List of top Mathematics Questions asked in MHT CET

The derivative of \(log_{10}x\) with respect to \(log_x10\) is

The sum of all real values of \(λ\) for which the vectors \(\overset{⃗}{a} = λ\hat{i}+\hat{j}+\hat{k}\), \(\overset{⃗}{b} = \hat{i}+λ\hat{j}+2\hat{k}\), \(\overset{⃗}{c} = 2\hat{i}+3\hat{j}+λ\hat{k}\) are coplanar is...

A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is

The Cartesian equations of the line passing through \(A(0,1,1)\) and parallel to the X-axis are ....

For the following probability distribution of a random variable \(X\), the Expected value and Variance of \(X\) are respectively

\(X = x\)	\(1\)	\(2\)	\(3\)
\(P(X = x)\)	\(1/5\)	\(2/5\)	\(2/5\)

The LPP maximize \(z = 2x+5y\) subject to \(x+3y\leq 6\), \(2x+6y\leq 18\), \(x\geq 0\), \(y\geq 0\) has

Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

Given the following expression
A) \((\overset{⃗}{a}\times \overset{⃗}{b})\cdot \overset{⃗}{c}\)
B) \(\overset{⃗}{a}\times (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
C) \(\overset{⃗}{a}\cdot (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
D) \(|\overset{⃗}{a}|(\overset{⃗}{b}\cdot \overset{⃗}{c})\)
E) \((\overset{⃗}{a}\cdot \overset{⃗}{b})\times (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
Then which of the following is not correct

If the perpendicular distance of the plane passing through the point \(Q(1,0,-1)\) and containing the line \(\overset{⃗}{r} = (\hat{i}-3\hat{j}+\hat{k})+λ(2\hat{i}-2\hat{j}+\hat{k})\) from origin is \(\frac{p}{\sqrt{53}}\) then \(p =\) ...

Lines \(\overset{⃗}{r} = \overset{⃗}{a}+λ\overset{⃗}{b}\) and \(\overset{⃗}{r} = \overset{⃗}{b}+μ\overset{⃗}{a}\) intersect at point \((2,4,-4)\). If \(|\overset{⃗}{a}-\overset{⃗}{b}| = 4\), then \(\overset{⃗}{a}\cdot \overset{⃗}{b} =\)

The volume of the parallelopiped whose coterminous edges are \(2\hat{i}+\hat{j}-\hat{k},3\hat{i}-\hat{j}-\hat{k},\hat{j}+3\hat{k}\) is

If the line joining points \((2,1,4)\) and \((a-1,4,-1)\) is parallel to the line joining points \((0,2,b-1)\) and \((5,3,-2)\) then the values of \(b\) and \(a\) are respectively

If \(\overset{⃗}{a},\overset{⃗}{b},\overset{⃗}{c}\) are three non-coplanar vectors and \(\overset{⃗}{p},\overset{⃗}{q},\overset{⃗}{r}\) are defined as \(\overset{⃗}{p} = \frac{\overset{⃗}{b}\times \overset{⃗}{c}}{[\overset{⃗}{a} \overset{⃗}{b} \overset{⃗}{c}]},\overset{⃗}{q} = \frac{\overset{⃗}{c}\times \overset{⃗}{a}}{[\overset{⃗}{a} \overset{⃗}{b} \overset{⃗}{c}]},\overset{⃗}{r} = \frac{\overset{⃗}{a}\times \overset{⃗}{b}}{[\overset{⃗}{a} \overset{⃗}{b} \overset{⃗}{c}]}\), then \([(\overset{⃗}{a}+\overset{⃗}{b})\cdot \overset{⃗}{p}+(\overset{⃗}{b}+\overset{⃗}{c})\cdot \overset{⃗}{q}+(\overset{⃗}{c}+\overset{⃗}{a})\cdot \overset{⃗}{r}]\) is equal to

Let \(\overset{⃗}{a} = 2\hat{i}+\hat{k},\overset{⃗}{b} = \hat{i}+\hat{j}+\hat{k}\), and \(\overset{⃗}{c} = 4\hat{i}-3\hat{j}+7\hat{k}\). If \(\overset{⃗}{r}\) is a vector such that \(\overset{⃗}{r}\times \overset{⃗}{b} = \overset{⃗}{c}\times \overset{⃗}{b}\) and \(\overset{⃗}{r}\cdot \overset{⃗}{a} = 0\), Then \(\overset{⃗}{r}\cdot \overset{⃗}{c} =\)

The area in square units of the region bounded by the curve \(y = \sqrt{16-x^2}\) and lines \(x = 0,x = 4\) above the X-axis is

If \(\overset{⃗}{u} = \hat{i}+2\hat{j}-2\hat{k},\overset{⃗}{v} = 2\hat{i}+\hat{k}\) and \(\overset{⃗}{w}\) is unit vector then the maximum value of scalar triple product \([\overset{⃗}{u} \overset{⃗}{v} \overset{⃗}{w}]\) is

The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\), respectively are

If \(I_n = \int _0^{π/4}tan^nx dx,n\in N\) then \(I_{n+2}+I_n\) is equal to

The general solution of the differential equation \(\frac{dy}{dx}+\frac{y}{x} = x^2+5\) is ....

\(\int (x^{21}+x^6+x^3)(2x^{18}+7x^3+14)^{\frac{1}{3}} dx =\)

\(\int \frac{logx}{(1+logx)^2}dx =\)

\(\int \frac{1}{\sqrt{2x-x^2}}dx =\)

The value of the integral \(\int _{1/e}^e\frac{|logx|}{x^2}dx\) is

If \(\int _{-π/2}^{π/2}(sin^2x+sin^3x)dx = k\), then the value of \(k\)

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........