Solve the following :
Question: A proton exerts a force on a proton which isgravitationalelectromagneticnuclearweakCorrect Option: 1, 2, 3 Solution: Proton exerts gravitational, electromagnetic and nuclear force on a proton because proton is a charges particle (1), (2), (3)...
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Question: A proton exerts a force on a proton which isgravitational electromagneticnuclearweakCorrect Option: 1, 3 Solution: Neutron exerts gravitational force and nuclear force on proton because neutron is uncharged particle. (1),(3)...
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Question: A neutron exerts a force on a proton which isgravitationalelectromagneticnuclearweakCorrect Option: 3 Solution: Neutron exerts gravitational force and nuclear force on proton because neutron is uncharged particle. (a),(c)...
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Question: A $60 \mathrm{~kg}$ man pushes a $40 \mathrm{~kg}$ man by a force of $60 \mathrm{~N} . \mathrm{I}$ The $40 \mathrm{~kg}$ man has pushed the other man with a force of$40 \mathrm{~N}$ 0$60 \mathrm{~N}$$20 \mathrm{~N}$Correct Option: 3 Solution: $60 \mathrm{~N}$...
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Question: The sum of all electromagnetic forces between different particles of a system of charged particles is zeroonly if all the particles are positively charged only if all the particles are negatively chargedonly if half the particles are positively charged half are negatively chargedirrespective of the signs of the chargesCorrect Option: 4 Solution: irrespective of the signs of the charges...
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Question: Let $\mathrm{E}, \mathrm{G}$ and $\mathrm{N}$ represent the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation. Then$NEG$ $ENG$$GNE$$EGN$Correct Option: 4 Solution: $EGN$...
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Question: When Neils Bohr shook hand with Werner Heisenberg, what kind of force they exerted? (a) Gravitational (b) Electromagnetic (c) Nuclear (d) Weak(a) Gravitational (b) Electromagnetic(c) Nuclear(d) WeakCorrect Option: 2 Solution: (b) Electromagnetic...
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Question: Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particle will take to meet each other. Solution: Relative velocity $=v-v \cos \theta$ $V-\frac{v}{2}$ $=\frac{v}{2}$ $\mathrm{S}_{\mathrm{rel}}=\mathrm{a}$ Speed= $\frac{\text { distance }}{\text { time }}$ $\frac{v}{2}=\frac{a}{t}$ $t=\frac{2 a}{v}$...
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Question: Suppose $\mathrm{A}$ and $\mathrm{B}$ in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation $x$. What will be the time lad $B$ finds between seeing and hearing the drum beating by $A$ ? Solution: Let $v$ be the velocity of sound along direction $A C$ so it can reach $B$ with resultant velocity $A D$ Velocity along $A B=\sqrt{V^{2}-U^{2}}$ Time= distance speed $\mathrm{t}=\f...
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Question: Two friends $A$ and $B$ are standing a distance $x$ apart in an open field and wind is blowing from $A$ to $B$. $A$ beats $a$ drum and $B$ hears the sound $t_{1}$ time after he sees the event. $A$ and $B$ interchange their positions and the experiment is repeated. This time $B$ hears the drum $t_{2}$ time after he sees the event. Calculate the velocity of sound in still air $v$ and the velocity of win $u$. Neglect the time light takes in travelling between the friends. Solution: Initia...
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Question: An aero plane has to go from point $A$ to another point $B, 500 \mathrm{~km}$ away due to $30^{\circ}$ east of north. A wind is blowing due north at a seed of $20 \mathrm{~m} / \mathrm{s}$. The air speed of the plane is $150 \mathrm{~m} / \mathrm{s}$. (a) Find the direction in which the pilot should head the plane to reach the point $B$. (b) Find the time taken by the plane to gr from $A$ to $B$. Solution: (a) In $\triangle \mathrm{ACB}$ Using sin formula $\frac{20}{\sin \phi}=\frac{15...
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Question: Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point, Find the minimum distance that he has to walk. Solution: When $\mathrm{V}_{\text {river }}\mathrm{v}_{\text {manand }}$ for minimum drift $\sin \theta=\frac{\mathrm{V}_{\text {Man }}}{\mathrm{V}_{\text {river }}}$ $\sin \theta=\frac{3}{5}$ $\theta=37^{\circ}$ Time to cr...
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Question: A swimmer wishes to cross $500 \mathrm{~m}$ wide river flowing at $5 \mathrm{~km} / \mathrm{h}$. His speed with respect to water is 3 $\mathrm{km} / \mathrm{h}$. (a) If he heads in a direction making an angle $\theta$ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river. Solution: (a) Velocity responsible for $\operatorname{cros} \operatorname{sing}=3 \sin \theta \mathrm{kmph}$ $=3 \times \frac{5}{18} \sin \theta$ Time to cros...
Read More →If the curves,
Question: If the curves, $x^{2}-6 x+y^{2}+8=0$ and $x^{2}-8 y+y^{2}+16-k=0,(k0)$ touch each other at a point, then the largest value of $\mathrm{k}$ is________. Solution:...
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Question: If $\mathrm{C}_{\mathrm{r}} \equiv{ }^{25} \mathrm{C}_{\mathrm{r}}$ and $\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots \cdot+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}$ then $\mathrm{k}$ is equal to________. Solution:...
Read More →If the distance between the plane,
Question: If the distance between the plane, $23 x-10 y-2 z+48=0$ and the plane containing the lines $\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}$ and $\frac{\mathrm{x}+3}{2}=\frac{\mathrm{y}+2}{6}=\frac{\mathrm{z}-1}{\lambda}(\lambda \in \mathrm{R})$ is equal to $\frac{\mathrm{k}}{\sqrt{633}}$, then $\mathrm{k}$ is equal to__________. Solution:...
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Question: Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}|=\sqrt{3}$, $|\vec{b}|=5, \vec{b} \cdot \vec{c}=10$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$. If $\vec{a}$ is perpendicular to the vector $\vec{b} \times \vec{c}$, then $|\vec{a} \times(\vec{b} \times \vec{c})|$ is equal to_________ Solution:...
Read More →The number of terms common to the two
Question: The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots ., 709$ is________. Solution:...
Read More →Let f and g be differentiable functions on
Question: Let $f$ and $\mathrm{g}$ be differentiable functions on $\mathbf{R}$ such that fog is the identity function. If for some $a, b \in \mathbf{R}, g^{\prime}(a)=5$ and $g(a)=b$, then $f^{\prime}(b)$ is equal to :$\frac{2}{5}$1$\frac{1}{5}$5Correct Option: , 3 Solution:...
Read More →Let a_n be the
Question: Let $a_{n}$ be the $n^{\text {th }}$ term of a G.P. of positive terms. If $\sum_{\mathrm{n}=1}^{100} \mathrm{a}_{2 \mathrm{n}+1}=200$ and $\sum_{\mathrm{n}=1}^{100} \mathrm{a}_{2 \mathrm{n}}=100$, then $\sum_{\mathrm{n}=1}^{200} \mathrm{a}_{\mathrm{n}}$ is equal to :225175300150Correct Option: , 4 Solution:...
Read More →In the expansion of
Question: In the expansion of $\left(\frac{\mathrm{x}}{\cos \theta}+\frac{1}{\mathrm{x} \sin \theta}\right)^{16}$, if $\ell_{1}$ is the least value of the term independent of $x$ when $\frac{\pi}{8} \leq \theta \leq \frac{\pi}{4}$ and $\ell_{2}$ is the least value of the term independent of $x$ when $\frac{\pi}{16} \leq \theta \leq \frac{\pi}{8}$, then the ratio $\ell_{2}: \ell_{1}$ is equal to :$1: 8$$1: 16$$8: 1$$16: 1$Correct Option: , 4 Solution:...
Read More →Let a-2 b+c=1
Question: Let $a-2 b+c=1$ If $f(x)=\left|\begin{array}{lll}x+a x+2 x+1 \\ x+b x+3 x+2 \\ x+c x+4 x+3\end{array}\right|$, then :$f(-50)=501$$f(-50)=-1$$f(50)=1$$f(50)=-501$Correct Option: , 3 Solution: $\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}+\mathrm{R}_{3}-2 \mathrm{R}_{2}$ $f(x)=\left|\begin{array}{ccc}a+c-2 b 0 0 \\ x+b x+3 x+2 \\ x+c x+4 x+3\end{array}\right|$ $=(a+c-2 b)\left((x+3)^{2}-(x+2)(x+4)\right)$ $=x^{2}+6 x+9-x^{2}-6 x-8=1$ $\Rightarrow f(x)=1 \Rightarrow f(50)=1$...
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Question: If $\mathrm{p} \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})$ is false, then the truth values of $\mathrm{p}$ and $\mathrm{q}$ are respectively :$\mathrm{F}, \mathrm{T}$$\mathrm{T}, \mathrm{T}$$\mathrm{F}, \mathrm{F}$$\mathrm{T}, \mathrm{F}$Correct Option: 2 Solution:...
Read More →If z be a complex number satisfying
Question: If $z$ be a complex number satisfying $|\operatorname{Re}(z)|+|\operatorname{Im}(z)|=4$, then $|z|$ cannot be$\sqrt{\frac{17}{2}}$$\sqrt{10}$$\sqrt{8}$$\sqrt{7}$Correct Option: , 4 Solution:...
Read More →An urn contains 5 red marbles, 4 black marbles and 3 white marbles.
Question: An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is .... Solution:...
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