The shortest distance between line y - x = 1 and curve x = y2 is
√3/4
3√2 /8
8/3√2
8/3√2
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity is
3x2 + 5y2 -32 = 0
5x2 + 3y2 - 48 = 0
3x2 + 5y2 - 15 = 0
3x2 + 5y2 - 15 = 0
The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0) touch each other if
2|a| = c
|a| = c
a = 2c
a = 2c
Let A and B be two symmetric matrices of order 3.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is false.
Statement-1 is true, Statement-2 is false.
If A = sin2 x + cos4 x, then for all real x
3/4 ≤ A ≤ 1
31/16 ≤ A ≤ 1
1≤ A ≤2
1≤ A ≤2
A.
3/4 ≤ A ≤ 1
A = sin2x + cos4x = sin2x + (1 - sin2 x)
2 = sin4x - sin2x + 1
The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is:
3
2
1
1