List of top Mathematics Questions asked in UPSEE

If $\cos \, 3x \, \cos \, 2x \, \cos \, x = \frac{1}{4} $ and $0 < x < \frac{\pi}{4}$, then the value of $x$ is

If $(1 + \tan \, 1^{\circ})(1 + \tan \, 2^{\circ}) ...... (1 + \tan \, 45^{\circ}) = 2^n$, then n is

If $\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} k$, then the value of $k$ is

If $\log_{\sin \frac{\pi}{6}} \left\{\frac{\left|z-2\right| + 3 }{3\left|z - 2\right| - 1 }\right\}>1 $ , then

The value of the integral $\int \frac{dx}{x \sqrt{x^{2} - a^{2}} } $ is equal to:

The maximum value of the function $y = 2 \, \tan \, x - \tan^2 \, x $ over $\left[ 0 , \frac{\pi}{2} \right]$ is :

The $\displaystyle \lim_{x \to \frac{\pi}{2}} \left\{ 2x \tan x - \frac{\pi}{\cos x }\right\} $ is

The point of inflection of the function $y - \int^{x}_{0} \left(t^{2} - 3t + 2 \right) dt $ is

A chord of the parabola $y = x^2 - 2x + 5$ joins the point with the abscissas $x_1 =1, x_2 = 3$ Then the equation of the tangent to the parabola parallel to the chord is :

The points of the curve $y = x^3 + x - 2$ at which its tangents are parallel to the straight line $y = 4x - 1$ are

For what interval of variation of $x$, the identity $arc \, \cos \frac{1 - x^2}{1 + x^2} = - 2 \, arc \, \tan \, x$ is true ?

If a , b , c are three vectors such that $[ a\,b\,c]= 5 $ then the value of $[a \times b , \times c , \,c \times a] $ is :

The $\displaystyle\lim_{y \to a} \left\{ \left(\sin \frac{y-a}{2}\right) . \left(\tan \frac{\pi y}{2a}\right)\right\} $ is

Let $l_{n } = \frac{2^{n } + \left(-2\right)^{n} }{2^{n}} $ and $L_{n} = \frac{2^{n} + \left(- 2\right)^{n}}{3^{n}}$ then as $ n \to\infty$

Let $f(x) = \begin{cases} a (x) \sin \frac{\pi \ x }{2} & \text{for } x \neq 0 \\ -(n+1)/2 & \text{for} x = 0 \end{cases} $ where $\alpha (x) $ is such that $\displaystyle\lim_{x \to 0} |\alpha (x) | = \infty $ Then the function $f(x)$ is continuous at $x = 0$ if $\alpha (x) $ is chosen as

Let $f(x) = \begin{cases} - 2 \sin x & \quad \text{if } x \leq - \frac{\pi}{2}\\ A \ \sin x + B & \quad \text{if } - \frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos & \quad \text{if } x \leq \frac{\pi}{2} \end{cases} $ For what values of A and B, the function $f (x)$ is continuous throughout the real line ?

The derivative of $y = x^{\sin\,x}$ is

Value of $\left[\left(\log_{b}\,a\right)\left(\log_{c}\,b\right)\left(\log_{a}\,c\right)\right]$ is

$\sin^{2}\,\theta\, \cos^{3}\,\theta-\sin^{4}\,\theta\, \cos\,\theta$ is equal

$\log_3\,2, \log_6\,2, \log_{12}\,2$ are in

If function $f(x) = \begin{cases} x\, \sin\left(\frac{1}{x} \right) ; & \text{x $\ne$ 0} \\[2ex] a \,;& \text{x = 0} \end{cases}$ is continuous at $x = 0$, then value of $a$ is

The tangents to curve $y=x^{3}-2x^2+x-2$ which are parallel to straight line $y = x$ are

Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$. The projection of the vector $B$ on the vector $R$ is

Value of the following expression is $\displaystyle \lim_{n \to \infty}$$\frac{1}{n^{3}}\left(1^{2}+2^{2}+3^{2}+ ..... +n^{2}\right)$

The Solution of the differential equation $\left(x+2y^{3}\right) \frac{dy}{dx}=y$ is