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Add the following vectors:

$\overrightarrow{A}=5\hat{i}+6\hat{j}-10\hat{k}$

$\overrightarrow{B}=-10\hat{i}-6\hat{j}+10\hat{k}$

In the figure shown, the tension at the mid – point of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the tension in the rope at point $C$.

Find out the value of resistance $R$ in figure.

What is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$

In the arrangement shown in figure, $m_A=1\text{kg},m_B=4\text{kg}$. String is light and inextensible while pulley is smooth. Coefficient of friction between block $A$ and the table is $\mu =0.2$. Find the speed of both the blocks when block $B$ has descended by a height $h=1\text{m}$. ( Take $g=10{\text{m/s}}^2$).

Two balls are projected upward simultaneously with speeds $40\text{m/s}$ and $60\text{m/s}$. Relative position $\left(x\right)$ of second ball w.r.t. first ball at time $t=5\text{s}$ is :

[Neglect air resistance]

A point mass m start froms rest and slides down the surface of a frictionless solid sphere of radius r as shown in the figure. Measure angle from the vertical and potential energy from the top. Find:

(i) The angle at which the mass files off the sphere.

(ii) If there is friction between the mass and sphere, does the mass fly off at a greater or lesser angle than in part (a)?

Many identical point masses $m$ are placed along $x-$axis, at $x=0,1,2,4,....$. The magnitude of gravitational force on mass at origin $(x=0)$ will be

A horizontal rod of mass m and length L is pivoted smoothly at one end. The rod’s other end is supported by a spring of force constant k. The rod is rotated (in the vertical plane) by a small angle from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is

An ac source is connected to a resistive circuits. Which of the following is true

A $20\text{N}$ metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads $40\text{N}$. The spring balance is now lowered slowly into the beaker such that the block gets immersed in the water. The spring balance now reads $16\text{N}$. The reading of the weighing machine will be

is air resistance dependant of mass of the object?

The wavelength of the carrier waves in a modern optical fibre communication network is close to

A uniform but time varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper as shown in Fig. 25.21.



The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

Which of the following is not an application of LASER?

In the figure, a carbon resistor has bands of different colors on its body as mentioned in the figure, then the value of the resistance is

In figure shown, velocity of mass $m$ at the moment shown is $U$. Find the velocity of the ring along the rod if it can slide along the smooth rod.

With what minimum pressure (in $\text{kPa}$), a given volume of an ideal gas $(C_{p.m}=\frac{7}{2}R)$, originally at $400\text{K}$ and $100\text{kPa}$ pressure can compressed irreversibly adiabatically in order to raise its temperature to $600\text{K}$?

A wire of density $9\times {10}^{3}kg/m^3$ is stretched between two clamps 1 m apart and is subjected to an extension of $4.9\times {10}^{-4}m$. The lowest frequency of transverse vibration in the wire is $(Y=9\times {10}^{10}N/m^2)$

What
will be the minimum pressure required to compress 500 dm³
of air at 1 bar to 200 dm³
at 30°C?

Paragraph for below question

चे दिए गए प्रश्न के लिए अनुच्छेद



A uniform rod of mass M and length l is released from vertical position on a frictionless horizontal surface as shown in figure. If the equilibrium of rod is slightly disturbed, then



M द्रव्यमान तथा l लम्बाई की एक समरूप छड़ को चित्रानुसार ऊर्ध्वाधर स्थिति से किसी घर्षणहीन क्षैतिज पृष्ठ पर छोड़ा जाता है। यदि छड़ की साम्यावस्था थोड़ी विचलित हो जाती है, तब







Q. If rod does not lose contact with surface, then relation between velocity of centre of mass (v) of rod and angular velocity (ω) of rod at the instant shown will be



प्रश्न - यदि छड़, पृष्ठ के साथ सम्पर्क नहीं हटाती है, तब दर्शाए गए क्षण पर छड़ के द्रव्यमान केन्द्र के वेग (v) तथा छड़ के कोणीय वेग (ω) के मध्य सम्बन्ध होगा

In the following circuit diagram, the value of resistance $X$, for which the potential difference between the points $\text{B}$ and $\text{D}$ is zero is equal to

A body of mass $m=3.513\text{kg}$ is moving along the $x-$axis with a speed of $5.00{\text{ms}}^{–1}$. The magnitude of its momentum is recorded as

(Consider significant figures)

A body cools from ${60}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ in $10$ minutes. If the room temperature is ${25}^{\circ }\text{C}$ then the temperature of the body at the end of the next $10$ minutes will be

A nucleus $A$, with a finite de Broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into two nuclei $B$ and $C$ of equal masses. $B$ flies in the same direction as that of $A$, while $C$ flies in the opposite direction with a velocity equal to half of that of $B$. The de Broglie wavelengths ${\lambda }_B$ and ${\lambda }_C$ of $B$ and $C$ are, respectively,

Two particles of equal mass $5\times {10}^{-30}\text{kg}$ moving towards each other, collide and come to rest. This collision produces a photon. If the velocity of the particles is ${10}^6{\text{ms}}^{-1}.$ What is the frequency of light emitted. (Ignore the relativistic effects).