List of top Mathematics Questions asked in AMUEEE

For all real $ x, 4^{sin^2x}+ 4cos^{2x} $ is

Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx = $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then $ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is

The length of the perpendicular drawn from $(1,2,3)$ to the line $ \frac{x-6}{3} = \frac {y-7}{2} = \frac {z-7}{-2} $ is

$ lim_{n\rightarrow \infty} \frac {(n!)^{1/n}}{n} $ equals

The equation $ \sqrt{\left(x-2\right)^{2}+y^{2}}+\sqrt{\left(x+2\right)^{2}+y^{2}}=4 $ represents

If $ C_o, C_1,C_2,....C_{15} $ are the binomial coefficients in the expansion of $ (1+x)^{15} $ then $ \frac {C_1}{C_o} +\frac {2C_2}{C_1}+\frac {3C_3}{C_2} +....+\frac {15C_{15}}{C_{14}} $ is equal to

A fair die is rolled. Consider the events A = { $ 1, 3, 5 $ }, B = { $ 2, 3 $ } and C = { $ 2, 3, 4, 5 $ }. Then, the conditional probability $ P (A \cup B / C) $ is

If $ x, y $ and $ z $ are all different and $ \begin{vmatrix}x&x^{2}&1+x^{3}\\ y&y^{2}&1+y^{3}\\ z&z^{2}&1+z^{3}\end{vmatrix}=0 $ then

Let the straight line $ x = b $ divide the area enclosed by $ y = (1 - x)^2 $ , $ y = 0 $ and $ x = 0 $ into two parts $ R_1(0 \le x \le b) $ and $ R_2(b \le x \le 1) $ such that $ R_1-R_2 = \frac {1}{4}. $ Then, $b$ equals

If $ \alpha,\beta $ are the roots of the equation $ ax^2+bx+c = 0 $ and $ S_n = \alpha^n + \beta^n, $ then a $ S_{n+1} + bS_{n} + cS_{n-1} $ is equal to

Let, $\vec {a} = - \hat {i} - \hat {k}, \vec {b} = - \hat {i} +\hat {j} $ and $\vec {c} = \hat {i}+2\hat {j}+3\hat {k} $ be three given vectors. If $\vec {r} $ is a vector such that $ \vec {r} \times \vec {b} = \vec {c} \times \vec{b} $ and $\vec {r} \cdot \vec{a} = 0 $ , then the value of $\vec {r} \cdot \vec {b} $ is

If $ \int_{0}^{\frac{\pi}{3}}\frac{cos x}{3 + 4 sin x}dx = k\, log \left(\frac{3+2\sqrt{3}}{3}\right) $ then $k$ is

The existence of the unique solution of the system of equations $ x + y + z = \beta $ $ 5x - y + az = 10 $ $ 2x + 3y - z = 6 $ depends on

If three-digit numbers $ A28, 3B9 $ and $ 62C $ , where $ A, B $ and $ C $ are integers between $ 0 $ and $ 9 $ , are divisible by a fixed integer $ k $ , then the determinant $ \begin{vmatrix}A&3&6\\ 8&9&C\\ 2&B&2\end{vmatrix} $ is

If $ A = \begin{bmatrix}2&3\\ 5&-2\end{bmatrix} $ be such that $ A^{-1} = kA, $ then $ k $ is equal to

Set $ A $ and $ B $ have $ 3 $ and $ 6 $ elements respectively. What can be the minimum number of elements in $ A \cup B $ ?

Let $ f(x) $ be differentiable on the interval $ (0, \infty) $ such that $ f(1) = 1 $ and $ lim_{t \rightarrow x} \frac {t^2f(x)-x^2f(t)}{t-x} =1 $ for each $ x>0 $ . Then, $ f(x) $ is

Let $ V_r $ denote the sum of the first $ r $ terms of an arithmetic progression $ (AP) $ whose first term is $ r $ and the common difference is $ (2r - 1) $ . The sum $ V_1 + V_2 + ..... + V_n $ is

Let $ f $ be the function $ [-\pi, \pi] $ given by $ f(0) = 9 \,and\,f(x) \,=\, f(x) = sin (\frac {9x}{2})/sin(\frac {x}{2}) $ for $ x \neq 0 $ . The value of $ \frac{2}{\pi} \int^{\pi}_{-\pi} $ $ f(x) dx $ is

If $ (1+x+x^2)^n = a_o +a_1x +a_2x^2 +.....+a_{2n} x^{2n}, $ then $ a_o+a_3+a_6+.....= $

Which of the following is a correct solution of $ x\,cosx\,\left(\frac{dy}{dx}\right) + y(x sin x +cos x) = 1 ? $

$ \frac {C_1}{C_o} + 2 \frac {C_2}{C_1} +3\frac {C_3}{C_2} + .... +n \frac {C_n}{C_{n-1}} $ =

The set of zeros of $ f(x) = 0 $ is a non-empty set, when $ f(x) = 0 $ , when $ f(x) $ is equal to

Let $ L $ denote the set of all straight lines in a plane. Let a relation $ R $ be defined on $L$ by $ L_1 $ $R L_2 $ if and only if the straight line $ L_1 $ is perpendicular to the straight line $ L_2 $ . Then, $ R $ is