List of top Mathematics Questions

Solve the linear equations \(3x + y = 14\) and \(y = 2\) graphically.

Find the approximate value of \(\sqrt[3]{63}\).

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

Assertion (A) : The mean of first 'n' natural numbers is \( \frac{n - 1}{2} \).
Reason (R) : The sum of first 'n' natural numbers is \( \frac{n(n + 1)}{2} \).

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :

If the statement $(p \wedge q) \rightarrow (r \vee \neg s)$ is False (F), then the truth values of $p, q, r$ and $s$ are respectively

Let \( f(x) = \begin{cases} x^3 + 8 & x < 0 \\ x^2 - 4 & x \ge 0 \end{cases} \) and \( g(x) = \begin{cases} (x-8)^{1/3} & x < 0 \\ (x+4)^{1/2} & x \ge 0 \end{cases} \) then find number of points of discontinuity of \( g(f(x)) \).

Find the eigenvalues of the matrix \(A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\).

Let \(O\) be the vertex of the parabola \(y^2 = 4x\). Let \(P\) and \(Q\) be two points on parabola such that chords \(OP\) and \(OQ\) are perpendicular to each other. If the locus of mid-point of segment \(PQ\) is a conic \(C\), then latus rectum of \(C\) is

The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observation is

Let \( f(x) = \sin x \), \( g(x) = \cos x \), \( h(x) = x^2 \) then
\[ \lim_{x \to 1} \frac{f(g(h(x))) - f(g(h(1)))}{x - 1} = \]

If \( A = 1 + r^a + r^{2a} + r^{3a} + \cdots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \cdots \infty \), then \( a/b \) is equal to

Evaluate the definite integral: \[ \int_{0}^{\frac{\pi}{2}} \sin^2 x \, dx \]

Evaluate the integral: \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1+(\cot x)^{101}} \]

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

If \( h(x) = \sqrt{4f(x) + 3g(x)} \), \( f(1)=4 \), \( g(1)=3 \), \( f'(1)=3 \), \( g'(1)=4 \), then \( h'(1) \) is equal to:}

Evaluate the integral: \[ \int \frac{x+1}{x(1+xe^x)^2}\,dx \]

Evaluate the integral: \[ \int_{1}^{4}\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{e^x}}\right)dx \]

Identify the truth value of the statement pattern \( (p \land \sim q) \rightarrow r \).

Find the area of the region bounded by the parabola \( y^2 = 4ax \) and its latus rectum.

Find the value of \( k \) if the function \( f(x) = \frac{k \cos x}{\pi - 2x} \) is continuous at \( x = \frac{\pi}{2} \).

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec a, \vec b, \vec c\), find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

Evaluate the integral: \[ \int \frac{x}{x+2}\, dx \]

For the curve \( y = 3x^3 - 3x^2 + 1 \) at \( x = 1 \), find the equation of the tangent.

If \( \vec{a} \) and \( \vec{b} \) are unit vectors and the angle between them is \(60^\circ\), find \( |\vec{a}-\vec{b}| \).