List of top Mathematics Questions asked in MHT CET

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the store will receive at most one defective bulb is

The differential equation of family of circles whose centres lie on X-axis is

The general solution of the differential equation $y(1+\log x)\left(\frac{dx}{dy}\right) - x\log x = 0$ is

The area of the region bounded by the curve $y^2 = 4x$ and the line $y = x$ is

If $\frac{\cos(A+B)}{\cos(A-B)} = \frac{\sin(C+D)}{\sin(C-D)}$, then $\tan A \tan B \tan C =$

If the lines $\frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{z-3}{2}$ and $\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles, then $\lambda =$

The vertices of triangle ABC are $A \equiv (3,0,0) ; B \equiv (0,0,4) ; C \equiv (0,5,4)$. Find the position vector of the point in which the bisector of angle A meets BC is

If the two lines given by $ax^2 + 2hxy + by^2 = 0$ make inclinations $\alpha$ and $\beta$, then $\tan(\alpha + \beta) =$

The distance between parallel lines $\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 2\hat{k})$ and $\bar{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 2\hat{k})$ is

In a meeting 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take $X = 0$ if he opposed and $X = 1$ if he is in favour, then $\text{Var}(X) =$

The general solution of the differential equation $(3xy + y^2)dx + (x^2 + xy)dy = 0$ is

$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$, then $\tan \theta=$

$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=$

The area of the parallelogram with vertices \( A(1, 2, 3) \), \( B(1, 3, a) \), \( C(3, 8, 6) \) and \( D(3, 7, 3) \) is \( \sqrt{265} \) sq. units, then \( a = \)

If \( y = \tan^{-1} \left\{ \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right\} \), then \( \frac{dy}{dx} = \)

If \( y = \tan^{-1} \left( \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right) \), then \( \frac{dy}{dx} = \)

With usual notations, perimeter of a triangle \( ABC \) is 6 times the arithmetic mean of sine of its angles. If \( a = 1 \), then measure of angle \( A = \)

If \( m \) is order and \( n \) is degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^5 + 4 \left( \frac{\frac{d^2y}{dx^2}}{\frac{d^3y}{dx^3}} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 \] then

Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)

If \( \theta + \phi = \alpha \) and \( \tan \theta = k \tan \phi \) (where \( k > 1 \)), then the value of \( \sin(\theta - \phi) \) is

If \( p \to (\sim p \lor q) \) is false, then the truth values of \( p \) and \( q \) are, respectively

If \[ \int \frac{5 \tan x}{\tan x - 2} dx = x + a \log | \sin x - 2 \cos x | + c \], then \( a = \) (Where \( c \) is constant of integration)

The general solution of the differential equation. \[ \left( \frac{y}{x} \right) \cos \left( \frac{y}{x} \right) dx - \left[ \left( \frac{x}{y} \right) \sin \left( \frac{y}{x} \right) + \cos \left( \frac{y}{x} \right) \right] dy = 0 \] is

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3, ₹ 1.5, ₹ 1 and ₹ 2. The demands for these cakes are 20%, 5%, 10%, 50% and 15% respectively, then the expected profit per cake is