If \(f(x)=\left\{\begin{array}{lc}x^2+1 & x \lt 0 \\ x^3-a & 0 \leq x \lt 1 \text { and it is continuous } \\ 2 b-x & x \geq 1\end{array}\right.\) \(\forall x \in R\), then

If the straight lines \(\dfrac{x-2}{1}=\dfrac{y-3}{1}=\dfrac{z-4}{-t}\) and \(\dfrac{x-1}{t}=\dfrac{y-4}{2}=\dfrac{z-5}{1}\) are intersecting then \(t\) can have

The centre of the circle passing through \((0,0)\) and \((1,0)\) and touching the circle \(x^2+y^2=9\) is

The probability distribution of a discrete random variable X is given as

X	1	2	4	2A	3A	5A
P(X)	\(\dfrac{1}{2}\)	\(\dfrac{1}{5}\)	\(\dfrac{3}{25}\)	K	\(\dfrac{1}{25}\)	\(\dfrac{1}{25}\)

\(\text { Then the value of } A \text { if } E(X)=2.94 \text { is }\)

\(\text { The area (in sq units) enclosed by the parabola } y^2=8 x \text {, its latus-rectum and the } x \text {-axis is }\)

If the angles of a triangle are in the ratio \(3: 4: 5\), then the sides are in the ratio

If \(\int \dfrac{1}{\sqrt{\sin ^3 x \cos x}} d x=\dfrac{k}{\sqrt{\tan x}}+c\) then the value of \(k\) is

The area of the region bounded by the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\) is

The resistance of a galvanometer is \(2.5 \Omega\) and it requires \(50 \mathrm{~mA}\) for full scale deflection. The value of shunt resistance required to convert it into an ammeter of range 0 to \(5 \mathrm{~A}\) is

For all gases, at any given pressure, the graph of volume \(v s\) temperature (in celsius) is a straight line. This graph is called

Which one of the following structures in Column I does not have the correct IUPAC name as given in Column II.
\(\begin{array}{|c|l|l|} \hline \text { S.No. } & \text { Structure } & \text { IUPAC name. } \\ \hline \text { A } & {\left[\mathrm{CoBr} r_2(\mathrm{en})_2\right] \mathrm{Cl}} & \text { Dibromidodi-( ethan-1, 2 - diamine)cobalt (III) chloride } \\ \hline \text { B } & \mathrm{Na}\left[\mathrm{PtBrCl}\left(\mathrm{NO}_2\right)\left(\mathrm{NH}_3\right)\right] & \text { Sodium amminebromidochloridonitrito- N- palatinate(II) } \\ \hline \text { C } & {\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_2\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}\right] \mathrm{SO}_4} & \text { Tetraamminediaquachloridochromium (III) sulphate. } \\ \hline \text { D } & {\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{PtCl}_4\right]} & \text { Tetraammineplatinum (II) tetrachloridoplatinate (II) } \\ \hline \end{array}\)

A balloon is rising vertically up with a velocity of \(29 \mathrm{~ms}^{-1}\), A stone is dropped from it and it reaches the ground in \(10 \mathrm{~s}\). The height of the balloon when the stone was dropped from it is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

A wire of \(24 \Omega\) resistance is bent to form a square loop. A 10 V battery negligible internal resistance is connected across the diagonals of the square loop. The potential drop across one of its sides is: