If \(x = 2\sin\theta\) and \(y = 2\cos\theta\), then the value of \(\frac{d^2y}{dx^2}\) at \(\theta = 0\) is

A line makes the angle \(\theta\) with each of the \(x\) and \(z\) axes. If the angle \(\beta\) which it makes with \(y\)-axis is such that \(\sin^2\beta = 3\sin^2\theta\), then the value of \(\cos^2\theta\) is

If \(x = e^{y + e^{y + \cdots\infty}}\), \(x > 0\), then \(\frac{dy}{dx}\) is equal to

If the vertices of a triangle \(ABC\) are \(A(1,2,1)\), \(B(4,2,3)\) and \(C(2,3,1)\), then the equation of the median passing through the vertex A, is

\(\sin^{-1}(1 - x) - 2\sin^{-1}x = \frac{\pi}{2}\), then \(x\) is equal to (A) 0 (B) 1 (C) \(\frac{1}{2}\) (D) 2 Choose the most appropriate answer from the options given below:

If R is a relation on Z (set of all integers) defined by \(xRy\), if \(|x - y| \leq 1\), then (1) \(R\) is reflexive (2) \(R\) is symmetric (3) \(R\) is transitive (4) \(R\) is not symmetric (5) \(R\) is not transitive Choose the most appropriate answer from the options given bel…

The smaller of the areas enclosed by the circle \(x^2 + y^2 = 4\) and the line \(x + y = 2\) is

In linear programming, the optimal value of the objective function is attained at the points given by

If \(0 < x < \pi\) and the matrix \(\begin{bmatrix}4\sin x & -1\\ -3 & \sin x\end{bmatrix}\) is singular, then the values of \(x\) are: