List of top Mathematics Questions asked in JKCET

A normal to the curve $2x^{2 }- y^{2} = 14$ at the point $(x_{1}, y_{1})$ is parallel to the straight line $x + 3y = 4$ . Then the point $(x_{1}, y_{1})$ is

When $y = vx$ , $y$ and $x$ are variables, the differential equation $\frac{dy}{dx}=\frac{2xy}{x^{2}-y^{2}}$ reduces to

The value of integral $\int{e^x}(\frac{cosx+sinx}{cos^2x})dx$

Let the function $f(x)$ be continuous in the interval $[a, b]$ and differentiable in $(a, b)$ . Then there is at least one point $c$ in $(a, b)$ at which the tangent to the curve $y = f (x)$ is parallel to

Let $P\left(x\right)=^{10}C_{x} \left(\frac{1}{2}\right)^{10} , x=0, 1, 2, \ldots,10$ be the probability mass function of a binomial distribution $X$ . Then the mean of $X$ is

If tan $y=\frac{sin\,x+cos\,x}{cos\,x-sin\,x}$ , then $\frac{dy}{dx}=$

The function $f (x) = |x-10|$ , $x$ is real number, is

If $25^{th}$ term of an $A.P.$ is $15$ and if its $15^{th}$ term is $25$ , then the $40^{th}$ term of the $A.P.$ is

A pair of unbiased dice is thrown once. Let $X$ be the random variable denoting the product of numbers that appear on the two dice. Then $P\left(X \ge21\right)=$

The integrating factor of the differential equation $\left(1+x^{2}\right)\frac{dy}{dx}+xy=cos\,x$ is equal to

If $^{32}{{P}_{6}}=k\,{{(}^{32}}{{C}_{6}}),$ then $k$ is equal to

Consider the curve given by ${{({{x}^{2}}+{{y}^{2}})}^{2}}=4({{x}^{2}}-{{y}^{2}})$ . Which of the following is not true?

Which of the following is a tangent to the curve given by ${{x}^{3}}+{{y}^{3}}=2xy?$

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

The sum of lengths of major and minor axes- of an ellipse whose eccentricity is $\frac{4}{5}$ and length of latuserectum is $14.4$ , 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

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

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