List of top Questions asked in MHT CET- 2026

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 ...
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
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 ...
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 equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is
The area (in square units) bounded by the line \(y = x\), the X-axis and the lines \(x = -2\) and \(x = 4\) is...
If the tangent to the curve \(xy+ax+by = 0\) at \((1,1)\) makes an angle of \(tan^{-1}2\) with positive direction of the \(x\)-axis, then the value of \(\frac{ab}{a+b}\) is...
The value of \(\int \frac{n\sqrt{\text{cosec}^2x^n-1}}{x^{(1-n)}}\,dx\) 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 \(B-C =\)
\(\int sin(logx)\,dx =\)
\(\int \frac{(x+1)\,dx}{x(1+xe^x)} = \ldots \ldots\)
The number of point / points where the function \(f(x) = \frac{1}{x^2-5|x|+6}\) is discontinuous is......
If \(0\leq x\leq 1\) and \((sin^{-1}x)^3+(cos^{-1}x)^3 = aπ^3\) then
If \(g(x) = (x^2+2x+1)\cdot f(x)\) such that \(f(0) = 5\) and \(\underset{x\rightarrow 0}{lim}\frac{f(x)-5}{x} = 4\) then \(g^'(0) =\)
If \(\sum _{n = 1}^{2026}tan^{-1}(\frac{1}{n^2+n+1}) = tan^{-1}(1-\frac{1}{x})\), where \(x\neq 0\), then \(x =\)
If \(x\,e^{xy} = y+sin^2x\), then the value of \(\frac{dy}{dx}\) at \(x = 0\) is equal to
Let \(f(x) = ax+b\) and \(g(x) = cx+d\). The condition \(f(g(x)) = g(f(x))\) holds for all \(x\) if and only if ...
Let \(A = [\begin{array}{cc}3 & -4 \\ 1 & -1\end{array}]\) and \(B = [\begin{array}{cc}6 & -13 \\ 5 & -10\end{array}]\) be two matrices. If the variables \(x\) and \(y\) satisfy the matrix equation \(((A^{-1})^2+B)[\begin{array}{c}x \\ y\end{array}] = [\begin{array}{c}0 \\ 0\end{array}]\), then the ordered pair \((x,y) =\)
Let \(t\in (0,1)\) and \(α\in (0,\frac{π}{4})\). If \(x = \text{cosec}^{-1}(\frac{1+t^2}{2t})\), \(y = cot^{-1}(\frac{\sqrt{1-t^2}}{t})\) and \(\frac{dy}{dx} = f(t)\), then the value of \(f(tanα)\) is
If \(y = tan^{-1}⎛⎝\frac{log(\frac{e}{x^3})}{logex^3}⎞⎠+tan^{-1}⎛⎝\frac{log(e^4x^3)}{log(\frac{e}{x^{12}})}⎞⎠\), \(x\in (e^{-\frac{1}{3}},e^{\frac{1}{12}})\) then \(\frac{dy}{dx}\) is equal to...
Let \(A = \left[ \begin{array}{ccc}cosα & -sinα & 0 \\ sinα & cosα & 0 \\ 0 & 0 & 1\end{array} \right]\). If \(B = \text{adj}\,A\), then the matrix \(B^{-1}\) is equal to...
If \(0\leq x\leq 1\), \(I_1 = \int sin^{-1}\sqrt{1-x^2}\,dx\) and \(I_2 = \int sin^{-1}x\,dx\), then which of the following is true?