List of top Mathematics Questions asked in AMUEEE

If $ H_n = 1+\frac{1}{2} + ..... + \frac{1}{n}, $ then the value of $ S_n = 1+\frac{3}{2} + \frac{5}{3} + .....+\frac{2n-1}{n} is $

If the normal at the point $ P(\theta) $ to the ellipse $ \frac{x^2}{14} + \frac {y^2}{5} = 1 $ intersects it again at the point $ Q(2\theta), $ then $ cos \theta $ equals to

The eccentricity of the hyperbola with latus rectum $ 12 $ and semi-conjugate axis $ 2\sqrt{3} $ , is

If the parabolas $ y^2 = 4x $ and $ x^2 = 32y $ intersect at $ (16, 8) $ at an angle $ \theta $ , then $ \theta $ equals to

If algebraic sum of distances of a variable line from points $ (2,0) $ , $ (0,2) $ and $ (-2- 2) $ is zero, then the line passes through the fixed point

If $ asin^{-1}x - bcos^{-1} x = c $ , $ a sin^{-1}x + b cos^{-1} x $ is equal to

$ \int e^{xloga }e^{x} dx $ is equal to

The complex number $ z = \begin{vmatrix}2&3+i&-3\\ 3-i&0&-1+i\\ -3&-1-i&4\end{vmatrix} $ is equal to

Let $ f : R $ - { $ \frac {5}{4} $ } $ \rightarrow R $ be a function defined as $ f(x) = \frac{5x}{4x+5} $ . The inverse of $ f $ is the map $ g : Range\,f\,\rightarrow R $ - { $ \frac {5}{4} $ } given by

Let $ * $ be a binary operation on the set $ Q $ of rational numbers defined by $ a*b $ = $ \frac{ab}{4} $ . The identity with respect to this operation is

For the equations $ x + 2y + 3z = 1 $ , $ 2x + y + 3z = 2 $ , $ 5x + 5y + 9z = 4 $

Three cards are drawn successively without replacement from a pack of $ 52 $ well shuffled cards. The probability that first two cards are queens and the third card is a king, is

The interior angles of a polygon are in arithmetic progression. The smallest angle is $ 120 $ and the common difference is $ 5 $ . The number of sides of the polygon is

$ \int e^{x}\left(cosec^{-1}x+\frac{-1}{x\sqrt{x^{2}-1}}\right) \, dx$ is equal to

In a $G.P.$ $ t_2 + t_5 = 216 $ and $ t_4 : t_6 $ = $ 1 : 4 $ and all terms are integers, then its first term is

In a certain progression three consecutive terms are $ 30, 24, 20 $ . The next term of the progression is

For the function $ f(x) = \frac {4}{3} x^3-8x^2+16x+5, $ $ x = 2\,is \,a\,point\, of $

Bag $I$ contains $3$ red and $4$ black balls, while another bag $II$ contains $5$ red and $6$ black balls. One ball is drawn at random from one of the bags and it is found to be black. The probability that it was drawn from bag $II$ is

Let $A = \{ 0,1,2 \}$, $B =\{ 4,2,0 \}$ and $ f,g $ : $ A \rightarrow B $ be the functions defined by $ f(x) = x^2-x $ and $ g(x) = 2|x-\frac{1}{2}|-1 $ Then,

Let $f = \{ (1,1),(2,4),(0,- 2),(-1,- 5) \}$ be a linear function from $ Z $ into $ Z $ . Then, $ f (x) $ is

The ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, - 8)$ is divided by xy-plane is

If $ A $ is a square matrix such that $ A^2 $ = $ A $ , then $ (I-A)^3+A $ is equal to

The value of $\lambda$ for which the lines $\frac{1-x}{3}=\frac{y-2}{2\lambda}=\frac{z-3}{2}$ and $ \frac{x-1}{3\lambda}=\frac{y-1}{1}=\frac{6-z}{7}$

The co-ordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1, - 1, 0)$ are

A fair coin is tossed $ n $ number of times. If the probability of having at least one head is more than 90%, then $ n $ is greater than or equal to