List of practice Questions

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

Spore bearing leaf is called

In mammals which organ acts as blood bank ?

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

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

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

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

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 :

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

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} - 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 ?

Hygroscopic roots are found in :

Hydra can not digest :

Gravitational force acts on a particle due to fixed uniform solid sphere. Neglect other forces. Then particle

Which of the following is a lyophobic colloid :

For car battery which one is correct statement ?

The enthalpy of the formation of $CO_2$ and $H_2O$ are - $395\, kJ$ and - $285\, kJ$ respectively and the enthalpy of combustion of acetic acid is $869\, kJ.$ The enthalpy of formation of acetic acid is:

Among the following compounds of Boron, the species which also forms $\pi $ - bond in addition to $\sigma$ - bonds is:

Give the IUPAC name for the following structure :

In terms of polar character which one of the following orders is correct?

Epinasty movement is found in :

Dinosaurs disappeared during :

Imbibtion is a :