List of top Questions asked in JKCET- 2014

If $ y=x{{e}^{2y}}, $ then find $\frac{ dy}{dx} $ .

A bag contains $n + 1$ coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $\frac{7}{12}$, then the value of $n$ is.

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) $ .

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

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

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

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

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

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

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

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 $

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

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

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?

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

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

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

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

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

An infinite line charge produces a field of $ 18\times 10^{5}\,N/C $ at a distance of $ 4\,cm $ . What is the linear charge density?

What kinds of bonds are present in ethene molecule?

Which acid is present in vinegar?