List of top Mathematics Questions

The point of inflexion of a function \( f(x) \) is the point where: {5pt}
Let \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] be a square matrix such that \[ \text{adj } A = A. \] Then, \( (a + b + c + d) \) is equal to:
A function \( f : \mathbb{R} \to A \) defined as \( f(x) = x^2 + 1 \) is onto, if \( A \) is: {5pt}
For any square matrix \( A \), \( (A - A') \) is always: {5pt}
If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} \] then \( A^{-1} \) is:

Of the following, which group of constraints represents the feasible region given below?
 

The derivative of \( 5^x \) w.r.t. \( e^x \) is: {5pt}

If \[ \begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \] has a determinant of \( \pm 6 \), then the value of \( k \) is:
It is given that function \( f(x) = x^4 - 62x^2 + ax + 9 \) attains a local maximum value at \( x = 1 \). Find the value of \( a \), hence obtain all other points where the given function \( f(x) \) attains local maximum or local minimum values.
Find: \[ \int \frac{2 + \sin 2x}{1 + \cos 2x} e^x \, dx \]
Find the position vector of point \( C \) which divides the line segment joining points \( A \) and \( B \) having position vectors \( \hat{i} + 2\hat{j} - \hat{k} \) and \( -\hat{i} + \hat{j} + \hat{k} \), respectively, in the ratio 4:1 externally. Further, find \( | \overrightarrow{AB} | : | \overrightarrow{BC} | \).
If \( x \cos(p + y) + \cos p \sin(p + y) = 0 \), prove that \( \cos p \frac{dy}{dx} = -\cos^2(p + y) \), where \( p \) is a constant.
Evaluate: \[ \int_{0}^{\pi/4} \frac{1}{\sin x + \cos x} \, dx \]
Assertion (A): Projection of \( \vec{a} \) on \( \vec{b} \) is the same as the projection of \( \vec{b} \) on \( \vec{a} \).
Reason (R): The angle between \( \vec{a} \) and \( \vec{b} \) is the same as the angle between \( \vec{b} \) and \( \vec{a} \) numerically.
Let \( E \) and \( F \) be two events such that \( P(E) = 0.1, P(F) = 0.3, P(E \cup F) = 0.4 \). Then \( P(F \,|\, E) \) is:
Evaluate: \[ \int_{0}^{\pi/2} \sin 2x \cos 3x \, dx \]
If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - 2\hat{j} + \hat{k} \), then \( \vec{a} \) and \( \vec{b} \) are:
\( x \log x \frac{dy}{dx} + y = 2 \log x \) is an example of a:
If \( \alpha, \beta \), and \( \gamma \) are the angles which a line makes with the positive directions of \( x, y, z \) axes respectively, then which of the following is not true?
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:
If a line makes an angle of \( \frac{\pi}{4} \) with the positive directions of both \( x \)-axis and \( z \)-axis, then the angle which it makes with the positive direction of \( y \)-axis is:
A function \( f(x) = |1 - x + |x|| \) is:
If \( |a| = 2 \) and \( -3 \leq k \leq 2 \), then \( |a| |k| \in: \)
Given \[ \frac{d}{dx} F(x) = \frac{1}{\sqrt{2x - x^2}} \] and \( F(1) = 0 \), find \( F(x) \).
Let \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] be a square matrix such that \[ \text{adj } A = A. \] Then, \( (a + b + c + d) \) is equal to: