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If the nth term of an arithmetic progression is 3n + 7, then what is the sum of its first 50 terms?

(a) 3925 (b) 4100 (c) 4175 (d) 8200 Solution: Given nth term of A.P, tn = 3n+7 t1 = 3+7... View Article

Mercury vapour lamp gives

1) continuous spectrum 2) line spectrum 3) band spectrum 4) absorption spectrum Answer: 2) line spectrum Solution: Mercury vapour lamp givesline... View Article

At the time of total solar eclipse, the spectrum of solar radiation will have

1) a large number of dark Fraunhofer lines 2) a smaller number of dark Fraunhofer lines 3) no lines at... View Article

The wavelength of the first spectral line of sodium is 5896 A. The first excitation potential of sodium atom will be (h = 6.63 × 10^-34 Js)

1) 4.2 V 2) 3.5 V 3) 2.1 V 4) None of these Answer: 3) 2.1 V Solution: The energy of... View Article

Electrons in a certain energy level n = n₁, can emit 3 spectral lines. When they arc in another energy level, n = n₂ they can emit 6 spectral lines. The orbital speed of the electrons in the orbits are in the ratio

1) 4 : 3 2) 3 : 4 3) 2 : 1 4) 1 : 2 Answer: 1) 4 : 3... View Article

Ionisation potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr’s theory, the spectral lines emitted by hydrogen will be

1) two 2) three 3) four 4) one⇒ Answer: 2) three Solution: Ionisation potential of hydrogen atom is 13.6eV. Energy rquired... View Article

Assuming f to be the frequency of the first-line in the Balmer series, the frequency of the immediate next (i.e. second) line is

1) 0.50f 2) 1.35f 3) 2.05f 4) 2.70f Answer: 2) 1.35f Solution: For Balmer series, nf=2 and ni=3,4,5,… Frequency, of 1... View Article

First Bohr radius of an atom with Z = 82 is R. Radius of its third orbit is

1) 9R 2) 6R 3) 3R 4) R Answer: 1) 9R Solution: for n = 1, Radius, r1= r \(\begin{array}{l}r_{n}= \frac{h^{2}}{4\pi... View Article

The ionisation potential of hydrogen atom is –13.6 eV. An electron in the ground state of hydrogen atoms absorbs a photon of energy 12.75 eV. How many different spectral lines can one expect when the electron make a downward transition?

1) 1 2) 4 3) 2 4) 6 Answer: 4) 6 Solution: ΔE = –13.6 eV \(\begin{array}{l}\Delta E = 13.6\left [ \frac{1}{n_{1}^{2}-\frac{1}{n_{2}^{2}}}... View Article

Solar spectrum is an example for

1) line emission spectrum 2) continuous emission spectrum 3) band absorption spectrum 4) line absorption spectrum Answer: 4) line absorption spectrum... View Article

If the sum to infinity of the series,1 + 4x + 7x² + 10x³ +…….., is 35/16, where | x | < 1, then x equals to

(a) 19/7 (b) 1/5 (c) 1/4 (d) None of these Solution: Let S = 1 + 4x + 7x2 +... View Article

If a + b + c = 3 and a > 0, b > 0, c > 0, then the greatest value of a²b³c² is

(a) 310.24/77 (b) 39.24/77 (c) 38.24/77 (d) none of these Solution: A.M ≥ G.M Taking A.M and G.M of 7... View Article

The sum of an infinite GP is x and the common ratio r is such that |r| <1. If the first term of the GP is 2, then which one of the following is correct?

(a) -1 < x < 1 (b) – ∞ < x < 1 (c) 1 < x < ∞ (d)... View Article

Which one of the following options is correct?

(a) sin2 300, sin2 450, sin2 600 are in GP (b) cos2 300, cos2 450, cos2 600 are in GP... View Article

What is the product of first (2n + 1) terms of a geometric progression?

(a) The (n + 1)th power of the nth term of the GP (b) The (2n + 1)th power of... View Article

The minimum value of (x⁴ + y⁴ + z²)/xyz for positive real number x, y, z is

(a) √2 (b) 2√2 (c) 4√2 (d) 8√2 Solution: x, y, z > 0 We know A.M ≥ G.M x4... View Article

If (1 + 3 + 5 + … + p) + (1 + 3 + 5 + … + q) = (1 + 3 + 5 +…+ r) where each set of parentheses contains the sum of consecutive odd integers as shown, what is the smallest possible value of (p + q + r) where p > 6?

(a) 12 (b) 21 (c) 45 (d) 54 Solution: We know that the nth term of A.P = a +... View Article

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