List of top Mathematics Questions

If the area under the curve \( y=\sqrt{a^2-x^2} \) included between the lines \( x=0 \) and \( x=a \) is 4 sq units. Then the value of \( a \) is
Two finite sets have \( m \) and \( n \) elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of \( m-n \)
If the length of the diagonal of a square is increasing at the rate of \( 0.1 \) cm/secWhat is the rate of increase of its area when the side is \( \frac{15}{\sqrt{2}} \) cm?
The relation \( R = \{(1,1),(2,2),(3,3)\ \) on the set \( \{1,2,3\} \) is}
If \( x = a\left\{ \cos t + \frac{1}{2}\log\!\left(\tan^2\frac{t}{2}\right) \right\} \) and \( y = a\sin t \), then \( \frac{dy}{dx} = \) __________.
Given that \( n \) number of arithmetic means are inserted between two pairs of numbers \( a,2b \) and \( 2a,b \); where \( a,b \in R \). If the \( m^{th} \) means in the two cases are the same, then the ratio \( a:b \) is equal to
\( \int_{-2}^{2} \frac{|x-3|}{x-3} dx = \)
The number of solutions of \( \frac{dy}{dx} = \frac{y+1}{x-1} \), when \( y(1) = 2 \) is:
Find the function \( f \) which satisfies the equation \( \frac{df}{dx} = 2f \), given that \( f(0) = e^3 \)
Evaluate: \( \lim_{x \to 0} \frac{\sqrt[3]{1+x} - \sqrt[3]{1-x}}{x} \)
In a game, a man wins \( ₹1000 \) if he gets an even number greater than or equal to 4 on a fair dice and loses \( ₹200 \) for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in \( ₹ \) is -----------
A geometric progression consists of an even number of termsIf the sum of all the terms is five times the sum of the terms occupying the odd places, then the common ratio of the geometric progression is
The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is
If \( \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^3}{x^2 - k^2} \), then the value of \( k \) is:
Area of the region bounded by the curve \( y = \cos x \) between \( x = -\frac{\pi}{2} \) and \( x = \pi \) is ----------------
If a quadratic function in \( x \) has the value 19 when \( x = 1 \) and has a maximum value 20 when \( x = 2 \), then the function is
\( \int \left(e^{x\log_e 6}\right)e^x dx = \phi(x) + c \) then \( \phi(x) = \)
The solution of the differential equation: \( x\cos y\,dy = (xe^x\log x + e^x)dx \) is
If \( A \) and \( B \) are two events such that \( P(A) = 0.3, P(B) = 0.4, P(A \cap \bar{B}) = 0.5 \), then find the value of \( P(B \cap \bar{A}) \)
If the function \( f(x) = \mu \sin x + \frac{1}{3} \sin 3x \) has its derivative equal to zero at \( x = \frac{\pi}{3} \), then the value of \( \mu \) is __________.
The relationship between \( a \) and \( b \) for the continuity of the function \( f(x) = \begin{cases} ax + 1, & x \leq 3 \\ bx + 3, & x \gt 3 \end{cases} \) at \( x = 3 \) is __________.
If \( z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5 \), then
\( \sin^{-1}(x - 1) + \cos^{-1}(x - 3) + \tan^{-1}\!\left(\frac{x}{2 - x^2}\right) = \cos^{-1} k + \pi \), then the value of \( k \) is __________.
A man is moving away from a tower 41.6 m high at a rate of 2 m/sIf the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance 30 m from the foot of the tower is:
Given that \( z \) is a real number and \( z = \frac{\lambda + 4i}{1+\lambda i} \) where \( \lambda \in R \), then the possible value of \( \lambda \) is: