When one end of a capillary tube is dipped in water, the height of water column is ' \(h\) '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is
(Surface tension of water \(=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) )
In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength \(5000 \mathop {\rm{A}}\limits^{\rm{o}}\). Without disturbing the set up of the experiment, the source of light is replaced by a source of wavelength \(6400 \mathop {\rm{A}}\limits^{\rm{o}}\).
The fringe width will
The probability distribution of a random variable X is given by\[ \begin{array}{|l|c|c|c|c|c|} \hline \mathrm{X}=x_i & 0 & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}\left(\mathrm{X}=x_i\right) & 0.4 & 0.3 & 0.1 & 0.1 & 0.1 \\ \hline \end{array} \]
Then the variance of X is
\[ \int \sqrt{x^2+3 x} d x= \]
\[ \int \frac{x}{1+x^4} d x= \]
Let \(\mathrm{A} \equiv(0,0), \mathrm{B}(3,0), \mathrm{C}(0,-4)\) are vertices of \(\triangle A B C\), then the co-ordinates of incentre of \(\triangle \mathrm{ABC}\) is
Which of the following compounds has difficulty in breaking of \(\mathrm{C}-\mathrm{X}\) bond?
Which from following is a polyester fibre?
\[ \text { Which of the following is NOT phenol? } \]
The foci of the conic \(25 x^2+16 y^2-150 x=175\) are
The motion of the particle is given by the equation \(\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}\).
The motion of the particle is
A solid cylinder of length \(l\) and cross-sectional area \(\frac{a}{5}\) is immersed such that it floats with its axis vertical at the liquid-liquid interface with length \(l / 4\) in the denser liquid as shown in figure. The lower density liquid ( \(\rho\) ) is open to atmosphere having pressure \(\mathrm{P}_0\). The density d of solid cylinder is
Identify the major product formed in the following reaction.
Chlorobenzene \(\xrightarrow[\text { Antilyctous } \mathrm{FeCl}_3]{\mathrm{Cl}_2}\) Product
If the point \((1, \alpha, \beta)\) lies on the line of the shortest distance between the lines \(\frac{x+2}{-3}=\frac{y-2}{4}=\frac{z-5}{2}\) and \(\frac{x+2}{-1}=\frac{y+6}{2}, \mathrm{z}=1\), then \(\alpha+\beta=\)
\[ \int \frac{x^3}{x^4+5 x^2+4} d x= \]
The differential equation satisfied by \(y = X\sin(6t+5) + Y\cos(6t+5)\) (where \(X\) and \(Y\) are constants) is
\[ \mathop {\lim }\limits_{x \to 1}\left(\log _3 3 x\right)^{\log _x 8}=\ldots \]
\[ \int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x d x= \]
Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is
Given \(\quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})\) and \(\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C}\) will be
In the logic circuit given, \(\mathrm{A}, \mathrm{B}\) and C are the inputs and Y is the output. The output Y is HIGH
In an a.c. circuit containing \(L, C\) and \(R\) in series, the ratio of apparent power to the true power is (\(Z\) and \(R\) are the impedance and resistance respectively, \(\phi\) = phase angle)
Identify from following reactions that exhibits negative work done.
If \(x=\operatorname{acos}^3 \theta y=\operatorname{asin}^3 \theta\)
Then \(\sqrt{1+\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2}=\)
