List of top Questions asked in MHT CET

The probability mass function (p.m.f) of a random variable \(X\) is \(p(x)=\frac{x+3}{k},x=-2,-1,0,1\) and \(p(x)=0\) otherwise, then the value of \(E(x)=...\)

A man is known to speak the truth in \(75\%\) of cases. If he throws an unbiased die and tells his friend that it is a six. Assuming that when he tells a lie, he specifically reports the result as a six, the probability that it is actually a six is...

A coin whose faces are marked as \(5\) and \(3\) is tossed \(4\) times. The probability that the sum of the numbers on the coin is greater than \(17\) is ___

The volume of the tetrahedron formed by the plane \(6x+4y-5z-60=0\) and the coordinate planes is ........... cubic units

If the line \(\frac{x-2}{3}=\frac{y-1}{5}=\frac{z+2}{2}\) lies in the plane \(x+3y-pz+q=0\), then the value of \(p-q=\).........

The minimum and maximum values of the objective function \(Z=3x+9y\), subject to \(x+3y\leq 60,x+y\geq 10,x\leq y,x\geq 0,y\geq 0\) are respectively...

The ratio in which the point \(\hat{i}+2\hat{j}+3\hat{k}\) divides the line segment joining \(-2\hat{i}+3\hat{j}+5\hat{k}\) and \(7\hat{i}-\hat{k}\) is....

The vector equation of the line passing through the point \((1,2,-4)\) and perpendicular to the two the lines \(\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}\) and \(\frac{x-5}{3}=\frac{y-33}{8}=\frac{5-z}{5}\) is...

The differential equation of the family of lines perpendicular to the line passing through the point \((3,-5)\) with inclination \(\frac{\pi }{3}\) is...

If \(|\vec{u}|=5,|\vec{v}|=13,|\vec{u}\times \vec{v}|=25\), then \(\vec{u}\cdot \vec{v}=...\)

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is...

If \(\bar{a},\bar{b}\) are unit vectors and \(\bar{a}\cdot \bar{b}=0\), then \((\bar{a}-2\bar{b})\cdot \{(2\bar{a}+\bar{b})\times (\bar{a}\times \bar{b})\}=...\)

If \(\vec{a},\vec{b},\vec{c}\) are three vectors such that \(\vec{a}\cdot (\vec{b}+\vec{c})+\vec{b}\cdot (\vec{c}+\vec{a})+\vec{c}\cdot (\vec{a}+\vec{b})=0\) and \(|\vec{a}|=8,|\vec{b}|=1,|\vec{c}|=4\), then \(|\vec{a}+\vec{b}+\vec{c}|=...\)

The length of the perpendicular from the point \((3,2,1)\) to the line \(\frac{x-7}{-2}=\frac{y-7}{2}=\frac{z-6}{3}\) is \(k\) units. then the value of \(k\)....

If \(g(x)\) denotes the integrating factor of the differential equation \(x\log x\frac{dy}{dx}+y=2\,\log x\) and \(\int g(x)dx=h(x)[g(x)-1]+c\), then \(h(x)=\).........

If \(f(x)=\begin{cases} \frac{[x]\cdot |x|}{x}, & x\neq 0 \\ 0, & x=0 \end{cases}\), where \([x]\) and \(|x|\) denote the greatest integer function and the modulus function respectively, then \(\int _{-2}^{1}f(x)dx=...\)

If \(\frac{dy}{dx}=y+3\), where \(y+3>0\) and \(y(0)=2\), then \(y(\log 2)\) is equal to...

The value of the integral \(\int _{-1}^{1}\frac{1}{(1+e^{x})(1+x^{2})}dx\) is....

The value of the integral \(\int _{8}^{15}\frac{dx}{(x-3)\sqrt{x+1}}\) is....

The area of the region bounded by the parabola \(y^{2}=4x-2\) and the line \(y=2x-1\) is...(in sq. units)

The value of the integral \(\int \frac{1}{\cos x\cdot \log \left(\tan \left(\frac{\pi }{4}+\frac{x}{2}\right)\right)}dx\) is....

A tangent is drawn from the origin \((0,0)\) to the curve \(y=\sin x\). If \((x,y)\) is the point of contact and \(x\neq 0\), then which of the following relations is true?

If \(\int x^{7}e^{x}dx=e^{x}f(x)+c\), then \(f(x)\) is equal to...

The sum of the abscissae of the points on the curve \(y=x^{3}-6x^{2}+x+3\) whose normal is parallel to the line \(x+y=1975\) is...

The value of the integral \(\int \frac{1}{\sin x-\sqrt{3}\cos x}dx\) is....