List of top Mathematics Questions asked in MHT CET

The smallest positive integer \(n\) for which \(\frac{(1+i)^n}{(1-i)^{n-2}}\) is a real number, is ...

A straight line L passes through the point of intersection of the lines \(x-y+1 = 0\) and \(2x+y-7 = 0\). If L intersects the positive x-axis at \(A(a,0)\) and the positive y-axis at \(B(0,b)\), then the minimum area of the triangle \(OAB\) (where \(O\) is the origin) is ....

Let \(a\) be an integer selected at random from the set \(\{0,1,2,3,\ldots ,9\}\). The probability that the equation \(ax^2-ax+1 = 0\) has real roots is ...

The maximum value of \(z = 4x+y\) subject to the constraints \(x+y\leq 5,2x+y\leq 7,3x+2y\leq 11,x\geq 0,y\geq 0\) is \(\ldots\)

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is \(\ldots\)

The acute angle between the lines \(2x = 3y = -z\) and \(6x = -y = -4z\) is \(\ldots\)

In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

If the p. d. f. of a continuous random variable X is given by \(f(x) = \{\begin{array}{cc}k(9+8x-x^2), & \text{for }-1\leq x\leq 4 \\ 0, & \text{otherwise}\end{array}\) then the value of \(k\) is \(\ldots\)

If the equation of a plane passing through \(A(1,p,2)\), \(B(3,2,4)\) and parallel to the z axis, is \(3x-2y-q = 0\), then \(\ldots\)

The value of \(θ\in (0,\frac{π}{2})\) for which vectors \(\overset{̄}{a} = (sinθ)\hat{i}+(cosθ)\hat{j}\) and \(\overset{̄}{b} = \hat{i}-\sqrt{3}\hat{j}+2\hat{k}\) are perpendicular is

The angle between the line \(\overset{̄}{r} = (\hat{i}+2\hat{j}+\hat{k})+λ(\hat{i}+\hat{j}+\hat{k})\) and the plane \(\overset{̄}{r}\cdot (2\hat{i}-\hat{j}+\hat{k}) = 8\) is \(\ldots\)

If \(\overset{̄}{a}\cdot \overset{̄}{b} = β\) and \(\overset{̄}{a}\times \overset{̄}{b} = \overset{̄}{c}\) then \(\overset{̄}{a} =\)

If \(|\overset{̄}{a}| = |\overset{̄}{b}| = 1,|\overset{̄}{c}| = 2\) and \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is \(\ldots\)

The value of \(|\overset{̄}{a}\cdot \overset{̄}{b}|^2+|\overset{̄}{a}\times \overset{̄}{b}|\cdot |\overset{̄}{a}\times \overset{̄}{b}|\) is \(\ldots\)

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

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

The equation of the plane passing through the points having position vectors \((\overset{̄}{a}+\overset{̄}{b}),(\overset{̄}{b}+\overset{̄}{c})\) and \((\overset{̄}{a}+\overset{̄}{c})\) is \(\ldots\)

The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

If the volume of the tetrahedron whose coterminous edges are given by the vectors \(\overset{̄}{a} = -2\hat{i}+3\hat{j}-3\hat{k}\), \(\overset{̄}{b} = 4\hat{i}+5\hat{j}+(λ-10)\hat{k}\), \(\overset{̄}{c} = 6\hat{i}+2\hat{j}-3\hat{k}\) is 11 cubic units, then the sum of the possible values of \(λ\) is \(\ldots\)

If the area bounded by \(y = x^3+ax\) (where \(a > 0\)), the \(x\)-axis and the lines \(x = -2\) and \(x = 1\) is \(\frac{37}{4}\) square units, then \(\ldots\)

\(\int _0^2|4x-5|\,dx = \ldots\)

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

Let \(f(x) = x\), \(f_1(x) = f(logx)\), \(f_2(x) = f_1(logx)\), \(f_3(x) = f_2(logx)\), \(\ldots\) and so on. Then \(\int \frac{1}{f(x)\,f_1(x)\,f_2(x)\,\ldots f_{2026}(x)}\,dx = \ldots\)

If \(\int _0^2x(2-x)^b\,dx = \frac{32}{7}\), where \(b\in N\) then \(b =\)