List of top Mathematics Questions

Let \[ f(x) = \frac{x^2 - 1}{|x| - 1}. \] \(\text{Then the value of}\) \[ \lim_{x \to 1} f(x) \text{ is:} \]

If \( \theta = \cos^{-1} \left( \frac{3}{\sqrt{20}} \right) \) is the angle between \( \mathbf{a} = \hat{i} - 2x\hat{j} + 2y\hat{k} \) and \( \mathbf{b} = x\hat{i} + \hat{j} + y\hat{k} \), then the possible values at \( (x, y) \) that lie on the locus are:
If \( f(x) \) is a polynomial of degree 4, \( f(n) = n + 1 \) and \( f(0) = 25 \), then find \( f(5) \)?

If the equation \[ |x^2 - 6x + 8| = a \] \(\text{has four real solutions, then find the value of \( a \):}\)
 

A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely to contradict each other while narrating some incident?
If \[ \int f(x) \, dx = g(x), \text{ then } \int x^5 f(x^3) \, dx \] is

If \( n_1 \) and \( n_2 \) are the number of real valued solutions of \( x = |\sin^{-1} x| \) \(\text{and}\) \( x = \sin(x) \text{ respectively, then the value of} \, n_2 - n_1 \text{ is:}\)

If A and B are square matrices such that \( B = -A^{-1}BA \), \(\text{ then }\) \( (A + B)^2 \) is

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2, and 6, then the mean deviation from the mean of the data is:

A real valued function \( f \) is defined as \[ f(x) = \begin{cases} -1 & \text{if} \, -2 \leq x \leq 0 \\ x - 1 & \text{if} \, 0 \leq x \leq 2 \end{cases} \] \(\text{Which of the following statements is FALSE?}\)

If \[ \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^2}{x^2 - k^2}, \text{ then find } k \]

The maximum value of \( f(x) = (x - 1)^2 (x + 1)^3 \) is equal to \[ \frac{2^p 3^q}{3125} \,\, \text{then the ordered pair of} (p, q) \text{ will be} \]

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is
A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. The tip of the pillar subtends angles \( \tan^{-1}(3) \) and \( \tan^{-1}(2) \) at A and B respectively. Which of the following choices represents the height of the pillar?
If the direction ratios of two parallel lines are \(a_1, b_1, c_1\) and \(a_2, b_2, c_2\) then \(\dfrac{a_1 c_2}{a_2}=\) ?
If the direction ratios of two parallel lines are \(x,\,5,\,3\) and \(20,\,10,\,6\) then the value of \(x\) is:
\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?
\([\,2a-7\ \ \ 1\,]=[\,a\ \ \ b-1\,]\Rightarrow (a,b)=\ ?\)
Evaluate \(\begin{vmatrix}1&1&5 \\ 4&9&17 \\ 5&10&22\end{vmatrix}\).

Evaluate \(\begin{vmatrix}1&2&-1 \\ 5&4&1 \\ 7&6&1\end{vmatrix}\).

Evaluate \(\begin{vmatrix}-\sin\theta&\cos\theta \\ \sec\theta&\csc\theta\end{vmatrix}\).

Compute \(\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\begin{bmatrix}2&-3 \\ 0&4\end{bmatrix}=\) ?
Compute \([\,6\ \ 5\,]\begin{bmatrix}1 \\ -1\end{bmatrix}=\) ?
\(\dfrac{d}{dx}\big(2\cos \tfrac{3x}{4}\big)=\) ?
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?