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
A ray of light along get reflected upon reaching X -axis, the equation of the reflected ray is
B.
Given equation of line
Slope of incident ray is
So, slope of reflected ray must be and the point of incident
So equation of reflected ray
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.