List of top Mathematics Questions

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

The solution set of the inequalities $4x+3y\le60$, $y\ge2x$, $x\ge3$, $x, y\ge0$ is represented by region

General solution of the differential equation $\cos x(1+\cos y)dx-\sin y(1+\sin x)dy=0$ is

The statement $[(p\rightarrow q)\wedge\sim q]\rightarrow r$ is tautology, when $r$ is equivalent to

If the line \( x - 2y = m \, (m \in \mathbb{Z}) \) intersects the circle \( x^{2} + y^{2} = 2x + 4y \) at two distinct points, then the number of possible values of \( m \) are

The negation of the statement "The number is an odd number if and only if it is divisible by 3."

Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \( \frac{4}{5} \), then the probability that he is unable to solve less than two problems is

In how many ways, can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student?

A perpendicular is drawn from the point \( P(2,4,-1) \) to the line \( \frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9} \). The equation of the perpendicular from \( P \) to the given line is

If \( \cos^2 A + \cos^2 C = \sin^2 B \), then \( \triangle ABC \) is

One mapping (function) is selected at random from all the mappings of the set \( A = \{1,2,3,\dots,n\} \) into itself. The probability that the mapping selected is one-one, is

If \( \begin{vmatrix} x+y+2z & x & y z & y+z+2x & y z & x & z+x+2y \end{vmatrix} = k(x+y+z)^3 \), then the value of \( k \) is

The minimum value of \( \frac{x}{\log x} \) is

\( \lim_{x \to 0} \left(1^{\csc^2 x} + 2^{\csc^2 x} + \cdots + n^{\csc^2 x}\right)\sin^2 x \) is equal to

The equations of the lines passing through the point \( (1,0) \) and at a distance \( \frac{\sqrt{3}}{2} \) from the origin are

The equation of the plane through the intersection of the planes \( 3x - y + 2z - 4 = 0 \) and \( x + y + z - 2 = 0 \) and the point \( (2,2,1) \) is

\( \int_{0}^{\pi/2} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \) is equal to

The area of the region bounded by $1 - y^2 = |x|$ and $|x| + |y| = 1$ is

The equation of circle which passes through the origin and cuts off intercepts 5 and 6 from the positive parts of the axes respectively, is \( \left(x - \frac{5}{2}\right)^2 + (y - 3)^2 = \lambda \), where \( \lambda \) is

If \( x\sin(a+y) + \sin a \cos(a+y)=0 \), then \( \frac{dy}{dx} \) is equal to

The function \( f(x) = [x]\cos\left( \frac{2x-1}{2}\pi \right) \), where \( [\,\cdot\,] \) denotes the greatest integer function, is discontinuous at

What are the values of \( c \) for which Rolle’s theorem for the function \( f(x) = x^3 - 3x^2 + 2x \) in the interval \( [0,2] \) is verified?

The approximate value of $f(5.001)$, where $f(x)=x^3 - 7x^2 + 15$, is

The function \( f(x) = (x^2 - 1)|x^2 - 3x + 2| + \cos|x| \) is non-differentiable at