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List of top Mathematics Questions

If $ \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} $, then $ \tan^2 \left( \frac{\theta}{2} \right) $ is equal to:

If $ x_1, i=2, 3, \ldots, n $ are $ n $ observations such that $ \sum_{i=1}^{n} x_i^2 = 550 $, mean $ \bar{x} = 5 $ and variance is zero, then the number of observations is equal to:

If the points (1, 2), (-1, k) and (2, 3) are collinear, then the value of k is

The minimum value of $ f(x) = 7x^4 + 28x^3 + 31 $ is:

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If $\frac{2}{\sqrt{x}} = 2$ and $\frac{4}{\sqrt{y}} = -1$, then

Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]

A circle passing through the points $ (1, 1) $ and $ (2, 0) $ touches the line $ 3x - y - 1 = 0 $. If the equation of this circle is $ x^2 + y^2 + 2gx + 2fy + c = 0 $, then a possible value of $ g $ is

The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets at least 3 gold coins is

The approximate value of $ \sqrt[3]{730} $ obtained by the application of derivatives is:

The general solution of $ 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 $ is:

If 1000! = 3ⁿ× m, where m is an integer not divisible by 3, then n =?

If $ f(x) = \int_0^{x^3} (t + 4)^2 \, dt $, then $ f'(2) $ is equal to:

A line makes angles $ \alpha, \beta, \gamma $ with $ x, y $, and $ z $-axes respectively. Then the value of $ \sin^2\alpha + \sin^2\beta - \cos^2\gamma $ is:

The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:

If $ A = \begin{pmatrix} x & y & y \\ y & x & y \\ y & y & x \end{pmatrix} $ and $ 5A^{-1} = \begin{pmatrix} -3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3 \end{pmatrix} $, then $ A^2 - 4A $ is:

If $ (\alpha, \beta, \gamma) $ are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then $ (\alpha + \beta + \gamma)^2 $ is:

If $ f $ is a real valued function from $ A $ onto $ B $ defined by $ f(x) = \frac{1}{\sqrt{|x| - |x|}} $, then $ A \cap B $ is:}

Numerically greatest term in the expansion of $ (5 + 3x)^6 $, when $ x = 1 $, is:

If A and B are arbitrary constants, then the differential equation having \[ y = Ae^{-x} + B \cos x \] as its general solution is:

If $ \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x $, where $ 0<x<\frac{\pi}{2} $, then the value of $ x $ is:

The solution set of the equation $\cos^2(2x) + \sin^2(3x) = 1$ is \;?

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and second throws and a number less than $4$ in the third throw?

If $ (1,1), (-2,2), (2,-2) $ are 3 points on a circle $ S $, then the perpendicular distance from the center of the circle $ S $ to the line $ 3x - 4y + 1 = 0 $ is:

Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is: