List of top Questions asked in MHT CET

The process during double fertilization in which non motile male gametes are carried through hollow pollen tube is called

What is the oxidation state of Phosphorus in \(H_3PO_4\)?

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

Which of the following is a soft metal?

Which of the following does not belong to Group 16 elements?

If \( n \in \mathbb{Z} \), then the expression \[ \frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n} \] is equal to:

If \( \sin x \cos x = \frac{1}{4} \), then the general solution is:

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to:

The ratio of specific heats $C_{p}/C_{v}$ for a mixture of 1 mole of helium and 1 mole of hydrogen is:

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to:

Solve the differential equation \( \frac{dy}{dx} = \frac{1+y^2}{1+x^2} \) given \(y(0)=1\).

Who coined the term “Root Pressure Theory”?

Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

Evaluate: \(\tan^{-1}(1) + \tan^{-1}(4) + \tan^{-1}(5) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\). Find the value of \(\alpha\).

The species-area relationship is represented on a log scale as

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

If \[ \left(\frac{2+\sin x}{1+y}\right)\frac{dy}{dx}=-\cos x \] and \[ y(0)=2, \] then find the value of \[ y\left(\frac{\pi}{2}\right). \]

If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \[ y(0)=1, \] then find the value of \[ y\left(\frac{\pi}{2}\right). \]

The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

If y = y(x) satisfies the differential equation \[ \left(\frac{2+\sin x}{1+y}\right)\frac{dy}{dx}=-\cos x \] and \( y(0)=2 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:

Let \[ \vec a=\hat i+\hat j+\hat k \] \[ \vec b=\hat i-\hat j+2\hat k \] If a vector \( \vec c \) is coplanar with \( \vec a \) and \( \vec b \) such that \[ \vec c\cdot \vec a=1 \] and \[ \vec c\cdot \vec b=2 \] then \( \vec c \) is:

If \[ y=(x-1)(x-2)(x-3)\cdots(x-100) \] and the value of \( \dfrac{dy}{dx} \) at \(x=0\) is equal to \[ \lambda\left(\frac{100!}{^{100}C_5}\right) \] then \( \lambda \) is: