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List of top Mathematics Questions

A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

n^th term of the series
$1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+...$ is

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Let $f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)$ and $S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}$. If $4\beta \sum_{\theta∈S}\theta$, then $f(\beta)$ is equal to

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse $x^2 + 4y^2 = 36$ is r, then $12r^2$ is equal to

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

The domain of $f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}$, $x∈R$ is

Let $ \mathbf{A} = 2\hat{i} + \hat{j} - 2\hat{k} $ and $ \mathbf{B} = \hat{i} + \hat{j} $. If $ \mathbf{C} $ is a vector such that $ |\mathbf{C} - \mathbf{A}| = 3 $ and the angle between $ \mathbf{A} \times \mathbf{B} $ and $ \mathbf{C} $ is $ 30^\circ $, then $ [(\mathbf{A} \times \mathbf{B}) \times \mathbf{C}] = 3 $, the value of $ \mathbf{A} \cdot \mathbf{C} $ is equal to:

If $ \mathbf{a} $ and $ \mathbf{b} $ are unit vectors such that $ 2\mathbf{a} + \mathbf{b} = 3 $, then which of the following statement is true?

The perimeter of a triangle $ \triangle ABC $ is 6 times the arithmetic mean of the sines of its angles. If the side $ a $ is 1, then the angle $ A $ is:

If \[ \prod_{i=1}^{n} \tan (\alpha_i) = 1 \forall \alpha_i \in \left[0, \frac{\pi}{2}\right] \text{where} i = 1, 2, 3, \dots, n. \] Then the maximum value of \[ \prod_{i=1}^{n} \sin (\alpha_i) \] is

The range of values of $ \theta $ in the interval $ \left( 0, \pi \right) $ such that the points $ (3, 2) $ and $ (\cos \theta, \sin \theta) $ lie on the same sides of the line $ x + y - 1 = 0 $, is:

The negation of $ \sim S \vee ( \sim R \wedge S) $ $\text{ is equivalent to}$

The locus of the mid-point of all chords of the parabola $ y^2 = 4x $ which are drawn through its vertex is:

For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are

Let $ a, b, c, d $ be non-zero numbers. If the point of intersection of the lines \[ 4ax + 2ay + c = 0 \text{and} 5bx + 2by + d = 0 \] lies in the fourth quadrant and is equidistant from the two, then the relation between $ a, b, c, d $ is

If \[ \int x \sin x \sec^3 x \, dx = \frac{1}{2} \left[ f(x) \sec^2 x + g(x) \left( \frac{\tan x}{x} \right) \right] + c, \] $\text{then which of the following is true?}$

Which of the following numbers is the coefficient of $ x^{100} $ in the expansion of \[ \log_e \left( \frac{1 + x}{1 + x^2} \right), \text{where} |x| < 1? \]

Between any two real roots of the equation $ e^x \sin x = 1 $, the equation $ e^x \cos x = -1 $ has:

The equation of the tangent at any point of the curve \[ x = a \cos 2t, \, y = 2 \sqrt{2a} \sin t \, \text{with} \, m \, \text{as its slope is} \]

Bag I contains 3 red, 4 black, and 3 white balls and Bag II contains 2 red, 5 black, and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball drawn is found to be black in colour. Then the probability that the transferred ball is red, is:

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is