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A fighter plane, flying horizontally with a speed \(360 \mathrm{kmph}\) at an altitude of \(500 \mathrm{~m}\) drops a bomb for a target straight ahead of it on the ground. The bomb .should be dropped at what approximate distance ahead of the target ? Assume that acceleration due to gravity \((\mathrm{g})\) is \(10 \mathrm{~ms}^{-2}\). Also neglect air drag

asked Dec 11, 2021 in Kinematics by kritika (90.1k points)

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Consider the vectors \(\vec{A}=\hat{i}+\hat{j}-\hat{k}, \vec{B}=2 \hat{i}-\hat{j}+\hat{k}, \vec{C}=\frac{1}{\sqrt{5}}(\hat{i}-2 \hat{j}+2 \hat{k})\). What is the value of \(\vec{C} \cdot(\vec{A} \times \vec{B}) ?\)

asked Dec 11, 2021 in Physics and measurements by kritika (90.1k points)

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The frequency \(v\) of the radiation emitted by an atom when an electron jumps from one orbit to another is given by \(v\) \(=\mathrm{k} \delta \mathrm{E}\), where \(\mathrm{k}\) is a constant and \(\delta \mathrm{E}\) is the change in energy level due to the transition. Then dimension of \(\mathrm{k}\) is

asked Dec 11, 2021 in Physics and measurements by kritika (90.1k points)

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A common emitter transistor amplifier is connected with a load resistance of \(6 \mathrm{k} \Omega\). When a small a.c. signal of 15 \(\mathrm{mV}\) is added to the base emitter voltage, the alternating base current is \(20 \mu \mathrm{A}\) and the alternating collector current is \(1.8 \mathrm{~mA}\). What is the voltage gain of the amplifier ?

asked Dec 11, 2021 in Kinematics by kritika (90.1k points)

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For nuclei with mass number close to 119 and 238 , the binding energies per nucleon are approximately \(7.6 \mathrm{MeV}\) and \(8.6 \mathrm{MeV}\) respectively. If a nucleus of mass number 238 breaks into two nuclei of nearly equal masses, what will be the approximate amount of energy released in the process of fission?

asked Dec 11, 2021 in Kinematics by kritika (90.1k points)

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A nucleus \(X\) emits a beta particle to produce a nucleus \(Y\). If their atomic masses are \(M_{x}\) and \(M_{y}\) respectively, the maximum energy of the beta particle emitted is (where \(m_{e}\) is the mass of an electron and \(c\) is the velocity of light)

asked Dec 11, 2021 in Kinematics by kritika (90.1k points)

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If \(R\) is the Rydberg Constant in \(\mathrm{cm}^{-1}\), then hydrogen atom does not emit any radiation of wave-length in the range of

asked Dec 11, 2021 in Kinematics by kritika (90.1k points)

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In a Frounhofer diffraction experiment, a single slit of width \(0.5 \mathrm{~mm}\) is illuminated by a monochromatic light of wavelength \(600 \mathrm{~nm}\). The diffraction pattern is observed on a screen at a distance of \(50 \mathrm{~cm}\) from the slit. What will be the linear separation of the first order minima?

asked Dec 11, 2021 in Optics by kritika (90.1k points)

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The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be \(1.5\) limes the intensity of light emerging from the other slit. What will be the approximate ratio of intensity of an interference maximum to that of an interference

asked Dec 11, 2021 in Properties of solids and liquids by kritika (90.1k points)

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Consider the function \(f(x)=\frac{x^{3}}{4}-\sin \pi x+3\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(f\) and \(g\) be differentiable on the interval \(I\) and let \(a, b \in I, a<b\). Then

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Equation of a tangent to the hyperbola \(5 x^{2}-y^{2}=5\) and which passes through an external point \((2,8)\) is

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Straight lines \(x-y=7\) and \(x+4 y=2\) intersect at \(B\). Points \(A\) and \(C\) are so chosen on these two lines such that \(A B\) \(=A C\). The equation of line AC passing through \((2,-7)\) is

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A=\left(\begin{array}{lll}3 & 0 & 3 \\ 0 & 3 & 0 \\ 3 & 0 & 3\end{array}\right) .\) Then the roots of the equation \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\) (where \(I_{3}\) is the identity matrix of order 3 ) are

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\theta \in \mathbb{R}\) and \(\frac{1-i \cos \theta}{1+2 i \cos \theta}\) is real number, then \(\theta\) will be (when I: Set of integers)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(x_{1}, x_{2}\) be the roots of \(x^{2}-3 x+a=0\) and \(x_{3}, x_{4}\) be the roots of \(x^{2}-12 x+b=0\). If \(x_{1}<x_{2}<x_{3}<x_{4}\) and \(x_{1}\), \(x_{2}, x_{3}, x_{4}\) are in G.P. then \(a b\) equals

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The area bounded by \(y=x+1\) and \(y=\cos x\) and the \(x\)-axis, is

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and \(h\) respectively. If \(A\) takes \(m\) seconds more than \(B\) and describes \(n\) units more than that of \(B\) acquiring the same speed, then

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(I_{n}=\int_{0}^{1} x^{n} \tan ^{-1} x d x\). If \(a_{n} I_{n+2}+b_{n} I_{n}=c_{n}\) for all \(n \geq 1\), then

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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A point is in motion along a hyperbola \(y=\frac{10}{x}\) so that its abscissa \(x\) increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate, when the point passes through \((5,2)\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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