List of top Mathematics Questions asked in MHT CET

The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)

A random variable X takes the values 0, 1, 2, 3 and its mean is \(1.3\). If \(P(X = 3) = 2P(X = 1)\) and \(P(X = 2) = 0.3\), then \(P(X = 0)\) is

A random variable X has the following probability distribution

\(X = x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)
\(P(X = x)\)	\(0.15\)	\(0.23\)	\(0.10\)	\(0.12\)	\(0.20\)	\(0.08\)	\(0.07\)	\(0.05\)

For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is

The odds in favour of A winning a game of table tennis against B are 1:2. If 3 games are to be played, then the probability of A winning at least two games out of the three is.....

Let \(X\sim B(6,\frac{1}{2})\). Then the maximum probability occurs at

In L.P.P., the corner points of the feasible region for the constraints \(3x-y\geq 6,x\leq 3,y\leq 2,y\geq 0,x\geq 0\) are .....

Let a plane P pass through the point \((3,7,-7)\) and contain the line \(\frac{x-2}{-3} = \frac{y-3}{2} = \frac{z+2}{1}\). If the distance of the plane P from the origin is d, then \(d^2\) is

A vector \(\overset{̄}{r}\) of magnitude \(3\sqrt{2}\) units which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) respectively with Y and Z axes is

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the co-ordinate axes at the points A, B, C respectively. Then the area of triangle ABC is

The point having position vector \(4\hat{i}-11\hat{j}+2\hat{k}\) lies on the line

The shortest distance between the lines, where the first line passes through \((0,0,0)\) and \((2,0,3)\) and the second line passes through \((2,5,0)\) and \((0,4,0)\) is

The value of the integral \(\int _{-\sqrt{3}}^{\sqrt{3}}\frac{(2x^9+3x^8-5x^7+9x^6+4x^3-x+3)}{x^2+3}\,dx\) is

The volume of a tetrahedron with vertices \(5\hat{i}-\hat{j}+\hat{k},7\hat{i}-4\hat{j}+p\hat{k},\hat{i}-6\hat{j}+10\hat{k}\) and \(-\hat{i}-3\hat{j}+7\hat{k}\) is 11 cubic units, then one of the values of p is

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors having magnitudes 1, 1 and 2 respectively. If \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is

A spherical balloon expands at a rate proportional to its surface area. Initially its radius is 2 cm and 5 minutes later it increases upto 7 cm, then surface area of spherical balloon after 12 minutes will be

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be unit vectors such that \(\overset{̄}{a}\) is perpendicular to the plane of \(\overset{̄}{b}\) and \(\overset{̄}{c}\). If the angle between \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(\frac{π}{3}\), then \(|\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c}| =\)

If a parallelogram is constructed on the vectors \(\overset{̄}{a} = 3\overset{̄}{p}-\overset{̄}{q},\overset{̄}{b} = \overset{̄}{p}+3\overset{̄}{q}\) and \(|\overset{̄}{p}| = 3,|\overset{̄}{q}| = 2\) and angle between \(\overset{̄}{p}\) and \(\overset{̄}{q}\) is \(\frac{π}{3}\), then the ratio of the lengths of adjacent sides \(\overset{̄}{a}\) and \(\overset{̄}{b}\) of the parallelogram is

\(\int e^{2x}\frac{2(sin2xcos2x-1)}{2sin^22x}\,dx = A\,e^{2x}cot2x+c\)
(Where c is the constant of integration.), then \(A^3 =\)

If a spherical balloon has a variable diameter \(3x+\frac{9}{2}\) units, then the rate of change of its volume with respect to \(x\) is

A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of the two pieces so that the combined area of the square and the circle is minimum, are respectively

\(\int \frac{30x^{14}+15^xlog225}{x^{15}+15^x}\,dx =\)

If \(\int \frac{sin2x}{sin^4x+cos^4x}\,dx = f(x)+c\) where c is constant of integration, then the value of \(tan(f(x))\) is

If \(\int _0^a\frac{dx}{1+4x^2} = \frac{π}{8}\), then \(a =\)

The equation of the normal to the curve \(xy+7 = 0\) is \(Ax+By+C = 0\), then

If \(y = x+e^x\), then \(\frac{d^2x}{dy^2}\) is equal to