List of top Mathematics Questions

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 \[ \int f(x) \, dx = g(x), \text{ then } \int x^5 f(x^3) \, dx \] 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 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
The integrating factor of the linear DE \(\dfrac{dy}{dx}-y\sin x=\cot x\) is
\([\,{-}1\,]\,[\,1\ \ {-}1\,]=\ \ ?\)
\(\begin{bmatrix}2&3 \\ 5&7\end{bmatrix}\!\begin{bmatrix}2 \\ 5\end{bmatrix}=\ \ ?\)
\(\begin{bmatrix}13&15 \\ -1&4\end{bmatrix}\begin{bmatrix}2&0 \\ 0&2\end{bmatrix}=\ \ ?\)