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A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is

Magnetic force F=qvB...(i)Centripetal forceF=mv2 / r ---(ii) On equating magnetic force to centripetal force, mv2 / r=qvBsin90o... View Article

ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO =AP, prove that 3 ∠POB = ∠AOP.

Given: ABCD is a square and the diagonals intersect at O.º P is the point on AB such that AO = AP To prove: 3 ∠POB = ∠AOP... View Article

From the graph between current i and voltage v shown below, identify the portion corresponding to negative resistance is

If the temperature and physical conditions remain constant, Ohm's law states that the current flowing through any conductor is directly... View Article

The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

From Distance formula we know that √ [(x2 - x1)2 + (y2- y1)2] Let us assume the ordinate as x... View Article

How does the displacement current flow in the dielectric of a capacitor when the potential difference is supplied across its plates?

The displacement current flows in the dielectric of a capacitor when the potential difference across its plates is increasing with time... View Article

Find the ratio in which the line segment joining points (-3, 10) and (6, – 8) is divided by (-1, 6).

From the section formula Let the ratio in which the line segment joining (-3, 10) and (6, - 8) is divided by (-1, 6) be k : 1.... View Article

If the sum of the first 11 terms of an arithmetical progression equals that of the first 19 terms. Then the sum of its first 30 terms is

An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is... View Article

In triangle ABC, DE || BC. AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value x.

Given ABC is a triangle DE || BC AD = x DB = x - 2 AE = x + 2 and EC = x - 1. Find out We have to determine the value of x Solution In... View Article

The probability of guessing the correct answer to a certain question is p/12 . If the probability of not guessing the correct answer to the same question is 3/4 then find the value of p.

Probability is the measurement of chances – the likelihood that an event will occur. If the probability of an event is high, it is more... View Article

Let * be a binary operation on Z defined by a * b = a + b – 4 for all a, b ∈ Z. (i) Show that * is both commutative and associative. (ii) Find the identity element in Z (iii) Find the invertible element in Z.

(i) First we have to prove the commutativity of * Let a, b ∈ Z. then, a * b = a + b – 4 = b + a – 4 = b * a Therefore,... View Article

The mass of bullet is 100 g. It is fired from a gun of mass 20 kg with a velocity of 100 m/s. Determine the recoil speed of the gun.

Given Mass of bullet =m=100g=100 /1000kg=1/10kg Velocity of bullet, v=100ms-1Mass of gun, M=20kg Find out We have to determine... View Article

Two equal negative charges – q are fixed at points (0,-a) and (0,a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will (A) Execute simple harmonic motion about the origin (B) Move to the origin and remain at rest (C) Move to infinity (D) Execute oscillatory but not simple harmonic motion

The correct answer is (D) Execute oscillatory but not simple harmonic motion Motion is simple harmonic only if the charge Q is released from... View Article

Find the length of the longest altitude of the ∆abc whose sides are 35 cm, 54 cm, and 61 cm respectively.

Given ABC be a triangle in which sides AB = 35 cm, BC = 54 cm, CA = 61 cm Find out We have to determine the a;altitude of the... View Article

If the sum of first 6 terms is 9 times to the sum of first 3 terms of the same G.P., then common ratio of the series will be

If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the sequence is... View Article

The area enclosed by the equation |x| + |y| = 4 is ___

Given equation can be expressed as When x < 0 and y > 0, - x + y = 4 When y < 0 and x > 0 x - y = 4 When x<0 and y<0,... View Article

If an infinite GP has the first term x and the sum 5, then which of the following is correct? a. x < –10 b. –10 < x < 0 c. 0 < x < 10 d. x > 10

The correct answer is (c) 0 < x < 10 Geometric progression If in a sequence of terms, each succeeding term is generated by... View Article

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