List of top Mathematics Questions

The value of \( \frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} \) is:

If \( \alpha, \beta \) are the roots of \( 2x^2 - 4x + 5 = 0 \), then \( (\alpha + 1)(\beta + 1) = \):

The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) represents the following:

If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then \( (a + \beta)^2 \) equals:

Let the mean and variance of the observations \( 2, 3, 3, 4, 5, 7, a, b \) be 4 and 2, respectively. Then, the mean deviation about the mode of the observation is:

Find: \( \int \frac{5x}{(x + 1)(x^2 + 9)} dx \).

f and g are continuous functions on interval \( [0, a] \). Given that \( f(a - x) = f(x) \) and \( g(x) + g(a - x) = a \), show that \( \int_{0}^{a} f(x) g(x) dx = \frac{a}{2} \int_{0}^{a} f(x) dx \).

Evaluate: \( \int_{0}^{\pi} \frac{\sin 2px}{\sin x} dx \), \( p \in N \).

Prove that \( f : N \rightarrow N \) defined as \( f(x) = ax + b \) (\( a, b \in N \)) is one-one but not onto.

The feasible region along with corner points for a linear programming problem are shown in the graph. Write all the constraints for the given linear programming problem.

If \( \vec{PQ} \times \vec{PR} = 4 \hat{i} + 8 \hat{j} - 8 \hat{k} \), then the area \( (\triangle PQR) \) is

In the following probability distribution, the value of p is:

The integral \( \int \frac{dx}{\sin^2 x \cos^2 x} \) is equal to

The principal value of \( \sin^{-1} \left( \cos \frac{43\pi}{5} \right) \) is

The values of \(x\) for which the angle between the vectors \( \vec{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k} \) and \( \vec{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k} \) is obtuse, is: