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List of top Mathematics Questions

The sum of the rational terms in the binomial expansion of $ \left( \sqrt{2} + 3^{1/5} \right)^{10} $ is:

For real values of $ x $ and $ a $, if the expression $ \frac{x+a}{2x^2 - 3x + 1} $ assumes all real values, then:

If both the roots of the equation $ x^2 - 6ax + 2 - 2a + 9a^2 = 0 $ exceed 3, then:

If power of a point $ (4,2) $ with respect to the circle $ x^2 + y^2 - 2x + 6y + a^2 - 16 = 0 $ is 9, then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

8 teachers and 4 students are sitting around a circular table at random. The probability that no two students sit together is:

Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]

If $ \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx = K \int_0^\pi \sin^2 x \, dx + L \int_0^\frac{\pi}{2} \cos^2 x \, dx $ and $ K, L \in \mathbb{N} $, then the number of possible ordered pairs $ (K, L) $ is}

Evaluate the integral $ \int_{-\frac{1}{24}}^{\frac{1}{24}} \sec(x) \log\left(\frac{1-x}{1+x}\right) \, dx $:

The general solution of the differential equation: $$ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. $$

The general solution of $ \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} $ is:

The square root of $ 7 + 24i $ is:

Assertion (A): If $ B $ is a $ 3 \times 3 $ matrix and $ |B| = 6 $, then $ | \text{Adj}(B) | = 36 $. Reason (R): If $ B $ is a square matrix of order $ n $, then $ |\text{Adj}(B)| = |B|^n $.

If $ A = [a_{ij}]$ where $ 1 \leq i, j \leq n $ with $ n \geq 2 $ and $ a_{ij} = i + j $ is a matrix, then the rank of $ A $ is:

If $ x $ is real and $ \alpha, \beta $ are maximum and minimum values of $ \frac{x^2 - x + 1}{x^2 + x + 1} $ respectively, then $ \alpha + \beta = $:

Match the items of List-I with those of List-II (Here $ \Delta $ denotes the area of $ \triangle ABC $).

Then the correct match is

If $ y = x + \sqrt{2} $ is a tangent to the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $, then equations of its directrices are:

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

If $ Z = x + iy $ is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is:

For $ x<0 $, $ \frac{d}{dx} [|x|^x] $ is given by:

If set $ A $ contains 8 elements, then the number of subsets of $ A $ which contain at least 6 elements is:

If $ AB = 2i + 3j - 6k $, $ BC = 6i - 2j + 3k $ are the vectors along two sides of a triangle ABC, then the perimeter of triangle ABC is:

Evaluate the integral \[ I = \int_0^1 \frac{x}{(1 - x)^{3/4}} \, dx \]

Let $ \vec{a} $ and $ \vec{b} $ be two vectors such that $ |\vec{b}| = 1 $ and $ |\vec{b} \times \vec{a}| = 2 $. Then $ \left| (\vec{b} \times \vec{a}) - \vec{b} \right|^2 $ is equal to

If $f(x) = (x - 2)^2 (x - 3)^3$ and $x ∈ [1, 4]$ and If $M$ and $m$ denotes maximum and minimum values respectively, then $M - m$ is

Let $ a $ and $ b $ be two distinct positive real numbers. Let the 11^th term of a GP, whose first term is $ a $ and third term is $ b $, be equal to the $ p $-th term of another GP, whose first term is $ a $ and fifth term is $ b $. Then $ p $ is equal to