List of top Mathematics Questions

Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is

Let $f(x)$ and $g(x)$ be two differentiable functions such that $f'(x)=g(x)$ and $g'(x)=-f(x)$. Let $h(x)=(f(x))^2+(g(x))^2$ and $h(3)=100$. Then $h(100)$ is equal to

The value of $\lim_{x \to 0} \dfrac{\sqrt{1 - \cos(x^2)}}{1 - \cos x}$ is equal to:

If $(3 + 5x)e^{\frac{y}{x}} = x$, then $\dfrac{dy}{dx}$ is equal to:

Which one of the following is not true?

The domain of the function $f(x) = \dfrac{\log_2 (x - 5)}{x^2 + 3x - 4}$ is:

The perpendicular drawn from the origin to the straight line $\sqrt{3}x + y - 24 = 0$ makes an angle $\alpha$ with the positive direction of x-axis. Then $\alpha$ is equal to:

The variance for the data: $65, 70, 75$ is

If the function $f(x)=\begin{cases}\dfrac{2x^2+3x-5}{x-1}, & x \ne 1 \\ k, & x=1\end{cases}$ is continuous at $x=1$, then the value of $k$ is:

Let $A, B, C$ be all the three possible mutually exclusive events of a random experiment. Which one of the following is not permissible in terms of their probabilities?

The value of $\lim_{x \to 1} \dfrac{x - 1}{3\sqrt{x} - 1}$ is equal to:

The value of $\lim_{x \to 0} \dfrac{\sin^2 x}{1 - \cos x}$ is equal to:

The shortest distance between the lines $\vec{r} = -\hat{i} + t\hat{k}, \; t \in \mathbb{R}$ and $\vec{r} = -\hat{j} + s\hat{i}, \; s \in \mathbb{R}$ is:

A fair die is rolled once. Which one of the following is not true?

The mean deviation about the mean for the data: $5, 6, 14, 15$ is

If $|\vec{a}| = \sqrt{26}, \; |\vec{b}| = \sqrt{3}$ and $\vec{a} \times \vec{b} = 5\hat{i} + \hat{j} - 4\hat{k}$, then $\vec{a} \cdot \vec{b} =$:

Consider the straight line $\vec{r} = (5\hat{i} + 2\hat{j} - 3\hat{k}) + t(4\hat{i} + 6\hat{j} - 7\hat{k}), \; t \in \mathbb{R}$. Which one of the following points is a point on the straight line?

A straight line passes through the point whose position vector is $\hat{k}$. The straight line also passes through the point of intersection of the lines $\vec{r} = \hat{j} + \lambda \hat{i}, \lambda \in \mathbb{R}$ and $\vec{r} = \hat{i} + s\hat{j}, s \in \mathbb{R}$. Then the equation of the straight line is:

The equation of a line passing through $(-1,2,-4)$ and parallel to the straight line $\dfrac{-x-1}{4} = \dfrac{2y+1}{-1} = \dfrac{-z+4}{3}$, is:

Let $\vec{a} = 2\hat{i} - 2\hat{j} + 4\hat{k}$, $\vec{b} = -5\hat{i} - \hat{j} + 8\hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j} - \lambda \hat{k}$. If $\vec{a} + \vec{b} + \vec{c}$ and $\vec{a} - \vec{b} + \vec{c}$ are perpendicular, then the values of $\lambda$ are:

Let $O$ be the origin. Let $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$ be the position vectors of the points $A$ and $B$ respectively. A point $P$ divides the line segment $AB$ internally in the ratio $m:n$. Then $\overrightarrow{AP}$ is equal to:

If $2\hat{i} - \hat{j} + \hat{k} = s(3\hat{i} - 4\hat{j} - 4\hat{k}) + t(\hat{i} - 3\hat{j} - 5\hat{k})$, where $s$ and $t$ are scalars, then $3s + 5t$ is equal to:

Let $R(-2,-2)$ be a point and let $\dfrac{(x-3)^2}{25} + \dfrac{(y+2)^2}{16} = 1$ be an ellipse. If $S$ and $T$ are the foci of the ellipse, then $RS + RT$ is equal to:

The equation of the latus rectum of the parabola $y^2 + 8x + 4y + 12 = 0$ is

If the one end of a diameter of the circle $x^2 + y^2 + 3x + y - 6 = 0$ is at $(-4,-2)$, then the other end of the diameter is at