List of top Mathematics Questions

If A denotes the set of continuous functions and B denotes the set of differentiable functions, then which of the following depicts the correct relation between set A and B?
set of continuous functions
f and g are continuous functions on interval \( [0, a] \). Given that \( f(a - x) = f(x) \) and \( g(x) + g(a - x) = a \), show that \( \int_{0}^{a} f(x) g(x) dx = \frac{a}{2} \int_{0}^{a} f(x) dx \).
Prove that \( f : N \rightarrow N \) defined as \( f(x) = ax + b \) (\( a, b \in N \)) is one-one but not onto.
The feasible region along with corner points for a linear programming problem are shown in the graph. Write all the constraints for the given linear programming problem.
feasible region along with corner points
Evaluate: \( \int_{0}^{\pi} \frac{\sin 2px}{\sin x} dx \), \( p \in N \).
The principal value of \( \sin^{-1} \left( \cos \frac{43\pi}{5} \right) \) is
In the following probability distribution, the value of p is:
probability distribution
If \( \vec{PQ} \times \vec{PR} = 4 \hat{i} + 8 \hat{j} - 8 \hat{k} \), then the area \( (\triangle PQR) \) is
The integral \( \int \frac{dx}{\sin^2 x \cos^2 x} \) is equal to
The values of \(x\) for which the angle between the vectors \( \vec{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k} \) and \( \vec{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k} \) is obtuse, is:
The centre of the circle of curvature for the curve \( y = e^x \) at \( (0, 1) \) is:
The integral value of \( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = \):
The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:
491400 =
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Evaluate \( (\sec A + \tan A)(1 - \sin A) = \ ? \)
If the graph of \( y = p(x) \) does not intersect the X-axis at all, then the zeroes of \( p(x) \) are:
The value of the integral \( \int_0^1 x^2 \, dx \) is:
The product of Karan’s age five years ago and his age after 9 years from now is 32. This is represented by the quadratic equation:
If $ \tan\left( \alpha - \frac{\pi}{12} \right) = \frac{1}{\sqrt{3}} $, find $ \alpha $.
Tenth term of the AP \( 1, -1, -3, -5, \dots \) is
A card is drawn from a set of 52 cards. The probability of getting a queen card is:
Which of the following has equally likely outcomes?
If \( P(E) = \), then:
Which of the following cannot be a probability?