List of top Mathematics Questions

Statement-I: The function \( u = x^2 + y^2 \), \( v = \tan^{-1}\left(\frac{y}{x}\right) \) are functionally independent.
Statement-II: The Jacobian \( \frac{\partial(u,v){\partial(x,y)} \) is non-zero.
The correct answer is}

Let the matrix \( A = \begin{bmatrix} 1 & 4 \\ 2 & -1 \end{bmatrix} \).
Statement-I: \( A^2 = 9I \)
Statement-II: The eigen values of \( A \) are \( -3 \) and \( 3 \)
The correct answer is

If \( \lambda_1, \lambda_2 \) and \( \lambda_3 \) are the eigen values of a square matrix \( A \), then the eigen values of \( A^{-1} + 2I + A \) are

A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use \(\sqrt{3} = 1.73\))

Prove that : \(\frac{1}{\sec x - \tan x} - \frac{1}{\cos x} = \frac{1}{\cos x} - \frac{1}{\sec x + \tan x}\)

The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of \(\theta\).

Verify that roots of the quadratic equation (p – q)x\(^2\) + (q – r)x + (r – p) = 0 are equal when q + r = 2p.

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

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

Assertion (A) : If probability of happening of an event is 0.2p, p $\gt $ 0, then p can’t be more than 5.
Reason (R) : P( \(\overline{E}\) ) = 1 – P(E) for an event E.

\(\alpha, \beta\) are zeroes of the polynomial p(x) = 3x\(^2\) – 6x – 5. Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2}\).

In the given figure, DE \(\parallel\) AC and DF \(\parallel\) AE. Prove that : \(\frac{BF}{FE} = \frac{BE}{EC}\).

If 2 tan A = 3, then value of sec A equals

In an A.P., a = –3 and S\(_{17}\) = 357. The value of a\(_{17}\) is

In the given figure, a circle is centred at (1, 2). The diameter of the circle is

The value of k for which the system of linear equations \(\frac{x}{2} + \frac{y}{3} = 5\) and \(2x + ky = 7\) is inconsistent, is

Area of sector of a circle with radius 18 cm is 198 cm\(^2\). The measure of central angle is

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?

A circle centred at (–1, 2) passes through the point (0, 3). Radius of the circle is

Observe the graph of polynomial p(x). Number of zeroes of p(x) is

PQ is tangent to a circle with centre O. If \(\angle POR = 65^\circ\), then m\(\angle PTR\) is

If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to :

ABCD is a parallelogram such that AF = 7 cm, FB = 3 cm and EF = 4 cm, length FD = equals