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A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true ? (A) The force applied on the particle is constant (B) The speed of the particle is proportional to time (C) The distance of the particle from the origin increses linerarly with time (D) The force is conservative

The correct options are A The force applied on the particle is constantB The speed of the particle is proportional to timeD The... View Article

If the distance between a point source of light and a screen is doubled, then the intensity will be

if the distance between a point source of light and a screen is doubled, then the intensity will be one fourth... View Article

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12ms⁻¹. If the mass of the ball is 0.15 kg, determine the change in momentum of the ball.

The Impulse-momentum formula is obtained from the impulse-momentum theorem which states that change in momentum of an object is equal... View Article

Which of the following graph depicts spring constant K versus length L of the spring correctly?

Tne correct answer is option (d) Solution According to Hooke’s law, the force required to compress or extend a spring... View Article

Find the sum of the first 7 terms of the series -4 + 8 – 16 + 32 -…?

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

If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h, and k? (a) p = -2, h = 2, k = -4 (b) p = -1, h = 1, k = -3 (c) p = 2, h = 3, k = -4 (d) p = 5, h = 4, k = -3

The corect answer is (c) p = 2, h = 3, k = -4 The simplest equation of a parabola is... View Article

If second term of a G.P is 2 and its sum to infinity is 8.Find its first term

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

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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

If tan θ + sin θ = p and tan θ – sin θ = q then prove that p2 – q2 = 4√pq

If tan θ + sin θ = p and tan θ – sin θ = q then prove that p2 – q2 = 4√pq Given According to... View Article

AB, CD and EF are perpendicular to the straight line BDF. If AB = x and, CD = z unit and EF = y unit, then (a) 1/x + 1/y = 1/z (b) 1/x – 1/y = 1/z (c) 1/x X 1/y = 1/z (d) None of these

In Δ FDC and Δ FBA, ∠FDC = ∠FBA [As DC || AB] ∠DFC = ∠BFA [common angle] Hence, ∆FDC... View Article

A physical quantity z depends on four observables a, b, c and d, as z = [a²b^2/3 / √c d³]. The percentages of error in the measurement of a, b, c and d are 2% , 1.5%, 4% and 2.5% respectively. The percentage of error in z is

Percentage Error Errors in measurement may also be expressed in terms of percentage. This is similar to relative error except... View Article

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 r=mv/qB The time taken by... 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... 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 10=√(10−2)2+(x+3)2 On... 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 \(\begin{array}{l}\large M (x,y) = \left ( \frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n} \right )\end{array} \) Solution Let the ratio... 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,... 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 +... 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... View Article

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