List of top Mathematics Questions

Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)

If \( y = \sin^{-1}(3x - 4x^3) \), find \( \dfrac{dy}{dx}. \)

What is the order of the differential equation \( \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^3 = 0 \)?

Find the slope of the normal to the curve \(y = 2x^2 + 3\sin x\) at \(x = 0\).

Evaluate \( \int \log x \, dx \).

If the line \( 2x - 3y + c = 0 \) passes through the focus of the parabola \( x^2 = -8y \), then the value of \( c \) is equal to:

A straight line passing through (6,1,3) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at Q. If the lines are perpendicular to each other, then the coordinates of Q are:

The three vertices of a triangle are \( (0,0), (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is:

Let \( U \) be the universal set and let \( A \) and \( B \) be any two subsets of \( U \). If \( n(U) = 25, n(A) = 14, n(A \cap B) = 6 \) and \( n(A \cup B) = 20 \), then \( n(B') \) is equal to:

Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:

The 25th term of 9, 3, 1, \( \frac{1}{3} \), \( \frac{1}{9} \), ... is:

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

Evaluate the integral: \( \displaystyle \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \) (where \(C\) is a constant of integration).

A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.

Evaluate the definite integral: \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x}\, dx \).

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is \(r\), volume of air inside the jar is

Find the value of \(k\) if the function \(f(x)=\dfrac{k\sin x}{x}\) for \(x\neq0\) and \(f(0)=3\) is continuous at \(x=0\).

The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.

If the vectors \(2i - j + k\), \(i + 2j - 3k\) and \(3i + aj + 5k\) are coplanar, find the value of \(a\).

Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

Determine the distance of the point \( (1,2,3) \) from the plane \( 2x + 3y - z = 7 \).

Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

Find the truth value of the statement: "If 2 is even, then 5 is prime."

The value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \) is:

Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).