List of top Questions asked in MHT CET

A company sells two types of notebooks, A and B. Each notebook requires two processes: printing and binding. Notebook A requires \(2\) minutes for printing and \(1\) minute for binding. Notebook B requires \(4\) minutes for printing and \(2\) minutes for binding. The company can spend \(6\) hours on printing and \(2\) hours on binding. If the profit made on notebooks A and B is Rs. \(2\) and Rs. \(5\) respectively, then the Linear Programming Problem (LPP) to maximize the total profit \(z\) is ...
If \(P(X)\) and \(F(X)\) are the probability mass function and cumulative distribution function of discrete random variable \(X\) where \(X=\{0,1,2,3,\ldots ,10\}\) and \(a,b\) are integers such that \(0\lt a\lt b\lt 10\), then the conditional probability \(P(X\geq a/X\leq b)\) is equal to ...
Given that \(X\sim B(20,p)\) if \(E(X)=8\) then \(Var(X)\) is
The number is selected randomly from the integers \(1\) to \(100\). The probability that the number selected has exactly three factors is ...
If \(\bar{a},\bar{b}\) and \(\bar{c}\) are three non-coplanar vectors and \(\lambda\) is a real number such that \([\lambda (\bar{a}+\bar{b})\lambda ^{2}\bar{b}\lambda \bar{c}]=[\bar{a}\bar{b}+\bar{c}\bar{b}]\), then there is (are) ...
Let \(O\) be the origin in 3D space. If the vertices \(A(2,p,-3),B(q,-2,5)\), and \(C(-5,1,r)\) of a triangle satisfy the vector relation \(\overline{PA}+\overline{PB}+\overline{PC}=3\overline{PO}\) for any point \(P\) in space, then the values of \((p,q,r)\) respectively are ...
The ratio in which the plane \(\bar{r}\cdot (\hat{i}-2\hat{j}+3\hat{k})=17\) divides the line segment joining the points \((-1,4,7)\) and \((3,-5,8)\) is ...
A line passing through \(A(1,3,2)\) and parallel to the line \(\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}\) intersects the plane \(x-y+3z-6=0\) at point B. Another line through B and perpendicular to the plane \(x-y+3z-6=0\) intersects the plane \(2x-y+z+4=0\) at the point C. Then the equation of median of \(\Delta ABC\) through the vertex A is ...
Let \(\bar{a}=\lambda \hat{i}+4\hat{j}\) and \(\bar{b}=\hat{i}+\lambda \hat{j}\) where \(\lambda \in Z\) such that \(|\bar{a}|\lt 6\). The number of possible values of \(\lambda\) for which \(\bar{a}\) and \(\bar{b}\) are non-collinear is ___
If the lines \(\bar{r}=(\hat{i}-\hat{j}+2\hat{k})+\lambda (\hat{i}+2\hat{k})\) and \(\frac{x-p}{2}=y+2=z+1\) intersect, then the value of \(p\) is ...
If \(4\hat{i}+7\hat{j}+8\hat{k},2\hat{i}+3\hat{j}+4\hat{k}\) and \(2\hat{i}+5\hat{j}+7\hat{k}\) are the position vectors of the vertices A, B and C respectively of the triangle ABC, then the largest angle of the triangle is (are) ...
If the function \(y=f(x)\) satisfies the differential equation \(x\frac{dy}{dx}=xy+y\) and \(y(1)=e\), then which of the following is true?
Let \(\bar{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\bar{b}=\hat{i}-\hat{j}+2\hat{k}\). If a vector \(\bar{c}\) is coplanar with \(\bar{a}\) and \(\bar{b}\) such that \(\bar{c}\cdot \bar{a}=1\) and \(\bar{c}\) is perpendicular to \(\bar{b}\), then \(\bar{c}\) is equal to ...
If \(yf(x)=g(x)+c\) where \(c\) is an arbitrary constant such that \(\frac{dy}{dx}+yg(x)=f(x)\) and \([f(x)]^{2}-[g(x)]^{2}=1\), then \(\int f(x)\cdot g(x)dx=\) ...
The differential equation of the family of all straight lines touching the circle \(x^{2}+y^{2}=1\) is ...
For any vector, \(\bar{a}\) if \(\hat{i}\times (\bar{a}\times \hat{i})+\hat{j}\times (\bar{a}\times \hat{j})+\hat{k}\times (\bar{a}\times \hat{k})=m\bar{a}\), then the value of \(m\) is ...
The area (in sq. units) of the region bounded by the line \(7x-5y=35\), the x-axis and the lines \(x=-2\) and \(x=3\) is ...
If \(n\) is an odd natural number and \(I_{n}=\int _{0}^{1}e^{x}(x-1)^{n}dx\), then the value of \(I_{n}+nI_{n-1}\) is equal to ...
The parabolas \(y^{2}=4x\) and \(x^{2}=4y\) divide the square region bounded by the lines \(x=4,y=4\) and the coordinate axes. If \(A1,A2,A3\) are respectively the areas of these parts numbered from top to bottom, then \(A1:A2:A3\) is ...
\(\int _{0}^{4}\sqrt{\frac{4-x}{4+x}}dx=\)
If \(\int \sin ^{4}x\cdot e^{\log (\cos x)}dx=\frac{1}{k}\sin ^{k}x+C\), for \(x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)\), then ...
If \(f(x)=\int \frac{x^{2}}{(1-x^{2})(1+\sqrt{1-x^{2}})}dx\) and \(f(0)=2\), then \(f\left(\frac{1}{2}\right)=\) ...
The sum of abscissa of the points on the curve \(y=x^{3}-3x^{2}+x-2\) at which the tangent is parallel to the line \(y=x\) is ___
If \(I_{1}=\int \frac{e^{x}}{e^{2x}+e^{x}+1}dx\) and \(I_{2}=\int \frac{1}{e^{-2x}+e^{-x}+1}dx\), then \(I_{1}-I_{2}=\)
If \(x=a\sin t-b\cos t,y=a\cos t+b\sin t\) and it is given that \(\frac{d^{2}y}{dx^{2}}=0\), then