List of top Mathematics Questions asked in MHT CET

In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $\overline{PS} + \overline{QR} = t\overline{MN}$, then $t =$

The complex number with argument $\frac{5\pi}{6}$ at a distance of 2 units from the origin is

A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, is

The equation of the plane passing through $(-2,2,2)$ and $(2,-2,-2)$ and perpendicular to the plane $9x-13y-3z=0$ is

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

If $F(\alpha)=\begin{bmatrix}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{bmatrix}$, where $\alpha \in R$, then $[F(\alpha)]^{-1} =$

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

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

Negation of the statement $\forall x \in R, x^2+1=0$ is

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

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

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

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 $\lambda =$

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

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

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 $\text{Var}(X) =$

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

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

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

If $e^{-y} \cdot y = x$, then $\frac{dy}{dx}$ is

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

Evaluate the sum of the series: \[ \frac{1^2}{2} + \frac{1^2 + 2^2}{3} + \frac{1^2 + 2^2 + 3^2}{4} + \frac{1^2 + 2^2 + 3^2 + 4^2}{5} + \cdots \quad \text{upto 8 terms} \]

If \( a \), \( b \), \( c \) are non-negative distinct numbers and \( ai + aj + ck \), \( i + j + k \), and \( ci + cj + bk \) are coplanar vectors, then

The value of \( m \) if the vectors \[ \mathbf{A} = i - j - 6k, \quad \mathbf{B} = i - 3j + 4k, \quad \mathbf{C} = 2i - 5j + mk \] are coplanar, is

If \( \frac{1}{4}, a, b, \frac{1}{19} \) form a harmonic progression (H.P.), then the values of \( a \) and \( b \) are respectively