List of top Mathematics Questions asked in MHT CET

If for the harmonic progression, \( t_7 = \frac{1}{10}, \, t_{12} = \frac{1}{25}, \) then \( t_{20} = \)

The domain of the function \( f(x) = \sqrt{x} \) is

If the length of perpendicular drawn from the point $(4,1)$ on the line $3x - 4y + k = 0$ is $2$ units, then the values of $k$ are

The value of \( \sin^{-1} \left( -\frac{1}{2} \right) + \cos^{-1} \left( -\frac{\sqrt{3}}{2} \right) \) is

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

If the points \( A(5, k) \), \( B(-3, 1) \) and \( C(-7, -2) \) are collinear, then \( k = \)

Evaluate \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)

If for an Arithmetic progression, 9 times the ninth term is equal to 13 times the thirteenth term, then the value of the twenty-second term is

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

For a sequence \( (t_n) \), if \( s_n = 7(3^n - 1) \), then \( t_n = \)

The equation of a line passing through the point of intersection of the lines \[ x + 2y + 8 = 0 \quad \text{and} \quad 3x - y + 4 = 0 \] and having x– and y–intercepts zero is

If $\vec a,\vec b,\vec c$ are nonzero vectors along the coterminous edges of a parallelepiped with volume $7$ cubic units, then the volume of the parallelepiped with $\vec a+\vec b,\ \vec b+\vec c,\ \vec c+\vec a$ as the coterminous edges 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