List of top Mathematics Questions

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

If \[ \int f(x) \, dx = g(x), \text{ then } \int x^5 f(x^3) \, dx \] is
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 \[ \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^2}{x^2 - k^2}, \text{ then find } k \]

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

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 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 \([\,6\ \ 5\,]\begin{bmatrix}1 \\ -1\end{bmatrix}=\) ?
\(\dfrac{d}{dx}\big(2\cos \tfrac{3x}{4}\big)=\) ?
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?
\(\dfrac{d}{dx}\left(11^x\right)=\) ?
\(\dfrac{d}{dx}\left(\dfrac{1}{3x-2}\right)=\) ?
If \(x=a\cos^2\theta,\ y=b\sin^2\theta\), then the value of \(\dfrac{dy}{dx}\) is
The solution of the differential equation \(x^2\,dx+y^2\,dy=0\) is
Evaluate \((\vec j-2\vec i)\cdot(\vec k+3\vec i-\vec j)\).
Solve \(e^{3x}\,dx+e^{4y}\,dy=0\).
The solution of \(\dfrac{dx}{x}+\dfrac{dy}{y}=0\) is