List of top Mathematics Questions

The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is

\[ \lim_{x \to \infty} \frac{1 - \tan\left(\frac{x}{2}\right)}{1 + \tan\left(\frac{x}{2}\right)} = ? \]

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .

The value of $\tan 10^{\circ}\, \tan 20^{\circ} \, \tan 30^{\circ} \, \tan 40^{\circ} \, \tan 50^{\circ}\, \tan 60^{\circ} \tan 70^{\circ} \, \tan 80^{\circ} =$

The value of the determinant \[ \begin{vmatrix} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 191 & 198 & 181 \end{vmatrix} \] is:

\[ \lim_{x \to \infty} \frac{1 - \tan\left(\frac{x}{2}\right)}{1 + \tan\left(\frac{x}{2}\right)} = ? \]

Let \( A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix} \) and \( (A + I)^5 - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). Find \( abc + abd + bcd + acd \):

Prabhat wants to invest the total amount of ₹15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹2,000 in saving certificates and ₹2,500 in national saving bonds. The interest rate is 8% on saving certificates and 10% on national saving bonds per annum. He invests \( x \) in saving certificate and \( y \) in national saving bonds. Then the objective function for this problem is:

In a triangle ABC, if \( A = a \), \( B = 60^\circ \), and \( C = 75^\circ \), then \( b \) equals:

If the line \( x \cos \alpha + y \sin \alpha = p \) represents the common chord of the circles \( x^2 + y^2 = a^2 \) and \( x^2 + y^2 + b^2 = 2b \), where \( a > b \), where A and B lie on the first circle and P and Q lie on the second circle, then \( AP \) is equal to:

For the function \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} - x^2 + x + 1, \] \( f'(1) = mf'(0) \), where \( m \) is equal to:

Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is:

Find the coordinates of the point where the line joining the points \( (2, -3, 1) \) and \( (3, -4, -5) \) cuts the plane \( 2x + y + z = 7 \):

If \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), then the correct statement is:

What is the value of \( n \) so that the angle between the lines having direction ratios \( (1, 1, 1) \) and \( (1, 1, n) \) is \( 60^\circ \)?

The foot of the perpendicular from the point \( (7, 14, 5) \) to the plane \( 2x + 4y - z = 7 \) is:

A boy is throwing stones at a target. The probability of hitting the target at any trial is \( \frac{1}{2} \). The probability of hitting the target 5th time at the 10th throw is:

The differential equation whose solution is \( Ax^2 + Bx + C = 1 \) where A and B are arbitrary constants is of:

Evaluate: \[ \int_0^{\pi/2} \frac{x}{\sqrt{4 - x^2}} \, dx \]

The unit vector perpendicular to the vectors \( 6i + 2j + 3k \) and \( 3i - 6j - 2k \) is:

The area bounded by the curve \( y = \sin x \), x-axis and the ordinates \( x = 0 \) and \( x = \pi/2 \) is:

If the normal to the curve \( y = f(x) \) at the point \( (3, 4) \) makes an angle \( 3\pi/4 \) with the positive x-axis, then \( f'(3) \) is:

The diagonal of a square is changing at the rate of \( 0.5 \, \text{cm/sec} \). Then the rate of change of area, when the area is 400 \( \text{cm}^2 \), is equal to: