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List of top Mathematics Questions

In $ \triangle ABC $, if $ (a+c)^2 = b^2 + 3ca $, then $ \frac{a+c}{2R} $ is:

The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is:

If \[ y = \tan^{-1} \left( \frac{2 - 3\sin x}{3 - 2\sin x} \right), \] then find $ \frac{dy}{dx} $.

The equations of the perpendicular bisectors of the sides AB and AC of $ \triangle ABC $ are $ x - y + 5 = 0 $ and $ x + 2y = 0 $ respectively. If the coordinates of $ A $ are $ (1, -2) $, then the equation of the line BC is:

If $ x_1, x_2, x_3, \dots, x_n $ are $ n $ observations such that $ \sum (x_i + 2)^2 = 28n $ and $ \sum (x_i - 2)^2 = 12n $, then the variance is:

Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots \text{ up to 50 terms=} \]

If $ A(1,0,2) $, $ B(2,1,0) $, $ C(2,-5,3) $, and $ D(0,3,2) $ are four points and the point of intersection of the lines $ AB $ and $ CD $ is $ P(a,b,c) $, then $ a + b + c = ? $

If $\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c$, then $h(x) [f(x) + f(\frac{1}{x})] =$

The triangle $ PQR $ is inscribed in the circle \[ x^2 + y^2 = 25. \] If $ Q = (3,4) $ and $ R = (-4,3) $, then $ \angle QPR $ is:

If $ A(1,2,0), B(2,0,1), C(-3,0,2) $ are the vertices of $ \triangle ABC $, then the length of the internal bisector of $ \angle BAC $ is:

If $ z_1 = 10 + 6i $, $ z_2 = 4 + 6i $ and $ z $ is any complex number such that the argument of $ \frac{z-z_1}{z-z_2} $ is $ \frac{\pi}{4} $, then the value of $ |z - 7 - 9i| $ is:

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:

The sum of the series $ 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty $ is:

The circumference of a circle passing through the point $ (4, 6) $ with two normals represented by $ 2x - 3y + 4 = 0 $ and $ x + y - 3 = 0 $ is:

If $ z = x+iy $, $ x^2+y^2 = 1 $ and $ z_1 = e^{i\theta} $, then the expression $ \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} $ simplifies to:

If $2.4^{2n+1} + 3^{3n+1}$ is divisible by $k$ for all $n \in \mathbb{N}$, then $k$ is:

If $(\alpha + \beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin(\alpha - \beta) = 5 \cos(\alpha + \beta)$, then \[ \tan\left(\frac{\pi}{4} + \alpha\right) + 4\tan\left(\frac{\pi}{4} + \beta\right) = \]

If $[x]$ is the greatest integer function, then evaluate the integral $ \int_{0}^{5} [x] \, dx $:

If $ L_1 $ and $ L_2 $ are two lines which pass through origin and have direction ratios $ (3, 1, -5) $ and $ (2, 3, -1) $ respectively, then the equation of the plane containing $ L_1 $ and $ L_2 $ is:

The largest among the distances from the point $P(15,9)$ to the points on the circle $x^2 + y^2 - 6x - 8y - 11 = 0$ is:

If $ \vec{f} = i + j + k $ and $ \vec{g} = 2i - j + 3k $, then the projection vector of $ \vec{f} $ on $ \vec{g} $ is:

Let $ \mathbf{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} $, $ \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} $. The projection of the sum of the vectors $ \mathbf{a}, \mathbf{b} $ on the vector perpendicular to the plane of $ \mathbf{a}, \mathbf{b} $ is:

The length of the latus rectum of $ 16x^2 + 25y^2 = 400 $ is:

If a function $f(x)$ is defined as: $$ f(x) = \begin{cases} \frac{\tan(4x) + \tan 2x}{x} & \text{if } x> 0 \\ \beta & \text{if } x = 0 \\ \frac{\sin 3x - \tan 3x}{x^2} & \text{if } x < 0 \end{cases} $$ and is continuous at $x = 0$, then find $|\alpha| + |\beta|$.

If the coefficients of the $ (2r + 6)^{th $ and $ (r - 1)^{th} $ terms in the expansion of $ (1 + x)^{21} $ are equal, then the value of $ r $ is:}