List of practice Questions

An aggregate fruit is one which develops from

Which one of the following is wrong about Chara?

Which one of the following shows isogamy with non-flagellated gametes?

Which of the following is responsible for peat formation?

If $ A=\left[ \begin{matrix} 2 & -1 \\ 1 & 2 \\ \end{matrix} \right], $ then $ {{A}^{2}}+2A-3I= $

The mean and variance of a random variable $X$ having a binomial distribution are $4$ and $2$ respectively, find the value of $ P(X=1) $ .

Two tangents are drawn from a point $(- 2, -1)$ to the curve, $y^{2}=4x.$ If $\alpha$ is the angle between them, then $|\tan \alpha|$ is equal to :

A manufacturer has $ 500\text{ }L $ of a $ 10\% $ solution of acid, find the range of 40% acid to be added to it , such that the acid content in the resultant mixture will be more than $ 15\% $ but less than $ 20\% $ .

Convert $ \frac {(i+1)}{(\cos \,(\frac{\pi}{4}) -i\,\sin (\frac {\pi} {4})} $ in polar form?

Discuss the continuity of the function $ f(x)=\sin 2x-1 $ at the point $ x=0, $ and $ x=\pi $ .

Find $ \frac{dy}{dx}, $ if $ y={{\sin }^{2}}x+{{\cos }^{4}}x $

Find the value of $ \sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1 $

Solve $ {{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi $

Find the area of the triangle with vertices $ (2,3), $ $ (0,\,\,1) $ and $ (1,\,\,2) $ .

Find the value of $ \cos \,\,(29\pi /3)? $

Find the derivative of $ \sqrt{2}x+2\sqrt{x}-\frac{1}{x} $ ?

Find the intersection of the spheres $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13 $ and $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8 $

Solve for $ x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0 < x < 1 $

Given two vectors are $ \hat{i}-\hat{j} $ and $ \hat{i}+2\hat{j}, $ the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?

Integrate $ \frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}} $

Differentiate $ \sin \,\,(\sin \,\,2x). $

For what values of $x$, the numbers $ -1,\,x,-3/4 $ are in $GP$ ?

Let $ A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\}, $ which among the following statements is incorrect?

Find the range of the function $ f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x $ ?

There are $7$ horses in a race, Mr. X selected $2$ horses at random and bet on them. The probability that Mr. X selected the winning horse, is