List of top Questions asked in MHT CET- 2020

Identify compound ‘B’ in following series of reactions?

Identify 'A' in the following reaction: 
\(\text{2 A + (C\(_6\)H\(_5\)CH\(_2\))\(_2\)Cd $\xrightarrow{}$ 2 CH\(_3\)-C-CH\(_2\)-C\(_6\)H\(_5\) + CdCl\(_2\)} \)
 

Identify the catalyst X used in the following reaction:
CH\(_3\)CH\(_2\)Br + 2[H] \(\xrightarrow{X}\) CH\(_3\)CH\(_3\) + HBr
What is the bond order of B\(_2\) molecule?
Which one of the following statements is NOT the property of light?
On mixing a highly soluble impurity in water, the surface tension \(T\) and angle of contact \(\theta\)
If \( A(-1,2,3) \), \( B(3,-2,1) \), \( C(2,1,3) \) and \( D(-1,-2,4) \) are the vertices of a tetrahedron, then its volume is
If \[ |3x - 2| \leq \frac{1}{2}, \] then \( x \in \)
The distance of the point \( (3,4,5) \) from the point of intersection of the line \[ \frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2} \] and the plane \( x+y+z=2 \) is
Simplify \( \cos\left(\dfrac{3\pi}{4}+x\right) - \sin\left(\dfrac{\pi}{4}-x\right) \)

If \[ y = \cot^{-1}\!\left(\sqrt{\frac{1-\sin x}{1+\sin x}}\right), \quad \text{then find} \quad \frac{dy}{dx}. \]

Evaluate the integral \[ \int_0^\infty \frac{dx}{(x^2 + 4)(x^2 + 9)} = \]
If \[ \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} \neq 0, \quad \text{then} \quad \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} = \]
If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively
If \( \frac{1-\tan\theta}{1+\tan\theta} = \frac{1}{\sqrt{3}}, \) where \( \theta \in \left(0,\frac{\pi}{2}\right) \), then \( \theta = \)
If $A$ and $B$ are two angles such that $A,B\in(0,\pi)$ and they are not supplementary angles such that $\sin A-\sin B=0$, then
The rate of decay of mass of a certain substance at time \( t \) is proportional to the mass at that instant. The time during which the original mass of \( m_0 \) gm will be left to \( m_1 \) gm is
The co-ordinates of the mid-point of the chord cut off by the line \( 2x - 5y + 18 = 0 \) by the circle \( x^2 + y^2 - 6x + 2y - 54 = 0 \) are
If the foot of perpendicular drawn from the origin to the plane is \( (3, 2, 1) \), then the equation of the plane is
If \( n(X) = 700 \), \( n(A) = 200 \), \( n(B) = 300 \), \( n(A \cap B) = 100 \), where \( X \) is the universal set and \( A \) and \( B \) are subsets of \( X \), then \( n(A' \cap B') = \)
Evaluate the integral \[ \int \frac{dx}{\sqrt{(x - 1)(x - 2)}} = \text{?}
The angle between the lines \( \frac{x - 1}{4} = \frac{y - 3}{1} = \frac{z}{8} \) and \( \frac{x - 2}{2} = \frac{y + 1}{2} = \frac{z - 4}{1} \) is
The rate of decay of a certain substance is directly proportional to the amount present at that instant. Initially, there are 27 grams of the substance and 3 hours later it is found that 8 grams are left, then the amount left after one more hour is
Evaluate the integral \[ \int \frac{dx}{\sqrt{5 + 4x - x^2}} = \]
The differential equation obtained from the function \( y = a(x - a)^2 \) is