If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is?

If pv = 81, then dp/dv at v = 9 is

The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is?

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is?

The image of the point(2,3)in the line y = -x is?

If a and b are the real roots of the equation x² − kx + c = 0, then the distance between the points (a, 0) and (b, 0) is?

The length of ┴ from the origin to the line x/3 – y/4 = 1 is?

Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ ∪[(A∩B)∪B’] is?

If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to?

If f (x) = x + 2, then f ‘(f (x)) at x = 4 is

Which of the following is not true ?

The equation of the locus of the point whose distance from y-axis is half the distance from origin is?

Let R be the set of all real numbers. Consider the following subsets of the plane R × R:
S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer } Then which of the following is true?

1 / cos 80⁰ – √3/sin 80⁰ = ?

The range of the function f(x) = | [x] − x|, x ∈ R is?

1 + 3 + 5 + 7 +……. + 17 is equal to

Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if?

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is?

If 8 and 2 are the roots of x² +ax+c = 0 and 3, 3 are the roots of x² +dx+b = 0, then the roots of the equation x² + ax + b = 0 are?

The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is

The value of log√2 512 is?

The number of five digit telephone numbers having at least one of their digits repeated is

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 +2√2 is?

Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0?

Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if

The relation R defined on a set A = {0,−1, 1, 2} by xRy if |x² + y² | ≤ 2, then which one of the following is true?

Let R be the universal relation on a set X with more than one element. Then R is?

If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to?

The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is?

The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. How many students take at least one of these two subjects is

The number of solutions of x² + |x − 1| = 1 is ?

If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) =

The solution set of the following inequality |x − 1| ≥ |x − 3| is ?

If log√x 0.25 = 4, then the value of x is?

If a and b are the roots of the equation x² − kx + 16 = 0 and satisfy a² + b² = 32, then the value of k is?

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

The value of logₐ b logb c logc a is?

For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to

The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is?

One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is?

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y – 20 =0, then the area of the square is?

The function f : R → R is defined by f(x) = sinx + cos x is?

The value of 1 – 1/2 (2/3) + 1/3 (2/3)² – 1/4 (2/3)³ + ….. is ?

The sum up to n terms of the series √2 + √8 + √18 + √32 + ….. is?

If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x- axis, then tan α tan β =?

If 3 is the logarithm of 343, then the base is?

The number of relations on a set containing 3 elements is?

If A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains?

The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ?

The value of log₃ 1/81 is?

The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is?

The intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are?

If a is the arithmetic mean and g is the geometric mean of two numbers, then

The equation whose roots are numerically equal but opposite in sign to the roots of 3x² − 5x − 7 = 0 is?

If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is?

If |x – 2| / x – 2 ≥ 0, then x belongs to?

If |x + 2| ≤ 9, then x belongs to?

If y = mx + c and f (0) = f ‘(0) =1, then f (2) is

The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is?

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and q passes through the point?

The number of constant functions from a set containing m elements to a set containing n elements is?

If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is?

(1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) =

The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is?

If A and B are symmetric matrices of order n, where (A ≠ B), then

The range of the function 1 / 1-2 sin x is?

The slope of the line which makes an angle 45⁰ with the line 3x – y = -5 are?

The value of (1/2!) + (1/4!) + (1/6!) + ….. Is?

The sum of an infinite GP is 18. If the first term is 6, the common ratio is?

The area of the triangle formed by the lines x² – 4y² = 0 and x = a is?

cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =?

If the two straight lines x + (2k – 7)y + 3=0 and 3kx + 9y – 5 = 0 are perpendicular then the value of k is?

The coefficient of x⁵ in the series e⁻²ˣ is?

Which of the following equation is the locus of (at²; 2at)?

Find a so that the sum and product of the roots of the equation 2x² + (a − 3)x + 3a − 5 = 0 are equal is?

If A and B are two matrices such that A + B and AB are both defined, then

If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to?

Given that x, y and b are real numbers x < y,b > 0, then?

The solution of 5x − 1 < 24 and 5x + 1 > −24 is?

The coordinates of the four vertices of a quadrilateral are (-2,4), (-1,2), (1,2) and (2,4)taken in order. The equation of the line passing through the vertex(-1,2) and dividing the quadrilateral in the equal areas is?

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is?

The derivative of f (x) = x | x | at x = −3 is

The rule f(x) = x² is a bijection if the domain and the co-domain are given by?

If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is?