Math Paper
Q.1:- In an ellipse, if the lines joining focus to the extremities of the minor axis from an
equilateral triangle with the minor axis, then the eccentricity of the ellipse is
- (b) (c) (d)
Q.2:- The curve has a vertical tangent at the point
(a) (1, 1) (b) (1, 0)
(c) (0, 1) (d) none of these
Q.3:- If = 4 , then the value of x2 + y2 + z2 + t2 is
(a) (b) 1 2𝑥𝑦𝑧𝑡
(c) 4 (d) 6
Q.4:- Four dice are rolled. The number of possible outcomes in which at least one dice
shows 2 is
(a) 625 (b) 671 (c) 1023 (d) 1296
Q.5:- If f( ) f(𝑥) f(𝑦) for all 𝑥 and 𝑦 & if f(5) 2 and f ‘(0) 3, then f ‘(5) is
(a) 0 (b) 2 (c) 5 (d) 6
Q.6:- The equation of the curve satisfying the differential equation 𝑦2 (𝑥2 1) = 2𝑥𝑦1 passing
through the point (0, 1) and having slope of tangent at = 0 as 3 is
(a) 𝑦 𝑥3 3𝑥 1 (b) 𝑦 𝑥3 3𝑥 1
(c) 𝑦 𝑥2 3𝑥 1 (d) 𝑦 𝑥2 3𝑥 1
Q.7:- For the function f(𝑥) which of the following is true?
(a) does not exist
(b) does not exist
(c) Both limits exist and
(d) Both limits exist and
Q.8:- If a hyperbola passes through the foci of the ellipse and its transverse
& conjugate axes coincide with the major and minor axes of the ellipse & product of
their eccentricities be 1, then the equation of hyperbola is
(a) (b)
(c) (d) none of these
Q.9:- If p, q, r are positive and are in A.P., then roots of the quadratic equation px2+qx+r=0
are complex for
(a) 4 (b) 4
(c) all p and r (d) no p and r
Q.10:- For any two sets A and B if A 0 and for some set X,
then
(a) A (b)
(c) B (d) none of these
Q.11:- If the coefficient of variation of a distribution is 45 and the mean is 12, then its
standard deviation is
(a) 5.2 (b) 5.3
(c) 5.4 (d) none of these
Q.12:- The largest term in the expansion of where is
(a) (b)
(c) (d) none of these
Q.13:- The curve described parametrically by and represents
(a) a pair of straight (b) an ellipse
(c) a parabola (d) a hyperbola
Q.14:- Lets r be a relation from R (set of real numbers) to R defined by
and is an irrational number}. The relation r is
(a) an equivalence relation (b) reflexive only
(c) symmetric only (d) transitive only
Q.15:- The set is
(a) a finite set (b) an infinite set
(c) an empty set (d) none of these
Q.16:- For lies in the interval
(a) (b)
(c) (d)
Q.17:- If and if , then the value of lies in the interval
(a) (b)
(c) (d)
Q.18:- If P is a point on the line such that P and the point are on the opposite sides of the line then
(a) (b)
(c) (d) none of these
Q.19:- In a sequence of 21 terms, the first 11 terms are in A.P. with common difference 2 & the last 11 terms are in G.P. with common ratio 2. If the middle term of A.P. be equal to the middle term of the G.P., then the middle term of the entire sequence is
(a) (b) (c) (d)
Q.20:- If n is an integer and if , then n equals
(a) 1 (b) 1
(c) 2 (d) none of these
Q.21:- A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail the first two times is
(a) (b) (c) (d)
Q.22:- A particle is acted on by a force of 6 units in the direction and is displaced from the point to the point . The work done is
(a) 18 (b) 15 (c) 12 (d) 9
Q.23:- A variable line through the point cuts the coordinate axes in the points A and B. If the point P divides AB internally in the ratio 3 : 1, then the locus of P is
(a) (b)
(c) (d)
Q.24:- The maximum value of is
(a) 5 (b) 6
(c) 7 (d) none of these
Q.25:- The number of positive integers satisfying the inequality n+1Cn-2 n+1Cn-1 50 is
(a) 9 (b) 8 (c) 7 (d) 6
Q.26:- The distance of the point on which is nearest to the line is
(a) (b) (c) (d)
Q.27:- Lets be a differentiable function such that . Then the value of is
(a) 25 (b) 26
(c) 27 (d) none of these
Q.28:- If be continuous function such that the area bounded by the curve , the -axis and the lines is Value of is
(a) (b) (c) (d)
Q.29:- A curve through and satisfying the differential equation
is
(a) a circle (b) a parabola
(c) an ellipse (d) a hyperbola
Q.30:-If for all and is
(a) 8 (b) 16 (c) 32 (d) 64
Q.31:- Equation can have a real solution for
(a) all values of a (b)
(c) (d)
Q.32:- Let The number of one to one function from A to B is
(a) 24 (b) 60 (c) 120 (d) 360
Q.33:- The sum of the series is
(a) (b)
(c) (d)
Q.34:- If occurs in , then must be of the form
(a) 3k (b) 3k (c) 3k (d) 3k
Q.35:- The equation of the circle which cuts orthogonally the circle , passes through (3, 0) and touches the axis of y is
(a)
(b)
(c)
(d) none of these
Q.36:- Let a relation R in the set N of natural number be defined as . The relation R is
(a) reflexive (b) symmetric
(c) transitive (d) an equivalence relation
is
(a) (b)
(c) (d) none of these
Q.38:- Solution set of inequality is
(a) (b)
(c) (d)
Q.39:- Let z and w be two complex numbers such that and Then z equals
(a) 1 or (b) (c) (d)
Q.40:- If the system of equations
has a non-trivial solution, then the value of is
(a) 0 (b) 1 (c) 2 (d) 3
Q.41:- A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is non-negative?
(a) (b) (c) (d)
Q.42:- If and then angle between and is
(a) (b) (c) (d)
Q.43:- A non-zero vector is parallel to the line of intersection of the plane determined
by the vectors and the plane determined by the vectors . The angle between and is
(a) (b) (c) (d) none of these
Q.44:- Number of solutions of is
(a) 2 (b) 3 (c) 4 (d) none of these
Q.45:- If the slope of the one of the lines represents by be the square of the other, then is
(a) 3 (b) 4 (c) 5 (d) 6
Q.46:- The value of is
(a) 1 (b) (c) 0 (d) none of these
Q.47:- If Pm stands for mPm then is equal to
(a) (b)
(c) (d)
Q.48:- Let a and b be two integers such that .
The integer n such that is
(a) 15 (b) 65 (c) 115 (d) 165
Q.49:- The mean age of a combined group of men and women is 25 years. If the mean age of the group of men is 26 and that of the group of women is 21, then the percentage of men and women in the group is
(a) 46, 60 (b) 80, 20 (c) 20, 80 (d) 60, 40
Q.50:- A variable chord is drawn through the origin to the circle . The locus of centre of circle drawn on this chord as diameter is
(a) (b)
(c) (d)
Q.51:- Let R and C denote the set of real numbers and complex numbers respectively. The function defined by is
(a) one to one (b) onto
(c) injective (d) neither one to one nor onto
Q.52:- If x is complex, the expression takes all which lie in the interval (a, b) where
(a) (b)
(c) (d)
Q.53:- If be an A.P. of non-zero terms, then is equal to
(a) (b)
(c) (d) none of these
Q.54:- A and B are two events such that and . If A & B be independent events then P(B) is
(a) (b)
(c) (d) none of these
Q.55:- If , then for all
(a) (b)
(c) (d)
Q.56:- The straight lines L1, L2, L3, are parallel and lie in the same plane. A total of m points are takes on L1, n points on L2, k points on L3. The maximum number of triangles formed with vertices at these points is
(a) m+n+kC3 (b) m+n+kC3 mC3 nC3
(c) m+n+kC3 mC3 nC3 (d) none of these
Q.57:- If -1( ), then is
(a) 1 in the whole plane (b) in the whole plane
(c) 1 in the 2nd and 3rd quadrants of the plane
(d) 1 in the 3rd and 4th quadrants of the plane
Q.58:- The range of function 7-xPx-3 is
(a) {1, 2, 3, 4} (b) {3, 4, 5, 6}
(c) {0, 1, 2, 3, 4, 5} (d) {1, 2, 3}
Q.59:- If and have a common root where a, b, c N (set of natural numbers), the least value of is
(a) 13 (b) 11 (c) 7 (d) 9
Q.60:- The eccentricity of the ellipse is
(a) (b)
(c) (d)
Q.61:- The sum of the series is
(a) (b)
(c) (d)
Q.62:- Range of the function is
(a) (b)
(c) (d)
Q.63:- equals
(a) (b)
(c) (d)
Q.64:-If then the value of is
(a) (b)
(c) (d)
Q.65:-
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