List of top Mathematics Questions asked in MHT CET

In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is \(\ldots\)

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by \(x^2-6xy+5y^2+10x-14y+9 = 0\) is \(\ldots\)

Let \(f_k(x) = \frac{1}{k}(cos^kx+sin^kx)\) where \(k\in N\), then \(f_6(x)-f_4(x) = \ldots\)

If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are \(0.6\), \(0.5\) and \(0.4\) respectively, while the probability of succeeding in both A and B is \(0.3\), in both B and C is \(0.2\), in both A and C is \(0.2\), and in all three is \(0.1\), then the probability that the student succeeds in exactly one of these tests is......

The maximum value of \(Z = 4x+5y\), subject to the constraints \(3x+y\leq 15,3x+4y\leq 24,x\geq 0,y\geq 0\) is

The coordinates of the point of intersection of the lines \(\frac{x-3}{1} = \frac{y-5}{2} = \frac{z-1}{-1}\) and \(\frac{x-4}{2} = \frac{y-2}{-1} = \frac{z-4}{2}\) are...

If the plane \(\overset{̄}{r} = (λ+μ)\hat{i}+(2+μ)\hat{j}+(3λ+2μ)\hat{k}\), where \(λ\) and \(μ\) are parameters, intersects coordinate axes at points \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\) then \(a+b+c =\)...

Let \(F(x)\) be the cumulative distribution function (c.d.f.) of a continuous random variable \(X\). If \(F(b) = 0.7\) and \(P(X > a) = 0.4\), then the value of \(P(a < X < b)\) is ...

A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

If \(\overset{̄}{a} = \hat{i}-\hat{k}\), \(\overset{̄}{b} = x\hat{i}+\hat{j}+(1-x)\hat{k}\) and \(\overset{̄}{c} = y\hat{i}+x\hat{j}+(1+x-y)\hat{k}\) then \([\overset{̄}{a} \overset{̄}{b} \overset{̄}{c}]\) depends on

The acute angle \(θ\) between the \(xy\)-plane and the plane passing through the point \((1,2,4)\) and parallel to the vectors with direction ratios \(3,2,-1\) and \(1,-2,-2\) is...

The line \(\ell\) passes through the point \((2,1,1)\) and is parallel to the plane \(x+y+2z = 18\). If line \(\ell\) intersects the line \(\frac{x+2}{3} = \frac{y+1}{-1} = \frac{z-2}{1}\), then equation of the line \(\ell\) is...

Let \(\overset{̄}{u},\overset{̄}{v},\overset{̄}{w}\) be three vectors such that \(|\overset{̄}{u}| = 1,|\overset{̄}{v}| = 2,|\overset{̄}{w}| = 3\). If the projection of \(\overset{̄}{v}\) along \(\overset{̄}{u}\) is equal to the projection of \(\overset{̄}{w}\) along \(\overset{̄}{u}\) and \(\overset{̄}{v},\overset{̄}{w}\) are perpendicular to each other, then \(|\overset{̄}{u}-\overset{̄}{v}+\overset{̄}{w}| =\)...

A vector which is orthogonal to the vector \(\overset{̄}{a} = \hat{i}+2\hat{j}+3\hat{k}\) and coplanar with the vectors \(\overset{̄}{b} = 3\hat{i}+2\hat{j}\) and \(\overset{̄}{c} = 2\hat{i}+\hat{j}+3\hat{k}\) is

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors of equal magnitude such that the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(α\), \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(β\), \(\overset{̄}{c}\) and \(\overset{̄}{a}\) is \(γ\).
Then the minimum value of \(cosα+cosβ+cosγ\) is ...

The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

The value of the definite integral \(\int _0^{log_e5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx\) is equal to...

If \([\cdot ]\) denotes the greatest integer function, then \(\int _0^{π/3}[tanx]\,dx =\)

The area (in square units) bounded by the line \(y = x\), the X-axis and the lines \(x = -2\) and \(x = 4\) is...

The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

If the side of an equilateral triangle increases at the rate of \(\sqrt{3} \text{cm/sec}\), then the rate of change of increase of its area when the side is \(12 \text{cm}\) is ____

If the line \(x+By+C = 0\) is the normal to the curve given by \(x = asin^3t\), \(y = bcos^3t\), (where \(a,b\neq 0\)) at a point \(t = \frac{π}{2}\), then \(B-C =\)

\(\int sin(logx)\,dx =\)