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A cat runs along a straight line with a constant velocity of magnitude v. A dog chases the cat such that the velocity of the dog is always directed towards the cat. The speed of a dog is u and always constant. At the instant, both are separated by distance x and their velocities are mutually perpendicular, the magnitude of the acceleration of the dog is.

a) u2/x b) uv/x c) v2/x d) (u2 + v2)/x Answer: b) uv/x Solution: The velocity of cat = v Speed of dog = u Let the velocity of the dog... View Article

In a magnetic field of 0.05T, the area of a coil changes from 101cm² to 100cm² without changing the resistance which is 2 Ω. The amount of charge that flow during this period is

a) 2.5 x 10-6 C b) 2 x 10-6 C c) 10-6 C d) 8 x 10-6 C Answer: a) 2.5 x 10-6 C Solution: Magnetic flux, Φ... View Article

The acceleration of a body moving with initial velocity u changes with distance x as a =k² √x where K is a positive constant. The distance travelled by the body when its velocity becomes 2u is

a) (3u/2k)3/4 b) (3u/2k)4/3 c) (3u/2k)3/2 d) (3u/2k)2/3 Answer: (3u/2k)4/3 Solution: Given, a... View Article

Find the equivalent thermal conductivity of the given rod

a) 2k/3 b) 3k c) 3k/2 d) 4k/3 Answer: d) 4k/3 Solution: Let A = Area T1 is the temperature of the sink T2 is the temperature of the... View Article

A current of 50 A is passed through a straight wire of length 6 cm, then the magnetic induction at a point 5 cm from either end of the wire is (1 gauss =10⁻⁴T)

a) 2.5 gauss b) 1.25 gauss c) 1.2 gauss d) 3.0 gauss Answer: c) 1.5 gauss Solution: B = (μ0I/4πr)[sinθ1 + sinθ2] = 10-7 x (50/(4 x... View Article

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. The ratio of surface charge densities of the sphere σ₁/σ₂ will be

a) R1/R2 b) R2/R1 c) √(R1/R2) d) R12/R22 Answer: b) R2/R1 The potential will be equal as they are connected with wire V1 =... View Article

The magnetic dipole moment of the current loop is independent of

a) number of turns b) area of the loop c) current in the loop d) magnetic field in which it is lying Answer: d) magnetic field in... View Article

In the adjoining figure, AE = DC = 13 cm BE = 5 cm, ∠ABC=90°& AD = EC = x cm. Calculate the length of AB & the value of x

Now, consider a triangle ABE, By using Pythagoras theorem, AE2 = AB2 + BE2 169 = AB2 + 25 AB2 = 169 - 25 = 144. Hence, AB = 12. Now,... View Article

A card is drawn from a well shuffled deck of 52cards. Find the probability of getting a king of red suit.

The total number of cards in a deck, n(S) = 52 cards. Let A be the event of getting a king of red suit No. of kings in red suit, n(A) = 2,... View Article

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3……12,then the probability that it will point to an odd number is

The total number of possible outcomes here is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. So, n(S) = 12 Let A be the event that the arrow will... View Article

For what value of k, the equation x^2 + 2(k – 4) x + 2k = 0 has equal roots ?

We know that the quadratic equation has equal roots, when the discriminant, D = 0. Given quadratic equation is x2 + 2(k - 4) x + 2k = 0 Here,... View Article

If the zeros of the quadratic polynomial ax^2+bx+c,c≠0 are equal, then

The zeroes of the quadratic polynomial are equal when the discriminant is equal to 0. ⇒ D = 0 ⇒ b2 - 4ac = 0 ⇒ b2 = 4ac... View Article

There are 30 boys and 25 girls in a class. A student is chosen at random. Find the probability that the chosen student is a boy

Given that, Number of boys = 30 Number of girls = 25 Therefore, the total number of students 30 + 25 = 55 = n(S) Let X be the event of... View Article

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Archives

In a magnetic field of 0.05T, the area of a coil changes from 101cm² to 100cm² without changing the resistance which is 2 Ω. The amount of charge that flow during this period is

The acceleration of a body moving with initial velocity u changes with distance x as a =k² √x where K is a positive constant. The distance travelled by the body when its velocity becomes 2u is

Find the equivalent thermal conductivity of the given rod

A current of 50 A is passed through a straight wire of length 6 cm, then the magnetic induction at a point 5 cm from either end of the wire is (1 gauss =10⁻⁴T)

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. The ratio of surface charge densities of the sphere σ₁/σ₂ will be

The magnetic dipole moment of the current loop is independent of

In the adjoining figure, AE = DC = 13 cm BE = 5 cm, ∠ABC=90°& AD = EC = x cm. Calculate the length of AB & the value of x

A card is drawn from a well shuffled deck of 52cards. Find the probability of getting a king of red suit.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3……12,then the probability that it will point to an odd number is

For what value of k, the equation x^2 + 2(k – 4) x + 2k = 0 has equal roots ?

If the zeros of the quadratic polynomial ax^2+bx+c,c≠0 are equal, then

There are 30 boys and 25 girls in a class. A student is chosen at random. Find the probability that the chosen student is a boy

If a + b + c = 3, then find the value of 1/(1 – a)(1 – b) + 1/(1 – b)(1 – c) + 1/(1 – c)(1 – a).

Varun has 10 cards with numbers 1 to 10. In how many ways can a total of 15 be made using only three cards at a time?

Write any 2 similarities and 2 differences of a right-angled isosceles triangle and obtuse-angled scalene triangle.

How to find the HCF of 24 and 36?

How do you find the GCD of two numbers?

Write the formula for the perpendicular distance of a point from a line.

The reduction of nitrobenzene in the presence of Zn/Ammonium chloride gives:

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