List of top Questions asked in MHT CET

If \(\vec u = \hat i - 2\hat j + \hat k\), \(\vec v = 3\hat i + \hat k\) and \(\vec w = \hat j - \hat k\), then the volume of the parallelepiped with \(\vec u \times \vec v\), \(\vec u + \vec w\) and \(\vec v + \vec w\) as coterminous edges is

Evaluate \[ \int_{2}^{3} \frac{dx}{x^2 + x} \]

If \(\sqrt{x} + \sqrt{y} = \sqrt{xy}\), then find \(\dfrac{dy}{dx}\).

If \(A, B, C\) are the angles of \(\triangle ABC\), then with usual notations, \[ \frac{c^2 - a^2 + b^2}{a^2 - b^2 + c^2} = \]

The domain of the real valued function \[ f(x) = \frac{x + 2}{9 - x^2} \] is

The differential equation whose solution is \(y = e^{ax}\) is

A body cools according to Newton’s law from \(100^\circ\text{C}\) to \(60^\circ\text{C}\) in 20 minutes. The temperature of the surroundings being \(20^\circ\text{C}\), the temperature of the body after one hour is

If \(A(3,-2,2)\), \(B(2,\lambda+1,5)\) are the end points of the diameter of a circle and if the point \((5,6,-1)\) lies on the circle, then \(\lambda =\)

The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is

An urn contains 4 red and 5 white balls. Two balls are drawn one after the other without replacement. Find the probability that both the balls are red.

The joint equation of two lines through the origin, each of which makes an angle of \(30^\circ\) with the line \(x + y = 0\), is

If \(\displaystyle \sin\!\left(\frac{x+y}{x-y}\right) = \tan \frac{\pi}{5}\), then find \(\displaystyle \frac{dy}{dx}\).

The probability mass function of a random variable \(X\) is given by \[ P(X = x) = \frac{5cx}{2^5}, \quad x = 0,1,2,3,4,5 \] \[ P(X = x) = 0, \quad \text{otherwise} \] Then find \(P(X \le 2)\).

If \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}, \] then find \((AB)^{-1}\).

Identify basic amino acid from following

If $2.0$ g of NaOH is dissolved in $500\ \text{cm^3$ of water, what is molarity of solution ?}

Find the value of the following expression:
\[ 5^2 + 6^2 + 7^2 + \cdots + 20^2 = \]

The probability density function of a random variable \(X\) is given by \[ f(x) = \frac{k}{\sqrt{x}}, \quad 0 \le x \le 4 \] \[ f(x) = 0, \quad \text{otherwise} \] Find \(P(1<X<4)\).

The acute angle between the line \[ \vec{r} = (i + 2j + k) + \lambda (i + j + k) \] and the plane \[ \vec{r} \cdot (2i - j + k) = 5 \] is

With usual notations in \( \triangle ABC \), \(a = 3\), \(c = 2\) and \(\sin C = \dfrac{2}{3}\), then \(\angle A =\)

Which of the following equations has $\Delta_f H^\circ$ and $\Delta H^\circ$ same ?

Separation of Acetone and Benzene from their mixture is carried out by

Which gas among the following contains maximum number of molecules at STP ?
(Molar masses in g mol$^{-1}$: CO$_2$ = 44, Ar = 39.9, CH$_4$ = 16, O$_2$ = 32)

How many isomers of monobromoderivatives are obtained on bromination of the following compound ?

When soap is added on an oily part of cloth, the hydrocarbon part of soap dissolves in