List of top Mathematics Questions

If the vectors \( i + j + k \), \( i - j + k \) and \( 2i + 3j + mk \) are coplanar, then \( m = \)

Evaluate: \[ \cos x \cos 7x - \cos 5x \cos 13x \]

If two angles of \( \triangle ABC \) are \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \), then the ratio of the smallest and greatest side is

The value of $\cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)$ is

If \[ f(x) = \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{\frac{1}{x}} \quad \text{if} \quad x \neq 0 \] \[ f(x) = k \quad \text{if} \quad x = 0 \] is continuous at \( x = 0 \), then \( k = \)

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

If \(3\cos x \ne 2\sin x\), then the general solution of \[ \sin^2 x-\cos 2x=2-\sin 2x \] is

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{5} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{8} \right) \] is

If \( f(x) = \begin{cases \dfrac{81^x - 9^x}{k^x - 1}, & x \neq 0
2, & x = 0 \end{cases} \) is continuous at \( x = 0 \), then the value of \( k \) is}

If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is

ABCD is a parallelogram. \(P\) is the midpoint of \(AB\). If \(R\) is the point of intersection of \(AC\) and \(DP\), then \(R\) divides \(AC\) internally in the ratio

The length of the latus rectum of the parabola \( x^2 + 2y = 8x - 7 \) is

If \( A \) and \( B \) are independent events and \( P(A) = \frac{2{3} \), \( P(B) = \frac{3}{5} \), then \( P(A' \cap B) = \)}

If the p.m.f. of a random variable \( X \) is given by \[ P(X = x) = \frac{5}{25} \quad \text{if} \quad x = 0, 1, 2, 3, 4, 5 \] then which of the following is not true?

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

The line through the points \( (1, 4), (-5, 1) \) intersects the line \( 4x + 3y - 5 = 0 \) in the point

If the planes \[ 2x - 5y + z = 8 \quad \text{and} \quad 2 \lambda x - 15y + 2z + 6 = 0 \] are parallel to each other, then the value of \( \lambda \) is

The differential equation whose solution is \( y = c_1 \cos ax + c_2 \sin ax \) (where \( c_1 \) and \( c_2 \) are arbitrary constants) is

If \[ y = \tan^{-1}(\sec x + \tan x), \quad \text{then} \quad \frac{dy}{dx} = \]

Evaluate \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\tan x}{\tan x + \cot x} \, dx \]

If \[ \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{9 + 16 \sin 2x} \, dx = k \log 3, \text{ then } k = \]

The joint equation of a pair of lines passing through \((2,3)\) and parallel to the lines \[ x^2 - y^2 = 0 \] is

The approximate value of the function \( f(x) = x^3 + 5x^2 - 7x + 10 \) at \( x = 1 \) is