List of top Questions asked in MHT CET- 2020

If the line \( \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \) is parallel to the plane \( \vec{r} = (3i - 2j - mk) = 5 \), then the value of \( m \) is

The integral \[ \int_0^a \frac{x}{\sqrt{a - x}} \, dx = \]

If the origin is the centroid of the triangle whose vertices are \( A(2, p, -3) \), \( B(q, -2, 5) \) and \( C(-5, 1, r) \), then

If \( P(A) = \frac{2}{5}, \, P(B) = \frac{1}{4}, \, P(A \cup B) = \frac{1}{2}, \) then \( P(A' \cup B') = \)

Evaluate the integral: \[ \int e^{\cos^{-1}x} \left[ x - \sqrt{1 - x^2} \right] \frac{dx}{\sqrt{1 - x^2}}. \]

The probability that a person who undergoes a certain operation will survive is 0.2. If 5 patients undergo similar operations, find the probability that exactly four will survive.

If \( x^2 + y^2 = 1 \), then find \( \dfrac{d^2x}{dy^2} \).

Evaluate \( \displaystyle \int_{-\pi}^{\pi} \frac{2x}{1+\cos^2 x}\,dx \)

If \( f(x) = \frac{3x+4}{5x-7} \), \( x \neq \frac{7}{5} \), and \( g(x) = \frac{7x+4}{5x-3} \), \( x \neq \frac{3}{5} \), then \[ (g \circ f)(3) = \]

Evaluate \( \displaystyle \int_{0}^{1} \tan^{-1}\!\left(\frac{2x}{1-x^2}\right)\,dx \)

If one of the lines given by the equation \( x^2 + kxy + 2y^2 = 0 \) is \( x + 2y = 0 \), then the value of \( k \) is

If \( X \sim B(4, p) \) and \( 2 P(X = 3) = 3 P(X = 2) \), then the value of \( p \) is:

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{1 + \sin^4 x} \, dx = \]

If \( A = \begin{bmatrix} 1 & 1 \\ 2 & 1 \end{bmatrix}, B = \begin{bmatrix} 4 & 3 \\ 1 & 1 \end{bmatrix} \), then \( (A + B)^{-1x} = \)

If \[ A = \{2, 4\}, \quad B = \{3, 4, 5\}, \quad \text{then} \quad (A \cap B) \times (A \cup B) = \]

If \(\vec a, \vec b, \vec c, \vec d\) are the position vectors of the points \(A,B,C,D\) respectively such that \[ 3\vec a - \vec b + 2\vec c - 4\vec d = \vec 0, \] then the position vector of the point of intersection of the line segments \(AC\) and \(BD\) is

If the points $A(2,1,-1)$, $B(0,-1,0)$, $C(4,0,4)$ and $D(2,0,x)$ are coplanar, then $x=$

If $\omega$ is a complex cube root of unity and $A=\begin{pmatrix}\omega & 0\\0 & \omega\end{pmatrix}$, then $A^{-1}=$

If the Cartesian equation of the line is \[ x - 1 = 2y + 3 = 3 - z, \] then its vector equation is

Evaluate the integral \[ \int \frac{x^2+1}{x^4+x^2+1}\,dx \]

If the tangent to the curve given by \( x = t^2 - 1 \) and \( y = t^2 - t \) is parallel to the x-axis, then the value of \( t \) is

If \( y\sqrt{1-x^2} + x\sqrt{1-y^2} = 1 \), then \( \dfrac{dy}{dx} = \)

Evaluate \( \int_{-4}^{4} \log \left( \frac{8 - x}{8 + x} \right) dx \)

If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is

The statement pattern \( \sim (p \vee q) \vee (\sim p \wedge q) \) is equivalent to