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List of top Mathematics Questions

Let ABC be an equilateral triangle of side $a$. M and N are two points on the sides AB and AC respectively such that $AN = K \cdot AC$ and $AB = 3 \cdot AM$. If the vectors $BN$ and $CM$ are perpendicular, then $K = $ ?

Let $ \vec{a} \times \vec{b} = 7\hat{i} - 5\hat{j} - 4\hat{k} $ and $ \vec{a} = \hat{i} + 3\hat{j} - 2\hat{k} $, if the length of projection of $ \vec{b} $ on $ \vec{a} $ is $ \frac{8}{\sqrt{14}} $, then $ |\vec{b}| $ is:

If $ L, M, N $ are the midpoints of the sides PQ, QR, and RP of triangle $ \Delta PQR $, then $ \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = $:

Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?

Find the shortest distance between the skew lines $\vec{r} = (-\hat{i} - 2\hat{j} - 3\hat{k}) + t(3\hat{i} - 2\hat{j} - 2\hat{k})$ and $\vec{r} = (7\hat{i} + 4\hat{k}) + s(\hat{i} - 2\hat{j} + 2\hat{k})$.

$\int\frac{2x^{2}\cos(x^{2})-\sin(x^{2})}{x^{2}}dx=$

Numerically greatest term in the expansion of $ (5 + 3x)^6 $, when $ x = 1 $, is:

The sum of the series $ 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty $ is:

If $ \frac{1}{x^4 + 1} = \frac{Ax + B}{x^2 + \sqrt{2}x + 1} + \frac{Cx + D}{x^2 - \sqrt{2}x + 1} $, then $ BD - AC = $:

There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:

The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is:

While solving a system of linear equations $ AX = B $ using Cramer’s rule, if \includegraphics[]{6.png}

The set of all real values of $ a $ such that the function $ f(x) = x^3 + 2ax^2 + 3(a+1)x + 5 $ is strictly increasing in its entire domain is:

Evaluate the integral: \[ \int \frac{1}{x^5 \sqrt{x^5+1}} dx. \]

In $ \triangle ABC $, given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find $ c $.

If $ H $ is the orthocenter of $ \triangle ABC $ and $ AH = x $, $ BH = y $, $ CH = z $, then evaluate: \[ \frac{abc}{xyz} \]

Evaluate the limit: $$ \lim_{n \to \infty} n^4 \left[ \sum_{k=0}^{\infty} \frac{1}{(n^2 + k)^{5/2}} \right]. $$