Engineering Entrance Sample Papers

PESSAT Maths Entrance Exam Sample Questions

PESSAT Maths question paper

Multiple choice sample practice questions for PES Scholastic Aptitude Test (PESSAT) entrance exam with answers.

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. nCr –1  + 3 nC + 3 nCr + 1 + nCr + 2   is equal to
(a) n + 2Cr + 1
(b) n + 2Cr + 2
(c) n + 2Cr + 3
(d) n + 3Cr + 2
Ans. (d)

Ques. If z1, z2 and z3 are non-zero, complex numbers such that 2/z1 = 1/z2 + 1/z3 then z1, z2, z3 are
(a) concyclic
(b) collinear
(c) vertices of a square
(d) none of these
Ans. (a)

Ques. The equation of the line touching both the parabolas y2 = 4x and x2 = -32y is
(a) x + 2y + 4 = 0
(b) 2x + y – 4 = 0
(c) x – 2y – 4 = 0
(d) x – 2y + 4 = 0
Ans. (d)

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Ques. The coefficient of xn in the expansion of (1 + 2x + 3x2 +  . . .  .)2 is
(a) 1
(b) n + 1
(c) -1
(d) n
Ans. (a)

Ques. If the roots of the equation x2 + 2ax + b = 0, are real and distinct and they differ by at most 2m, then b lies in the interval
(a) (a2 – m2, a2)
(b) [a2 – m2, a2)
(c) (a2, a2 + m2)
(d) none of these
Ans. (b)

Ques. How many 10 digit numbers can be written by using the digits 1 and 2 ?
(a) 10C1 + 9C2
(b) 210
(c) 10C2
(d) 10!
Ans. (b)

Ques. The number of divisors of the number 38808 (excluding 1 and the number itself) is
(a) 70
(b) 72
(c) 71
(d) none of these
Ans. (a)

Ques. If A is 2 × 2 matrix such that A2 = O then  is
(a) 1
(b) –1
(c) O
(d) none of these
Ans. (c)

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Ques. The line ax – by + c = 0 is a normal to the curve xy = –1, if
(a) a > 0, b > 0
(b) a < 0, b < 0
(c) a > 0, b < 0
(d) a > 1, b > 1
Ans. (c)

Ques. The number of real roots of |x|3 –3x2 + 3|x| -2 = 0 are
(a) 1
(b) 2
(c) 3
(d) none of these
Ans. (b)

Ques. Let f(x) = x3 + 3x2 + 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)

Ques. Total number of five digit numbers (having all non-zero digits) having atleast 2 but atmost 4 identical digits is equal to;
(a) 10120
(b) 10160
(c) 10200
(d) 10260
Ans. (c)

Ques. The orthogonal trajectories of a family of parallel lines is a family of
(a) parallel lines
(b) concurrent lines
(c) concentric circles
(d) concentric ellipses
Ans. (a)

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Ques. x2 = xy is a relation which is :
(a) symmetric
(b) reflexive
(c) transitive
(d) none of these
Ans. (c)

Ques. If the altitudes of a triangle be 3, 4, 6 then its in radius is
(a) 1
(b) ¾
(c) 12
(d) 4/3
Ans. (d)

Ques. In a plane there are 10 points out of which  4 are collinear, then the number of triangles that can be formed by joining these points are
(a) 60
(b) 116
(c) 120
(d) None of these
Ans. (b)

Ques. One vertex of the equilateral triangle with centroid at the origin and one side as x + y –2 = 0 is
(a) (-1, -1)
(b) (2, 2)
(c) (-2, -2)
(d) none of these
Ans. (c)

Ques. If f be the greatest integer function and g be the modulus function, then (gof)(–5/3) – (fog)(–5/3) =
(a) 1
(b) –1
(c) 2
(d) 4
Ans. (a)

Ques. If nC12 = nC6, then nC2 =
(a) 72
(b) 153
(c) 306
(d) 2556
Ans. (b)

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Ques. The probability that the same number appear on throwing three dice simultaneously, is (a) 1/36
(b) 5/36
(c) 1/6
(d) 4/13
Ans. (a)

Ques. (10101101)2 = (. . . . . )10 :
(a) 137
(b) 173
(c) 170
(d) none of these
Ans. (b)

Ques. If  the expression a2 (b2– c2) x2 + b2 (c2 – a2) x + c2 (a2 – b2) is a perfect square then
(a) a, b, c are in AP
(b) a2, b2, c2 are in AP
(c) a2, b2, c2 are in HP
(d) a2, b2, c2 are in GP
Ans. (c)

Ques. The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively. Then, P (X = 1) is
(a) 1/32
(b) 1/16
(c) 1/8
(d) ¼
Ans. (a)

Ques. The value of tan 42o tan 66o tan 78o is equal to
(a) 1
(b) tan 6o
(c) cot 6o
(d) tan 18o
Ans. (c)

Ques. In a projectile motion horizontal range R is maximum, then relation between height H and R is
(a) H = R/2
(b) H = R/4
(c) H = 2R
(d) H = R/8
Ans. (b)

Ques. The differential equation corresponding to the family of curves y = ex (a cos x + b sin x), a and b being arbitrary constant is
(a) 2y2 + y1 – 2y = 0
(b) y2 – 2y1 + 2y = 0
(c) 2y2 – y1 + 2y = 0
(d) none of these
Ans. (b)

Ques. If in a triangle ABC, cos A cos B + sin A sin B sin C = 1, then the triangle is
(a) isosceles
(b) right angled
(c) isosceles right angled
(d) equilateral
Ans. (c)

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Ques. The number of critical points of the function f(x) = (ax2 + bx + c) |x|, where ac < 0 is
(a) 1
(b) 2
(c) 3
(d) 4
Ans. (c)

Ques. If |x2 – x – 6| = x + 2, then the values of x are
(a) – 2, 2, –4
(b) – 2, 2, 4
(c) 3, 2, –2
(d) 4, 4, 3
Ans. (b)

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. Two such dice are thrown together. Then the probability that the product of the numbers is 4 is
(a) 5/81
(b) 6/81
(c) 7/81
(d) 8/81
Ans. (d)

Ques. The number of ways of pointing the faces of a cube with six different colours is
(a) 1
(b) 6
(c) 6 !
(d) 6C3
Ans. (a)

Ques. If T2/T3 in the expansion of (a + b)n and T3/T4 in the expansion of  (a + b)n + 3 are equal, then n =
(a) 3
(b) 4
(c) 5
(d) 6
Ans. (c)

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)

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Ques. Three vertices of parallelogram taken in order, are (1, 3), (2, 0) and (5, 1). Then its fourth vertex is
(a) (3, 3)
(b) (4, 4)
(c) (4, 0)
(d) (0, –4)
Ans. (b)

Ques. The value of x for which log3(21 – x + 3), log9 4, log27(2x – 1)3 are in A.P.
(a) 11/6
(b) 6/11
(c) log2(11/6)
(d) 1
Ans. (d)

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 points representing complex number z for which |z – 3| = |z – 5| lie on the locus given by
(a) circle
(b) ellipse
(c) straight line
(d) none of these
Ans. (c)

Ques. The roots of the equation 22x – 10. 2x + 16 = 0 are
(a) 2, 8
(b) 1, 3
(c) 1, 8
(d) 2, 3
Ans. (b)

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Ques. The eccentricity of ellipse, with centre at the origin, is ½. If one directrix is x = 4, the equation of the ellipse is
(a) 3x2 + 4y2 = 1
(b) 3x2 + 4y2 = 12
(c) 4x2 + 3y2 = 1
(d) 4x2 + 3y2 = 12
Ans. (b)

Ques. The number of selections of 2 candidates for a post out of 5 equally qualified candidates
(a) 5P2
(b) 5!
(c) 3!
(d) 10
Ans. (d)

Ques. If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 – 2x + 8y – d = 0, then c + d equals
(a) 60
(b) 50
(c) 40
(d) 56
Ans. (b)

Ques. Equations (b-c)x + (c-a)y + (a-b) = 0 and (b3-c3)x + (c3-a3)y + (a3 – b3) = 0 (a, b, c are all different) will represent the same line if and only if
(a) b + c = 0
(b) c + a = 0
(c) c + a = 0
(d) a + b + c = 0
Ans. (d)

Ques. 20Cr = 20Cr+4, then rC3 equals
(a) 50
(b) 54
(c) 56
(d) none of these
Ans. (c)

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Ques. If  m be  the  slope  of  common   tangents  of  y = x2 – x + 1  and  y = x2 – 3x + 1,  then m  is  equal to ;
(a) 16
(b) 7
(c) 9
(d) none of these
Ans. (b)

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