List of top Mathematics Questions

The image of a point \( P(3,5,3) \) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is \( P'(a,b,c) \). Then \( a+b+c = \)
How many natural numbers are there between 100 and 1000 such that at least one of their digits is 6?
The function \( y=\frac{\log x}{x^3} \) is strictly increasing function for
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
If \( P = \{5m : m \in N\} \) and \( Q = \{5^m : m \in N\} \), where \( N \) is set of natural numbers, then
If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \vec{a}\cdot\vec{b} = |\vec{a}\times\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is
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?
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
The relation \( R = \{(1,1),(2,2),(3,3)\ \) on the set \( \{1,2,3\} \) is}
\( \int_{-2}^{2} \frac{|x-3|}{x-3} dx = \)
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 \( x = a\left\{ \cos t + \frac{1}{2}\log\!\left(\tan^2\frac{t}{2}\right) \right\} \) and \( y = a\sin t \), then \( \frac{dy}{dx} = \) __________.
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
Find the function \( f \) which satisfies the equation \( \frac{df}{dx} = 2f \), given that \( f(0) = e^3 \)
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 solutions of \( \frac{dy}{dx} = \frac{y+1}{x-1} \), when \( y(1) = 2 \) is:
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 -----------
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:
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
The solution of the differential equation: \( x\cos y\,dy = (xe^x\log x + e^x)dx \) is
Area of the region bounded by the curve \( y = \cos x \) between \( x = -\frac{\pi}{2} \) and \( x = \pi \) is ----------------
\( \int \left(e^{x\log_e 6}\right)e^x dx = \phi(x) + c \) then \( \phi(x) = \)
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 __________.