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. **^{n}C_{r –1 } + 3^{ n}C_{r } + 3 ^{n}C_{r + 1 }+ ^{n}C_{r + 2 } is equal to

(a) ^{n + 2}C_{r + 1
}(b) ^{n + 2}C_{r + 2
}(c) ^{n + 2}C_{r + 3}

(d) ^{n + 3}C_{r + 2
}Ans. (d)

**Ques. **If z_{1}, z_{2} and z_{3} are non-zero, complex numbers such that 2/z_{1} = 1/z_{2} + 1/z_{3} then z_{1}, z_{2}, z_{3} 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 y^{2} = 4x and x^{2} = -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 x^{n} in the expansion of (1 + 2x + 3x^{2} + . . . .)^{2} is

(a) 1

(b) n + 1

(c) -1

(d) n

Ans. (a)

**Ques. **If the roots of the equation x^{2} + 2ax + b = 0, are real and distinct and they differ by at most 2*m*, then *b* lies in the interval

(a) (a^{2} – m^{2}, a^{2})

(b) [a^{2} – m^{2}, a^{2})

(c) (a^{2}, a^{2} + m^{2})

(d) none of these

Ans. (b)

**Ques. **How many 10 digit numbers can be written by using the digits 1 and 2 ?

(a) ^{10}C_{1} + ^{9}C_{2}

(b) 2^{10}

(c) ^{10}C_{2}

(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 A^{2} = 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} –3x^{2} + 3|x| -2 = 0 are

(a) 1

(b) 2

(c) 3

(d) none of these

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)

**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. **x^{2} = 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 (go*f*)(–5/3) – (*f*og)(–5/3) =

(a) 1

(b) –1

(c) 2

(d) 4

Ans. (a)

**Ques. **If ^{n}C_{12} = ^{n}C_{6}, then ^{n}C_{2} =

(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 a^{2} (b^{2}– c^{2}) x^{2} + b^{2} (c^{2} – a^{2}) x + c^{2} (a^{2} – b^{2}) is a perfect square then

(a) a, b, c are in AP

(b) a^{2}, b^{2}, c^{2} are in AP

(c) a^{2}, b^{2}, c^{2} are in HP

(d) a^{2}, b^{2}, c^{2} 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 42^{o} tan 66^{o} tan 78^{o} is equal to

(a) 1

(b) tan 6^{o}

(c) cot 6^{o}

(d) tan 18^{o
}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 = 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. **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) = (ax^{2} + bx + c) |x|, where *ac* < 0 is

(a) 1

(b) 2

(c) 3

(d) 4

Ans. (c)

**Ques. **If |x^{2} – 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) ^{6}*C*_{3
}Ans. (a)

**Ques. **If T_{2}/T_{3} in the expansion of (a + b)^{n} and T_{3}/T_{4} 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 log_{3}(2^{1 – x} + 3), log_{9 }4, log_{27}(2^{x} – 1)^{3} are in A.P.

(a) 11/6

(b) 6/11

(c) log_{2}(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 2^{2x} – 10. 2^{x} + 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) 3x^{2} + 4y^{2} = 1

(b) 3x^{2} + 4y^{2} = 12

(c) 4x^{2} + 3y^{2} = 1

(d) 4x^{2} + 3y^{2} = 12

Ans. (b)

**Ques. **The number of selections of 2 candidates for a post out of 5 equally qualified candidates

(a) ^{5}P_{2}

(b) 5!

(c) 3!

(d) 10

Ans. (d)

**Ques. **If the circle x^{2} + y^{2} + 4x + 22y + c = 0 bisects the circumference of the circle x^{2} + y^{2} – 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 (b^{3}-c^{3})x + (c^{3}-a^{3})y + (a^{3} – b^{3}) = 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. **^{20}C_{r} = ^{20}C_{r+4}, then ^{r}C_{3} 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 = x^{2} – x + 1 and y = x^{2} – 3x + 1, then m is equal to ;

(a) 16

(b) 7

(c) 9

(d) none of these

Ans. (b)

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