List of top Questions asked in MHT CET

If \(g\) is a differentiable function of \(x\) such that \(g(x^{5})=3x^{7}\), for \(x\neq 0\), \(x\in \mathbb{R}\) then \(g'(3125)=\ldots\)

Let \(3f(x)-2f\left(\frac{1}{x}\right)=x\) for \(x\neq 0\). Then the value of \(f'(2)\) is:

If \(y=\sin ^{-1}(y\cdot \cos 2x)\) such that \(\frac{dy}{dx}=\frac{2y\cdot f(x)}{g(x)-\cos y}\) then \(\{f(x)\}^{2}-\{g(x)\}^{2}=\)

The tangent to the curve \(y=e^{2x}\) is drawn at the point \(P(0,1)\). If this tangent intersects the \(x\)-axis at point \(A\) and the \(y\)-axis at point \(B\), then the area of \(\triangle OAB\) (where \(O\) is the origin) in square units is:

If \(\alpha \leq 2\sin ^{-1}x+\cos ^{-1}x\leq \beta\), then the values of \(\alpha\) and \(\beta\) are

If \(f(x)=\begin{cases} \frac{1-\sin ^{5}x}{5\cos ^{2}x} & ,x\lt \frac{\pi }{2} \\ a & ,\text{at }x=\frac{\pi }{2} \\ \frac{b(1-\sin x)}{8(\pi -2x)^{2}} & ,x>\frac{\pi }{2} \end{cases}\) is continuous at \(x=\frac{\pi }{2}\), then \(\left(\frac{b}{a}\right)^{\frac{5}{3}}=\ldots\)

If \(A=\begin{bmatrix} -\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & -\frac{1}{2} \end{bmatrix}\), the value of \(|\text{Adj}(A^{2026})|\) is equal to:

The negation of the inverse of \(\sim p\rightarrow q\) is equivalent to:

If \(A=\begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix}\), then \(A-A^{-1}=\)

Let \(A=\begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix}\) and \(A^{-1}=xA+yI\), then the pair \((x,y)=\cdots\)

The area (in sq.units) of a triangle formed by joining the vertex and the endpoints of the latus rectum of the parabola \(x^{2}=-20y\) is...

If one of the lines given by \(6x^{2}-xy+4ky^{2}=0\) is \(3x+4y=0\), then \(k\) lies in the interval:

The statement pattern \(p\rightarrow (q\rightarrow p)\equiv\)

The equation of the director circle of the circle \(x^{2}+y^{2}+3x-8y-3=0\) is:

\(\lim _{x\rightarrow \frac{\pi }{2}}\frac{[1-\tan (\frac{x}{2})](1-\sin x)}{[1+\tan (\frac{x}{2})](\pi -2x)^{3}}=\)

The equation of the line which passes through the point of intersection of lines \(x+2y+6=0\), \(2x-y=2\) and which makes intercept 5 on Y - axis is

The adjacent sides of a cyclic quadrilateral are 2 and 5, and the angle between them is \(60^{\circ }\). If the area of the quadrilateral is \(4\sqrt{3}\) sq. units then the perimeter of quadrilateral (in units) is:

There are 4 boys and 6 girls to be seated in a circle for a photograph. The probability that no two boys are sitting together is...

Everyone in the room handshakes with everyone else. If the total number of handshakes is 66, then the number of persons in the room is...

If \(P\) and \(P'\) denote respectively the circumcenter and the orthocenter of \(\triangle ABC\), then \(\overline{PA}+\overline{PB}+\overline{PC}=\)

If \(w=-\frac{1}{2}+\frac{i\sqrt{3}}{2}\), then the value of \(\begin{vmatrix} 1 & 1 & 1 \\ 1 & -1-w^{2} & w^{2} \\ 1 & w^{2} & w^{4} \end{vmatrix}\) is...

In \(\Delta ABC\), with the usual notations, if \(\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{6}=1\), then \(\frac{\sin A}{\sin B}=\ldots\)

Identify a polymer containing nitrogen.

Which of the following statements is true regarding fats?

Identify a monomer of natural rubber.