The probability of not getting 53 Tuesdays in a leap year is:

Let R be the relation over the set A of all straight lines in a plane such that \(l_1 R l_2 \Leftrightarrow l_1\) is parallel to \(l_2\). Then R is:

The angle between two lines whose direction ratios are proportional to \(1, 1, -2\) and \((\sqrt{3} - 1), (-\sqrt{3} - 1), -4\) is:

The degree of the differential equation \(\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = \left(k\frac{d^2y}{dx^2}\right)\) is :

If \((\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 27\) and \(|\vec{a}| = 2|\vec{b}|\), then \(|\vec{b}|\) is:

The second order derivative of which of the following functions is \(5^x\) ?

If \(\tan^{-1}\left(\frac{2}{3^{-x}+1}\right) = \cot^{-1}\left(\frac{3}{3^{x}+1}\right)\), then which one of the following is true?

The value of \(\int_0^1 \frac{a - bx^2}{(a + bx^2)^2}\,dx\) is:

If \(A, B\) and \(C\) are three singular matrices given by \(A = \begin{bmatrix} 1 & 4 \\ 3 & 2a \end{bmatrix}\), \(B = \begin{bmatrix} 3b & 5 \\ 4 & 2 \end{bmatrix}\) and \(C = \begin{bmatrix} a+b+c & c+1 \\ a+c & c \end{bmatrix}\), then the value of abc is: