List of top Mathematics Questions

The series \( \sum_{n=1}^{\infty} \frac{1}{n} \)
If a subset B is a basis of a vector space V, then
(A). B generates V.
(B). B contains zero vector.
(C). B is linearly independent.
(D). B is the only basis of V.
Choose the correct answer from the options given below:
The integral \( \int_{0}^{\pi/2} \sin^5 x \cos^7 x \,dx = \)
The equation of a straight line passes through the point (4,-5) and is perpendicular to the straight line 3x + 4y + 5 = 0.
Let an unbiased die be thrown and the random variable X be the number appears on its top. Then the expectation of X is
Every continuous real valued function on [a, b] is
(A). Constant.
(B). Bounded above.
(C). Bounded below.
(D). Unbounded.
Choose the correct answer from the options given below:
Let \(<G,*> \) be a group. Then for all a, b, c \(\in\) G
(A). (a*b)*c \(\in\) G
(B). a*b = b*a
(C). a*(b*c) = (a*b)*c
(D). a*b = a*c implies b = c.
Choose the correct answer from the options given below:
The solution of \(y = xp + \frac{m}{p}\) where \(p = \frac{dy}{dx}\) is
Let \(f\) be a continuous real valued function, defined by, \(f(x) = \sin x\), for all \(x \in [-\frac{\pi}{2}, \frac{\pi}{2}]\). Then which of the following does not hold.
Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$
There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.
Find the least value of ‘a’ so that $f(x) = 2x^2 - ax + 3$ is an increasing function on $[2, 4]$.
Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:
In \(\triangle ABC, \angle B = 90^\circ\). If \(\frac{AB}{AC} = \frac{1}{2}\), then \(\cos C\) is equal to
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
Nidhi received simple interest of ₹1,200 when she invested ₹x at 6% per annum and ₹y at 5% per annum for 1 year. Had she invested ₹x at 3% per annum and ₹y at 8% per annum for that year, she would have received simple interest of ₹1,260.Find the values of x and y.
If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), then prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).
Let the area of a triangle \( \triangle PQR \) with vertices \( P(5, 4) \), \( Q(-2, 4) \), and \( R(a, b) \) be 35 square units. If its orthocenter and centroid are \( O(2, \frac{14}{5}) \) and \( C(c, d) \) respectively, then \( c + 2d \) is equal to:
The number of ways of selecting 3 numbers that are in Arithmetic Progression (A.P.) from the set \(\{1, 2, 3, \ldots, 100\}\) is:
If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
Which of the following is not irrational?
The numerically greatest term in the expansion of $ (x + 3y)^{13} $, when $ x = \frac{1}{2},\ y = \frac{1}{3} $, is
The derivative of \(\sin^{-1}(2x^2 - 1)\) with respect to \(\sin^{-1}x\) is:
If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]