Maths EAMCET Sample paper (PDF) 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

Ans: (b)

**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

Ans: (b)

**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

Ans: (a)

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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

Ans: (b)

**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

Ans: (b)

**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

Ans: (b)

**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

Ans: (b)

**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
}Ans: (b)

**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

Ans: (a)

**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

Ans: (b)

**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

Ans: (a)

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

(a) 75

(b) 89

(c) 74

(d) 98

Ans: (c)

**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

Ans: (a)

**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

Ans: (d)

**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

Ans: (b)

**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

Ans: (b)

**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

Ans: (b)

**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

Ans: (b)

**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

Ans: (c)

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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

Ans: (c)

**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
}Ans: (c)

**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

Ans: (b)

**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

Ans: (a)

**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

Ans: (b)

**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

Ans: (d)

**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

Ans: (c)

**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

Ans: (d)

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