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If t_n denotes n^th term of the series 2 + 3 + 6 + 11 + 18… ,then t5₀ is (1) 2 + 49² (2) 2 + 48² (3) 2 + 50² (4) 2 + 51²

Answer: (1) 2 + 492 A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3,... View Article

lf (x + iy)^1/3 = a + ib then x/a+ y/b =? (1) a²− b ² (2) 2(a² −b²) (3) 3(a² − b²) (4) 4(a²− b²)

Answer: (4) 4(a2 - b2) Given (x + iy)1/3 = a + ib (x + iy) = (a + ib)3 (a + ib)3 = a3- iba3 + 3a2bi - 3ab2 (a + ib)3 = a3 - 3ab2 + i(-b3 +... View Article

Two masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass at the instant when the 10 kg mass has an acceleration of 12 towards right, the acceleration of the 20 kg mass is (1) m/s² (2) 4m/s² (3) 10m/s² (4) 20m/s²

Answer: (2) 4m/s2 Give m1= 10kg m2 = 20kg F2= 200N a1=12ms−2 a2= ? F = m1× a1 F = 10 × 12 F = 120N 20... View Article

A bullet fired at an angle of 30 degree with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0km away? Assume the muzzle speed to be fixed, and neglect air resistance.

Answer: Given parameters Horizontal range (R) = 3.0km Angle of projection = 30o Acceleration due to gravity (g) = 9.8m/s When a... View Article

An open vessel at 27^oC is heated until 3/5^th of the air in it has been expelled. Assuming that the volume of the vessel remains constant, find the temperature to which the vessel has been heated?

Answer: According to Charles’ law, when pressure is held constant, the volume of a fixed amount of dry gas is directly proportional to its... View Article

If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 has infinitely many solutions, then ______. (1) a = 2b (2) b = 2a (3) a + 2b = 0 (4) 2a + b = 0

Answer: (2) b = 2a Given two equations 2x + 3y = 7 2ax + (a + b)y = 28 Comparing 2x + 3y = 7 with a1x + b1y + c1= 0, we get, a1 = 2 b1 =... View Article

What is the application of linear algebra?

Answer: Linear algebra is one of the important branches of mathematics. Linear algebra is basically the study of vectors and linear functions.... View Article

The shortest wavelength for Lyman series is 912A^o. Find shortest wavelength for Paschen and Brackett series in Hydrogen atom.

Answer: Lyman series is displayed when electron transition takes place from higher energy states(nh=2,3,4,5,6,…) to nl=1 energy state.... View Article

If x is real, what is the maximum value of (3x²+9x+17)/(3x²+9x+7)? (1) 1 (2) 17/7 (3) 1/4 (4) 41

Answer: (4) 41 . . When 3x2 + 9x + 7 is minimum, f(x) will have the maximum value. Minimum value of 3x2 + 9x + 7 is . Where a = 3... View Article

A 12.5eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

A 12.5eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted? Answer: The energy... View Article

When a metallic surface is illuminate with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is 4V. The threshold wavelength for the metallic surface is (1) 4λ (2) 5λ (3) 5/2λ (4) 3λ

Answer: (4) 3λ The Threshold frequency is known as the minimum wavelength for the photoelectric effect that the light should have. If the... View Article

If the change in the value of g at a height h above the surface of the earth is the same as at a depth d below it. When both d and h are much smaller than the radius of earth, then (1) d = h (2) d = h² (3) d = h/2 (4) d = 2h

Answer: (4) d = 2h Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has... View Article

The ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series in the spectrum of hydrogen is_______

Answer: 5/27 Transition to n=1 and n=2 are refered to as Lyman and Balmer series. For Lyman Series wavelength will be longest when energy the... View Article

How do you simplify i^(-999)?

Answer: The value of i is √-1. The imaginary unit number is used to express the complex numbers, where i is defined as imaginary or unit... View Article

Which of the following chemicals dubstance has the strongest hydrogen bond? (1) HCl (2) H₂O (3) HI (4) H₂S

Answer: (2) H2O The strongest hydrogen bond is formed by an atom with a small size and a larger electronegative charge. Oxygen (O) is smaller in... View Article

The sum of the measures of interior angles of a polygon of n sides is equal to (1) 2n right angles (2) (2n – 2) right angles (3) 2(n – 2) right angles (4) 2(n – 4) right angles

The sum of the measures of interior angles of a polygon of n sides is equal to (1) 2n right angles (2) (2n - 2) right angles (3) 2(n - 2) right... View Article

Which of the following sets of quantum numbers is correct for an electron in 3d-orbital? (1) n = 3, l = 2, m = -3 , s = +1/2 (2) n = 3, l = 3, m = +3, s = -1/2 (3) n = 3, l = 2, m = -2, s = +1/2 (4) n = 3, l = 2, m =-3, s = -1/2

Answer: The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four... View Article

How to find resultant of two vectors?

Answer: In Maths, the resultant vector is defined as the combination of two or more single vectors. We know that a vector is a quantity that has... View Article

The distance of the point (α, β) from origin is (1) α.β (2) α².β² (3) √α² – β² (4) √α² + β²

Answer: (4) √α2 + β2 The distance between two points is the length of the line segment, joining the given two points.... View Article

The solid ball density to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, then the relative percentage error in the density is (1) 0.9% (2) 2.4% (3) 3.1% (4) 4.2%

Answer: (3) 3.1% The least count of the screw guage is defined as the distance moved by the tip of the screw when turned through one division of... View Article

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