List of top Questions asked in MHT CET- 2026

The symmetric form of the equation of the line \(x = ay+b\), \(z = cy+d\) is

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

The solution of the differential equation \(\frac{dy}{dx} = \frac{a+bx}{c+dy}\) represents a family of circles centered at the origin if...

The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

If \(|\overset{⃗}{a}| = 3\), \(|\overset{⃗}{b}| = 4\), \(|\overset{⃗}{c}| = 5\) such that each vector is perpendicular to the sum of the other two, then \(|\overset{⃗}{a}+\overset{⃗}{b}+\overset{⃗}{c}|\) is equal to

The value of \(x\) so that the volume of the parallelopiped formed by the vectors \(\hat{i}+x\hat{j}+\hat{k}\), \(\hat{j}+x\hat{k}\) and \(x\hat{i}+\hat{k}\) is minimum, is

If \(A(\overset{⃗}{a})\), \(B(\overset{⃗}{b})\) and \(C(\overset{⃗}{c})\) are vertices of \(△ABC\). Point D divides segment BC internally in the ratio \(2:1\). Point E divides segment AD internally in the ratio \(1:2\), then the position vector of E is ____

If \(f(x) = \frac{1}{logx}\) and \(g(x) = \frac{1}{(logx)^2}\), then the value of \(\int [f(x)-g(x)]\,dx\) is...

The value of \(\int _2^4(\{x\}+[x])\,dx =\)...(where \(\{x\}\) and \([x]\) are the fractional part function and the greatest integer function, respectively)

The area (in sq. units) of the region enclosed by \(\{(x,y)|y\leq x^2,xy\leq 8,y\geq 1\}\) is...

If the area of the region bounded by the parabola \(y^2 = 4kx\) and the line \(x = k\), (where \(k > 0\)) is \(\frac{128}{3}\) sq. units, then the value of \(sin^{-1}(\frac{2}{k})\) is equal to...

If \(\int \frac{dx}{x^{7/2}(x^4+1)^{3/8}} = m(\frac{x^4+1}{x^4})^n+c\), where \(c\) is a constant of integration, then the value of \(\frac{n}{m}\) is...

If \([x]\) is the greatest integer function not greater than \(x\), then the value of \(\int _0^2x[x^2]\,dx\) is...

A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is \(4\) m and its volume is \(36\) cubic meters. For making a tank cost of base material used is Rs. \(100\) per sq. meter and that of sides is Rs. \(50\) per sq. meter. Then minimum cost of tank is ..............

The value of integral \(\int \frac{dx}{sin^2x+tan^2x}\) is...

The value of \(c\) satisfied by the Rolle's theorem for the function \(f(x) = x^2(1-x)^2\), \(x\in [0,1]\) is...

The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...

A particle is fired straight up from the ground. Its height in feet after \(t\) second is given by \(s(t) = 128t-16t^2\). The velocity of the particle when it hits the ground is...

\(\sum _{k = 1}^{2026}sin^{-1}(cos\frac{kπ}{4}) =\)

If \(sin^{-1}(tan\frac{π}{4})-sin^{-1}(\sqrt{\frac{3}{x}}) = \frac{π}{6}\) then \(x\) is a root of the equation

Let \(x = at^2-1\), where \(a > 0\) and \(y = t^3+1\). If at \(t = 1\), \(\frac{d^2y}{dx^2} = \frac{3}{16}\), then the value of \(a\) is...

If \(y = cot^{-1}(\frac{1+sin5x}{cos5x})\), then the value of \(\frac{dy}{dx}\) is

If \(y = sin(2sin^{-1}x)\) then \(\frac{dy}{dx} =\)..

If \(f(x) = x^2\) and \(g(x) = [x^2]\) where \([\cdot ]\) represents the greatest integer function then, \((f\circ g)(\frac{3}{2})+(g\circ f)(\frac{3}{2})\) is equal to ...

The logical statement \((p∨q)∧[(\sim p∧q)∨(p∧\sim q)]∧\sim q\) is logically equivalent to ...