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

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?

1 / cos 80⁰ – √3/sin 80⁰ = ?

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

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

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

The number of solutions of x² + |x − 1| = 1 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 line (p + 2q)x + (p – 3q)y = p – q for different values of p and q passes through the point?

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

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

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

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

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

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

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

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

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

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

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

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

The value of log₃ 1/81 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?

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?

Which of the following is not true ?

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

1 + 3 + 5 + 7 +……. + 17 is equal to

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

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

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

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

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

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

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

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 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?

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

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

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

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

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

If |x + 2| ≤ 9, then x belongs to?

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

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

The value of log√2 512 is?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) 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 3 is the logarithm of 343, then the base is?

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

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

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

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

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

The value of logₐ b logb c logc a is?

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

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

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

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