List of top Mathematics Questions asked in AMUEEE

Let A = { $ (x,y): y = e^{-x} $ } and B = { $ (x,y):y=-x $ }. Then the correct statement is :

If $ p,q $ are positive real numbers such that $ pq = 1 $ , then the least value of $ (1 + p) (1 + q) $ is

Let $ f(x) = (x+2)^2 -2 , x \ge -2 $ . Then, $ f^{-1}(x) $ is equal to

Let $ Z $ be the set of integers. Then, the relation $R = \{ (a, b) :1 + ab > 0 \}$ on $z$ is

Which one of the following is not true?

The general solution of sin $ 3x + sin\, x - 3 \,sin 2x $ = $ cos\, 3x + cos\, x - 3 cos \,2x $ is

The line $ x = my + c $ is normal to $ x^2 = - 4ay $ , if c is equal to

If P is a point $ (x,y) $ and $ P_1 = (3,0),P_2 = (-3,0) $ and $ 16 x^2 + 25y^2 = 400 $ , then $ PP_1 + PP_2 $ is equal to

The total number of terms in the expansion of $ ( 1 + x ) ^{2n} - ( 1 - x ) ^{2n} $ after simplification is

If $f(x)$ = $ \begin{vmatrix}x+1&x&1\\ x\left(x+1\right)&x\left(x-1\right)&2x\\ x\left(x+1\right)\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&3x\left(x-1\right)\end{vmatrix} $ , then $ f(1000) $ is equal to

The equation of the plane through the points $ (2, 2,1) $ and $ (9, 3, 6) $ and perpendicular to the plane $ 2x + 6y + 6 z - 1 = 0 $ is

If $ f(x) = log_x $ { $ ln(x) $ },then $ f'(e) $ is equal to

If $ \begin{vmatrix}\left(x+a\right)&b&c\\ a&\left(x+b\right)&c\\ a&b&\left(x+c\right)\end{vmatrix} $ = 0 , then $ x $ =

If the sum of first $ n $ natural numbers is $ 1/5 $ times the sum of their squares, then $ n $ is equal to

If $ log_{10}2, log_{10}(2^x-1) $ and $ log_{10}(2^x+3) $ are in $AP$, then $x$ =

The inverse of a symmetric matrix is

If the $ (3r)^{th} \,and\, (r+2)^{th} $ terms in the binomial expansion of $ (1 + x)^{2n} $ are equal, then

The fixed point $P$ on the curve $ y = x^2 - 4x + 5 $ such that the tangent at $ P $ is perpendicular to the line $ x + 2y = 7 $ is given by

If $ I_{1}=\int_{0}^{\frac{\pi}{2}} f (sin \,2x)sin \,xdx $ and $ I_2 = \int^{\pi/4}_{0}\,f(cos2x) cosx \,dx\,then\, I_1/I_2 $ =

A line is drawn through the point $ P(3,11) $ to cut the circle $ x^2+ y^2 = 9 $ at point $ A $ and $ B $ . Then, $ PA \cdot PB $ is equal to

Total number of solutions of $ sin^4x +cos^4x = sin x cos x $ is $ [0,2\pi] $ is equal to

The locus of the point of intersection of the tangents at the extremeties of a chord of the circle $ x^2+y^2 = a^2 $ which touches the circle $ x^2 + y^2 - 2ax = 0 $ passes through the point

The projections of a directed lines segment on the coordinate axes are $ 12, 4, 3 $ . The direction cosines of the line are

If the lines joining the origin to the intersection of the line $ y = mx + 2 $ and the circle $ x^2 + y^2 = 1 $ are at right angles, then

The number of real values of $ x $ which satisfy the equation $ |\frac{x}{x-1}| + |x| = \frac{x}{|x-1|} $ is