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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx 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 two matrices such that A + B and AB are both defined, then

The value of log₃ 1/81 is?

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

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

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

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

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

The value of logₐ b logb c logc a is?

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

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

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

Which of the following is not true ?

The value of log√2 512 is?

1 / cos 80⁰ – √3/sin 80⁰ = ?

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

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

The coefficient of x⁵ in the series e⁻²ˣ 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

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

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

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

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

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

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

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

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

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 length of ┴ from the origin to the line x/3 – y/4 = 1 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 solution of 5x − 1 < 24 and 5x + 1 > −24 is?

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

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?

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

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

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

1 + 3 + 5 + 7 +……. + 17 is equal to

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

θ is acute angle between the lines x² – xy – 6y² = 0, then (2 cos θ + 3 sin θ / 4 sin θ + 5 cos θ) is ?

If |x + 2| ≤ 9, then x belongs to?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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