List of top Mathematics Questions asked in MHT CET

The equation of the plane passing through the points \( (2, 3, 1), (4, -5, 3) \) and parallel to the y-axis is

The adjoint of the matrix \[ A = \begin{pmatrix} 2 & 3
-3 & 5 \end{pmatrix} \] is

The probability that a bomb will miss the target is 0.2. Then the probability that out of 10 bombs dropped exactly 2 will hit the target is

If \( A \) and \( B \) are independent events such that odds in favour of \( A \) is 2:3 and odds against \( B \) is 4:5, then \( P(A \cap B) = \)

Given $X\sim B(n,p)$, if $E(X)=4$ and $\text{Var}(X)=2.4$, then $n=$

The general solutions of $\sin^2x\cdot\sec x=\tan x-\sin x+1$ are

If the p.m.f. of a random variable $X$ is given by
\[ \begin{array}{c|ccc} x & 0 & 1 & 2 \\ P(X=x) & q^2 & 2pq & p^2 \end{array} \] then, the standard deviation of $X$ is (given $p+q=1$)

The eccentricity of a rectangular hyperbola is

The c.d.f. $F(x)$ of a discrete random variable $X$ is given by
\[ \begin{array}{c|cccccccc} X & -3 & -1 & 0 & 1 & 3 & 5 & 7 & 9 \\ F(X) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \end{array} \] Then $P(X=3)=$

The direction ratios of the line perpendicular to the lines having direction ratios $2,3,1$ and $1,2,1$ are

If $a,b,c$ are distinct positive numbers and the vectors $a\hat i+a\hat j+c\hat k,\ \hat i+\hat k$ and $c\hat i+c\hat j+b\hat k$ lie in a plane, then

The negation of the statement “If $5<7$ and $7>2$, then $5>2$” is

If $\displaystyle \int \frac{x^2+1}{(x-3)(x-2)}\,dx = Px + Q\log|x-3| + R\log|x-2| + c$, where $c$ is constant of integration, then the values of $P,Q,R$ are respectively

Evaluate $\displaystyle \int_{-2}^{2} [x]\,dx$, where $[x]$ denotes the greatest integer function

The separate equations of the lines represented by $4x^2 - y^2 + 2x + y = 0$ are

The dual of the statement `Mangoes are delicious but expensive' is

The angle between the lines $\vec r = (2\hat i + \hat j - 3\hat k) + \lambda(\hat i - \hat j + \hat k)$ and $\dfrac{x-1}{1} = \dfrac{y+2}{3} = \dfrac{z-3}{2}$ is

If $AX = B$, where $A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4 \end{bmatrix}$, $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $B = \begin{bmatrix} 12 \\ 15 \\ 13 \end{bmatrix}$, then $x^2 + y^2 + z^2 =$

If $Z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$, $x \ge 0$, $y \ge 0$, then $Z$ is maximum at the point

A problem in statistics is given to three students $P$, $Q$ and $R$. Their chances of solving the problem are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently, then the probability that the problem is solved is

The vector equation of the line \[ \frac{x+3}{2}=\frac{2y-3}{5}, \quad z=-1 \] is

If \(\tan A = \dfrac{5}{6}\), \(\tan B = \dfrac{1}{11}\), then find \(A + B\).

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

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