List of top Mathematics Questions

In the sequence \( 18, a, 14, 32 \), the common difference is:
The sum of the first \(n\) natural numbers is:
If \( x<0 \) and \( y>0 \), then the point \( P(x, y) \) is in which quadrant?
If \( A = 45^\circ \), then the value of \( \sin A + \cos A + \cos 2A \) is?
The area of the triangle with vertices \( (1, 1), (-4, 6), (-3, -5) \) is?
The product of the zeroes of a polynomial \(x^3 - 3x^2 + x + 1\) is:
The terms 4, 7, 10, \dots form an A.P. The sum of the first 15 terms is?
Which term of G.P. \( 2, 2\sqrt{2}, 4, \dots \) is 128?
If a line is passing through the points (2, 5) and (x, 3) and its slope is 2. Then the value of 'x' is?
The total surface area of a hemisphere solid having radius 7 cm is:
If \( \frac{5}{x+1} + \frac{1}{y-3} = 2 \) and \( \frac{6}{x+1} - \frac{3}{y-3} = 1 \), then \( x = \dots \):
The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) represents the following:
If \( \alpha, \beta \) are the roots of \( 2x^2 - 4x + 5 = 0 \), then \( (\alpha + 1)(\beta + 1) = \):
Evaluate \( \dfrac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} \)
If \( 15 \cot A = 8 \), then \( \sin A = \, ? \)
The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:
Find: \( \int \frac{5x}{(x + 1)(x^2 + 9)} dx \).
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 \( \int_{0}^{a} f(x) g(x) dx = \frac{a}{2} \int_{0}^{a} f(x) dx \).
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
Prove that \( f : N \rightarrow N \) defined as \( f(x) = ax + b \) (\( a, b \in N \)) is one-one but not onto.
Evaluate: \( \int_{0}^{\pi} \frac{\sin 2px}{\sin x} dx \), \( p \in N \).
The integral \( \int \frac{dx}{\sin^2 x \cos^2 x} \) is equal to
The principal value of \( \sin^{-1} \left( \cos \frac{43\pi}{5} \right) \) is
If \( \vec{PQ} \times \vec{PR} = 4 \hat{i} + 8 \hat{j} - 8 \hat{k} \), then the area \( (\triangle PQR) \) is