The weight of man in a stationary lift is \(w_1\) and when it is moving downwards with uniform acceleration ' a ' is \(\mathrm{w}_2\). If the ratio \(\mathrm{w}_1: \mathrm{w}_2=4: 3\), then the value of ' a ' is ( \(\mathrm{g}=\) acceleration due to gravity)
For two different photosensitive materials having work function \(\phi\) and \(2 \phi\) respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials, the ratio of slope of graph for these two materials is
The activity of radioactive sample is measured as \(\mathrm{N}_0\) counts per minute at time \(\mathrm{t}=0\), and \(\frac{\mathrm{N}_0}{\mathrm{e}}\) counts per minute at time \(\mathrm{t}=3\) minute, The activity reduces to half its value in time (in minute)
When a current in the conducting coil is changed from 5 A in one direction to 5 A in opposite direction in 0.5 second, an average induced e.m.f in the coil is 2 V . The selfinductance of the coil is
The excess pressure inside first soap bubble is three times that of a second soap bubble. The ratio of volumes of the first to second bubble
The electric field intensity near a conducting surface having uniform surface charge density ' \(\sigma\) ' is given by ( \(\varepsilon_0=\) permittivity of free space)
The figure shows two masses ' \(m\) ' and ' \(M\) ' connected by a light string that passes through a small hole ' \(O\) ' at the centre of the table. Mass ' \(m\) ' is moved round in a horizontal circle with ' \(O\) ' as the centre. The frequency with which ' \(m\) ' should be revolved so that ' \(M\) ' remains stationary is
( \(\mathrm{g}=\) gravitational acceleration)
A particle performs S.H.M. of amplitude 'A' and wavelength ' \(\lambda\) ', Then the velocity of the wave (V) and the maximum particle velocity (v) are related as
Which of the following statements is TRUE for n-type semiconductor?
\[ 3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}= \]
The minimum distance and maximum distance of the point \(\mathrm{P}(2,-7)\) from the circle \(x^2+y^2-14 x-10 y-151=0\) are respectively _______units
The lines \(\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})\) and \(\overline{\mathrm{r}}=\overline{\mathrm{c}}+\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})\) will intersect if
The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10 lakhs and due to loss they reduce to ₹ 10000 after 3 years, then the number of years required for the person to be bankrupt will be
If the statement pattern \((p \wedge q) \rightarrow(r \vee \sim s)\) is false, then the truth values of \(p, q, r\) and \(s\) are respectively
The Y-intercept of the common tangent to the parabolas \(y^2=32 x\) and \(x^2=108 y\) is
If \(f(x)= \begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & \text { if } x>0 \\ e^x \sin x+x+\lambda \log 4, & \text { if } x \leqslant 0\end{cases}\)
is continuous at \(x=0\) then the value of \(1000 \mathrm{e}^\lambda=\)
The line of intersection of the planes \(\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1 \quad\) and \(\quad \bar{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2 \quad\) is parallel to the vector
If the line \(2 x+y=\mathrm{k}\) passes though the point which divides the line segment joining the points \((1,1)\) and \((2,4)\) internally in the ratio \(3: 2\) then, \((k+1):(k-1)=\)
The logical statement
\[ [\sim(\sim p \vee q) \vee(p \wedge r) \wedge(\sim q \wedge r)] \]
is equivalent to
The L.P.P. , minimize \(z=30 x+20 y, x+y \leq 8\), \(x+2 y \geq 4,6 x+4 y \geq 12, x \geqslant 0, y \geqslant 0\) has
The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two 'I's do not come together is
The equation of the plane containing the line \(\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-4}{-2}\) and the point \((0,5,0)\) is
The complex numbers \(\sin x+i \cos 2 x\) and \(\cos x\) - \(\mathrm{i} \sin 2 x,(\mathrm{i}=\sqrt{-1})\) are conjugate to each other for,
If the distance of the point \(\mathrm{P}(1,-2,1)\) from the plane \(x+2 y-2 z=\alpha\), where \(\alpha>0\) is 5 units, then the foot of the perpendicular from P to the plane is
If the function \(\mathrm{f}(x)=x(x+3) \mathrm{e}^{-\frac{x}{2}}\) satisfies all the conditions of Rolle's theorem in \([-3,0]\), then c is
