List of top Mathematics Questions

If \( \cosh \alpha + \sinh \alpha = e^x \) and \( \sinh x = \frac{\alpha}{\alpha + 1} \), then \( \tanh x = \)

If \[ \left| 1 - \cos \left( \frac{\pi}{2} - \alpha \right) + \sin \left( \frac{3\pi}{2} - \alpha \right) \right| \left[ 1 - \sin \left( \frac{3\pi}{2} - \alpha \right) - \cos \left( \frac{\pi}{2} - \alpha \right) \right] = a + b \sin \left( \frac{\pi}{4} + \alpha \right) \] then \( a^2 + b^2 = \)

In \( \triangle ABC \), if \( \frac{1}{r_1}, \frac{1}{r_2}, \frac{1}{r_3} \) are in arithmetic progression, then \( r_1 : r_2 : r_3 = \)?

If \( f(x) = px^3 + qx^2 + rx + t \) attains local minimum and local maximum values at \( x = -2 \) and \( x = 2 \) respectively and \( p \) is a root of \( 9x^2 - 1 = 0 \), then \( p + q + r = \)

If \( x^2 + x - 6 \) is a factor of \( 2x^3 + x^2 + ax + b \), then \( 6a + 13b = \) ?

If \( z_1, z_2, z_3 \) are the vertices of an equilateral triangle and \( z \) is its circumcentre, then

Let the length of the latus rectum of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be equal to the length of its semi-major axis. If the radius of its director circle is \( \sqrt{3} \) and \( e \) is its eccentricity, then the length of its latus rectum is:

Let \( P(h, k) \) be the point of contact of the tangent to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) which is parallel to the line \( \sqrt{3}x - y + 1 = 0 \). If \( P \) lies in the fourth quadrant then \( 3h^2 - 2k = \)

Let \(Z\) be the point of intersection of the axis and the directrix of the parabola \(4x^2 - 12x + 4y + 5 = 0\). If \(S\) is its focus, then the point which divides \(SZ\) in the ratio \(2:1\) is:

Let A=\(\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}\). If B=\(\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}\)A \(\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}\), then the sum of all the elements of the matrix \(\sum^{50}_{n=1}B^n\) is equal to

The C.P. of two shirts taken together is ₹910. If by selling one at a profit of 16% and and the other at a loss of 12%, there is no loss or gain in the whole transaction, then the C.P. of the two shirts are respectively:

The Curved Surface Area of a right circular cylinder of base radius r is obtained by multiplying its volume:

Match List I with List II

List-I		List-II
(A)	Volume of cone	(I)	\(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\)
(B)	Volume of sphere	(II)	\(\frac{1}{3}\pi r^2h\)
(C)	Volume of Frustum	(III)	\(\pi r^2h\)
(D)	Volume of cylinder	(IV)	\(\frac{4}{3}\pi r^3\)

Choose the correct answer from the options given below:

At what rate of simple interest, a sum of ₹1,800 will become ₹2,700 in 10 years?

If P, R, T are the areas of parallelogram. a rhombus and a triangle standing on the same base and between the same parallel lines, then which of the following is true?

The number \(0.4\overline{23}\) converted to a fraction, then it is equal to:

If you are head of your office, some media people come to your office and request you brief them about the pension plan of your office, you will:

\(tan^{-1}(\frac {1+\sqrt 3}{3+\sqrt 3})+sec^{-1}(\sqrt {\frac {8+4\sqrt 3}{3+3\sqrt 3})}\) is equal to:

Let S = {1, 2, 3, 4, 5}
if f : S → P(S), where P(S) is power set of S. Then number of one-one functions f can be made is

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the perpendicular from the origin O to this line makes an angle of \(\frac{\pi}{6}\) with the positive direction of the y-axis and the area of △OAB is \(\frac{98\sqrt{3}}{3},\) then a² − b² is equal to:

If [t] denotes the greatest integer \(≤ 1\), then the value of \(3\frac{(e - 1)^2}{e}\) is:

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

The statement B⇒((∼A) ∨ B) is equivalent to :