Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

• 256

• 220

• 219

• 219

The real number k for which the equation, 2x³ +3x +k = 0 has two distinct real roots in [0,1]

• lies between 1 and 2

• lies between 2 and 3

• lies between -1 and 0

• lies between -1 and 0

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

A ray of light along  get reflected upon reaching X -axis, the equation of the reflected ray is 

The number of values of k, for which the system of equations
(k+1) x + 8y = 4k
kx + (k+3)y = 3k -1
has no solution, is 

• infinite 

• 1

• 2

• 2

If the equations x² + 2x + 3 = 0 and ax² + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

• 1:2:3

• 3:2:1

• 1:3:2

• 1:3:2

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

• (-5,2)

• (2,-5)

• (5,-2)

• (5,-2)

If x, y, z are in A.P. and tan⁻¹ x, tan⁻¹ y and tan⁻¹ z are also in A.P., then

• x= y= z

• 2x =3y = 6z

• 6x = 3y= 2z

• 6x = 3y= 2z

Consider :
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.

• Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I 

• Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

• Statement -I is True; Statement -II is False.

• Statement -I is True; Statement -II is False.

• -1/4

• 1/2

• 1

• 1