 b

(c) 2b

(d) b

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**Ques.** A pregnancy test is done on 100 pregnant women and 100 non-pregnant women. Test suggests out of 100 pregnant woman, 2 are pregnant and 8 out of 100 non-pregnant woman are pregnant. A woman is selected randomly and test is done which says woman is pregnant. What is the probability woman is non-pregnant.

(a) ½

(b) 92/100

(c) 8/100

(d) none of these

**Ques.** The value of tan 42^{o} tan66^{o} tan78^{o} is equal to

(a) 1

(b) tan6^{ o}

(c) cot6^{ o}

(d) tan18^{ o
}

**Ques.** Karl Pearson’s coefficient of correlation between *x* and *y* for the following data is

x : |
3 | 4 | 8 | 9 | 6 | 2 | 1 |

y : |
5 | 3 | 7 | 7 | 6 | 9 | 2 |

(a) 0.480

(b) – 0.480

(c) 0.408

(d) – 0.408

**Ques. **The graph of the function y = f(x) is symmetrical about *x* = 2, then

(a) f(x + 2) = f(x – 2)

(b) f(2 + x) = f(2 – x)**
**(c) f(x) = f(–x)

(d) none of these

**Ques.** Value of 10C_{r}/11C_{R}, when numerator and denominator takes their greatest value, is

(a) 6/11

(b) 5/11

(c) 10/6

(d) 10/5

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**Ques.** If a variable line has its intercepts on the co–ordinates axes e, e’ , where e/2, e’/2 are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle x^{2} + y^{2} = r^{2}, where r =

(a) 1

(b) 2

(c) 3

(d) cannot be decided

**Ques.** If a_{1}, a_{2}, a_{3}, … is an A.P. such that a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225 then a_{1} + a_{2} + a_{3} + … + a_{23} + a_{24} is equal to

(a) 909

(b) 75

(c) 750

(d) 900

**Ques.** If *R* and R’ are the resultants of two forces P / Q and Q/P (P > Q) according as they are like or unlike such that R : R’ = 25 : 7, then P : Q =

(a) 2 : 1

(b) 3 : 4

(c) 4 : 3*
*(d) 1 : 2

**Ques.** In the group *G* = {2, 4, 6, 8} under multiplication modulo 10, the inverse of 4 is

(a) 2

(b) 4

(c) 6

(d) 8

**Ques.** If a, b, c are in A.P. 10^{ax + 10}, 10^{bx + 10}, 10^{cx + 10} are in

(a) A.P.

(b) G.P. when *x* > 0

(c) G.P. for all *x*(d) G.P. when

*x*< 0

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**Ques. **Sum of coefficients in the expansion of (x + 2y + z)^{10} is

(a) 2^{10
}(b) 3^{10
}(c) 1

(d) none of these

**Ques.** A student appears for test I, II and III. The student is successful if he passes either in tests I and II or test I and III. The probabilities of the student passing in tests I, II, III are *p*, *q* and 1/2 respectively. If the probability that the student is successful is 1/2, then

(a) p = 1, q = 0

(b) p = 2/3, q = ½

(c) There are infinitely many values of *p *and *q
*(d) All of the above

**Ques.** Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

(a) If a number is not a prime then it is odd

(b) If a number is not a prime then it is odd

(c) If a number is not odd then it is not a prime

(d) If a number is not odd then it is a prime

**Ques.** In the above question the iso-profit line is

(a) 3x + y = 30

(b) x + 3y = 20

(c) 3x – y = 20

(d) 4x + 3y = 24

**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

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**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

**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

**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

**Ques.** If the variance of x = 9 and regression equations are 4x – 5y + 33 = 0 and 20x – 9y – 10 = 0, then the coefficient of correlation between *x* and *y* and the variance of *y* respectively are

(a) 0.6; 16

(b) 0.16; 16

(c) 0.3; 4

(d) 0.6; 4

**Ques.** The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is

(a) 133

(b) 190

(c) 233

(d) 105