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The capacitor, whose capacitance is 6 μf, 3 μf and 2 μf respectively are connected with the 12-volt battery as shown in the figure. The charges on 6 μf capacitor will be

Answer: 24 x 10-6 C Solution: Combined capacity of C1 and C2 in series C’ = C1C2/(C1 + C2) = (6 x 3)/(6+3) = 18/9 = 2 μF Charge on 6 μf... View Article

Refer to the figure. The speed of the particle when its velocity becomes parallel to the inclined plane is

a) 5 m/s b) 5(√3 + 1)/2√3 m/s c) 5√3 m/s d) 5(√3 - 1) m/s Answer: d) 5(√3 - 1) m/s Solution: Vx = ucos300 - gsin45t = 10 x (√3/2) - 5 =... View Article

A monoatomic gas is taken in a vessel fitted with a light movable piston. If 50 cal of heat is supplied to 2 moles of gas then its rise in temperature will be (R = 2cal/mol-K)

a) 50 K b) 5 k c) 10 K d) 20 K Answer: b) 5 k Solution: Q = n Cp dT 50 = 2 x (5/2) x 2 .dT dT = 5 K... View Article

A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 300 N and is directly opposed to the motion. How much work does the road do on the cycle?

Answer: -3000 J Solution: Force on the cycle due to road = 300 N Cyclist comes to a skidding stop in 10 m Work done = Force x... View Article

Two vectors [latex]vec{F_{1}}[/latex] and [latex]vec{F_{2}}[/latex] each of magnitude are inclined to each other such that their resultant is to √3F then the resultant of [latex]vec{F_{1}}[/latex] and
[latex]-vec{F_{2}}[/latex] is

a) F b) √2F c) √3F d) 2F Answer: a) F Solution: Given that As we know, Parallelogram law of vector... View Article

When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after the collision they will move

a) opposite to one another b) in the same direction c) together d) at right angle to each other Answer: d) at right angle to each other... View Article

Consider a spherical gaseous cloud of mass density ρ(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If ρ(r) is constant in time, the particle number density n(r) = ρ(r)/m is [G is universal gravitational constant]

a) 3K/πr2m2G b) K/2πr2m2G c) K/6πr2m2G d) K/πr2m2G Answer: Solution:b) K/2πr2m2G Gravitational... View Article

A non-homogenous sphere of radius R has the following density variation.

A non-homogenous sphere of radius R R has the following density variation. The gravitational field at a distance 2R from the centre of the... View Article

What is the probability of getting any number when we roll a single die for once?

Solution: Possible outcomes are 1, 2, 3, 4, 5, 6. Number of outcomes = 6 The probability of getting any of the numbers = 1/6. Hence the... View Article

Find the intervals on which f(x) = x⁴ – 8x² is increasing and decreasing.

Solution: Given f(x) = x4 - 8x2 f’(x) = 4x3 - 16x f’(x) = 0 => 4x3 - 16x = 0 => 4x(x2-4) = 0 =>x = 0, 2, -2 We have... View Article

The LCM of two numbers is 25 times their HCF. the product of the two numbers is 2025. Find the HCF.

(a) 81 (b) 45 (c) 9 (d) 18 Solution: Given LCM = 25HCF Product of two numbers = 2025 We know LCM×HCF = Product of two numbers =>... View Article

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. What are the marks obtained by both of them?

(a) 25 and 78 (b) 58 and 77 (c) 33 and 42 (d) 56 and 63 Solution: Let x be the mark of one student. Then mark of other student = x+9 Sum... View Article

A bag contains 1 Rupee 2 Rupees and 5 Rupees coins in the ratio 4:8:5. The total amount was Rs.90. The number of 5 Rupee coins equal

(a) 8 (b) 16 (c) 15 (d) 10 Solution: Given ratio = 4:8:5 Total amount = 90 Let number of 1 rupee, 2 rupees, and 5 rupees... View Article

Set = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Evaluate the following expression for the given set of numbers. 3(mean)×2(mode) – 6(median).

Solution: Given set is {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Number of observations, n = 10 Mean = sum of observations/number of observations =... View Article

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
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Archives

The capacitor, whose capacitance is 6 μf, 3 μf and 2 μf respectively are connected with the 12-volt battery as shown in the figure. The charges on 6 μf capacitor will be

Refer to the figure. The speed of the particle when its velocity becomes parallel to the inclined plane is

A monoatomic gas is taken in a vessel fitted with a light movable piston. If 50 cal of heat is supplied to 2 moles of gas then its rise in temperature will be (R = 2cal/mol-K)

A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 300 N and is directly opposed to the motion. How much work does the road do on the cycle?

Two vectors [latex]vec{F_{1}}[/latex] and [latex]vec{F_{2}}[/latex] each of magnitude are inclined to each other such that their resultant is to √3F then the resultant of [latex]vec{F_{1}}[/latex] and
[latex]-vec{F_{2}}[/latex] is

When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after the collision they will move

A non-homogenous sphere of radius R has the following density variation.

What is the probability of getting any number when we roll a single die for once?

Find the intervals on which f(x) = x⁴ – 8x² is increasing and decreasing.

The LCM of two numbers is 25 times their HCF. the product of the two numbers is 2025. Find the HCF.

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. What are the marks obtained by both of them?

A bag contains 1 Rupee 2 Rupees and 5 Rupees coins in the ratio 4:8:5. The total amount was Rs.90. The number of 5 Rupee coins equal

Set = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Evaluate the following expression for the given set of numbers. 3(mean)×2(mode) – 6(median).

If x and y are two co-primes, then their LCM is?

Find the mode and median of the following frequency distribution:

On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

The number of permutations of letters a, b, c, d, e, f, g so that neither the pattern beg nor cad appears is

If f(x) be a polynomial function satisfying f(x).f(1/x) = f(x) + f(1/x) and f(4) = 65. Then find f(6).

The point on the curve 3y = 6x – 5x³, the normal at which passes through the origin is

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