A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least $2$ successes is

The area (in square units) of the region bounded by the curves \(x=y^2\) and \(x=3-2 y^2\) is

If \(\frac{x^3}{(2 x-1)(x+2)(x-3)}=A+\frac{B}{2 x-1}+\frac{C}{x+2}\) \(+\frac{D}{x-3}\), then \(A\) is equal to

If \(\sin \theta=-\frac{3}{4}\), then \(\sin 2 \theta=\)

If \(\frac{-x^2+6 x+1}{(x-1)^2\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x-3}{x^2+2}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}=\)

If \((a, b)\) is the common point for the circles \(x^2+y^2-4 x+4 y-1=0\) and \(x^2+y^2+2 x-4 y+1=0\), then \(a^2+b^2=\)

\(\cos 20^{\circ}+\cos 30^{\circ}+\cos 40^{\circ}=\)

A variable line passing through a fixed point \((\alpha, \beta)\) intersects the coordinate axes at \(A\) and \(B\). If \(O\) is the origin, then the locus of the centroid of the \(\triangle O A B\) is

\(\begin{aligned} & \text { If } \cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\frac{a}{\sqrt{b^2-a^2}}\right)\right\}: \\ & b>a, \text { then } \mathrm{x}=\end{aligned}\)

When the lead storage battery is in use (during discharge) the reaction that occurs at the anode is

The following configuration of gates is equivalent to

Vitamin-A is called

Match the following lists.
\begin{array}{|c|c|c|c|}
\hline & List I & & List II \\
\hline A & \begin{array}{l}\text { Zeroth law of } \\
\text { thermodynamics }\end{array} & 1 & \begin{array}{l}\text { Direction of flow of } \\
\text { heat }\end{array} \\
\hline B & \begin{array}{l}\text { First law of } \\
\text { thermodynamics }\end{array} & \| & Work done is zero \\
\hline\underline{\mathrm{C}} & Free expansion of a gas & III & Thermal equilibrium \\
\hline D & \begin{array}{l}\text { Second law of } \\
\text { Thermodynamics }\end{array} & IV & \begin{array}{l}\text { Law of conservation } \\
\text { of energy }\end{array} \\
\hline
\end{array}
The correct answer is
\(\begin{array}{lccccccccc} & \text { A } & \text { B } & \text { C } & \text { D } \end{array}\)