List of top Mathematics Questions asked in JKCET

The points $ (1,3,4),\,(-1,6,10),\,(-7,4,7) $ and $ (-5,1,1) $

At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $ \frac{dP}{dx}=100-12\sqrt{x}. $ . If the firm empower 25 more workers, then the new level of production of items is

If $ |\vec {a} |=7 $ and $ |\vec {b} |=11, $ then the angle between the vectors $\vec {a} +\vec {b} $ and $\vec {a} -\vec {b} $ is equal to

In an isosceles right angled triangle $ABC$, a value of $ \tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right) $ is

The function is $ f(x)=\frac{1}{2-\cos \,3x},\,x\,\in \left[ 0,\frac{\pi }{3} \right], $ is

Let function $ f(x)={{(x-1)}^{2}}{{(x+1)}^{3}}. $ Then, which of the following is false?

The last digit in the integer $ {{3}^{101}}+1 $ is

The derivative of $sin\, x$ with respect to $ cos\text{ }x $ is

$ \underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x} $ is

If getting a number greater than $4$ is a success in a throw of a fair die, then the probability of at least $2$ successes in six throws of a fair die is

The number of integer value(s) of $k$ for which the expression $ {{x}^{2}}-2(4k-1)x+15{{k}^{2}} $ $ -2k-7>0 $ for every real number $x$ is/are

If the plane $ 2x-3y+6z-11=0 $ makes an angle $ \theta $ with the $x-axis$, then the value of $ \tan \theta $ is equal to

Let $A$ and $B$ be points $ (8,\,\,10) $ and $ (18,\,20), $ respectively. If the point $Q$ divides AB externally in the ratio $ 2:3 $ and $M$ is the $S$ mid-point of $AB$, then the length $MQ $ is equal to

If the image of the point $ (1,\,-2,3) $ in the plane $ 2x+3y-z=7 $ is the point $ (\alpha ,\beta ,\gamma ) $ then $ \alpha +\beta +\gamma $ is equal to

The number of the solutions of the equation $ {{5}^{2x-1}}+{{5}^{x+1}}=250, $ is/are

Let $X$ be a random variable with its expectation $ E(X)=3 $ and its variance $ V(X)=2 $ . If $V$ is another random variable defined by $ Y=10X, $ then the ordered pair $ (E(Y),\,V(Y)) $ is equal to

The shortest distance between the lines $ \frac{x}{-1}=\frac{y}{1}=\frac{z}{1} $ and $ \frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1} $ is

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= $

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

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

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\% $ .

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