List of top Mathematics Questions

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is \(\frac{2}{7}\), then the probability of getting a white ball is
PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is
A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is
If \(-26\), x, 2 are in A.P., then the value of x is
If value of \(\cot \theta\) is \(\sqrt{5}\), then \(\sin \theta\) equals
The probability of getting sum greater than 10, when two dice are rolled together, is
A chord \(QR\) subtends an angle of \(105^\circ\) at the centre \(O\) of the circle. The measure of \(\angle RQP\) is
Which of the following statements is not always true?
\(n^{\text{th}}\) term of the A.P. : \(-\frac{1}{3}, \frac{4}{3}, 3, \ldots\) is
The graph of a polynomial \(p(x)\) is shown here. The number of zeroes of the polynomial \(p(x)\) is
The roots of the quadratic equation \(x^2 + 9 = 0\) are
The distance between the points \((-2, 5)\) and \((5, -2)\) is
A cylinder of radius \(r\) is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is
7 $\times$ 11 $\times$ 13 + 5 is
The shortest distance between the straight line \[ \vec{r} = 3\hat{i}+12\hat{j}+5\hat{k} +\lambda(2\hat{i}), \qquad \lambda\in\mathbb{R}, \] and the \(x\)-axis is:

The value of \(\lim_{x \to 0} \frac{6\sin(x) - 2\sin(3x)}{3x^3}\) is equal to 
 

\[ \int \left(27x^3(1-x^3)\right)^{\frac{2}{3}}\,dx = \]

\(\int \frac{1}{(1 - \cos x)}(1 + \sec x) dx = \) 
 

\(\int \frac{10e^x}{(2e^x + 5)^3} dx\) is equal to 
 

Let \(f(x) = \cos(5x)\cos(3x) - \sin(5x)\sin(3x), 0 \leq x \leq \frac{\pi}{4}\). Then \(f\) attains its minimum at \(x =\)
 

The point \(P\) lies on the curve with equation \[ y = x\sqrt{2\log_e(x)}, \qquad x>0. \] If \[ \frac{dy}{dx}=2 \] at \(x=k\), then the value of \(k\) is equal to: 

Let \(f(x) = \frac{\sin x}{x}\) for \(x \neq 0\). Then the value of \(f'(\frac{\pi}{2})\) is equal to
Let \(f(x)=2\sqrt{\,2\sin x+2\sqrt{2}\cos x\,},\; x\in\mathbb{R}\). Then the value of \(f\!\left(\frac{\pi}{12}\right)\) is equal to

If \[ f(x)= \begin{cases} x^2, & \text{if } x\leq 2,\\[4pt] 4x-\alpha, & \text{if } x>2, \end{cases} \] is continuous at \(x=2\), then the value of \(\alpha\) is equal to: 

Let the functions \(f\) and \(g\) be defined by \(f(x)=3\sin x,\; -\frac{\pi}{2}\le x\le \frac{\pi}{2}\) and \(g(x)=6-3x^2,\; x\in\mathbb{R}\). Then \(f^{-1}(g(x))=\)