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

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

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

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?

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

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

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

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

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

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

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

1 / cos 80⁰ – √3/sin 80⁰ = ?

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

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

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

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

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

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

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

The value of log√2 512 is?

The value of logₐ b logb c logc a is?

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

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

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

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?

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

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

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

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

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

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

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

The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) 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 : [0, 2π] → [−1, 1] defined by f(x) = sinx is?

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

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

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?

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

The area of the triangle formed by the lines x² – 4y² = 0 and x = a 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 intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are?

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

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

If |x + 2| ≤ 9, then x belongs to?

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

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

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

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

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

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

The value of log₃ 1/81 is?

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

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

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

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

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

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

Which of the following is not true ?

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

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

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

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

The equation of the locus of the point whose distance from y-axis is half the distance from origin 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 constant functions from a set containing m elements to a set containing n elements is?

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

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?

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?

1 + 3 + 5 + 7 +……. + 17 is equal to

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

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

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

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

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

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

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

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

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

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