If loge 5, loge (5x – 1) and loge (5x – 11/5) are in A.P then the values of x are (a) log5 4 and log5 3 (b) log3 4 and log4 3 (c) log3 4 and log3 5 (d) log5 6 and log5 7 Solution: Given that loge 5, loge... View Article
If tn denotes the nth term of a G.P. whose common ratio is r, then the progression whose nth term is 1/(tn2 + tn+12) is (a) A.P. (b) G.P. (c) H.P. (d) None of these Solution: The nth term of G.P = arn-1, where a is the first term and r is the... View Article
The perimeter of a triangle whose sides are in A.P. is 21 cm and the product of lengths of the shortest side and the longest side exceeds the length of the other side by 6 cm. The longest side of the triangle is (a) 1 cm (b) 7 cm (c) 13 cm (d) none Solution: Let a-d, a, a+d be the sides of the triangle. Given that perimeter =... View Article
An A.P. whose first term is unity and in which the sum of first half of any even number of terms to that of the second half of the same number of terms is a constant ratio, then the common difference is: (a) 2 (b) 1 (c) 3 (d) None of these Solution: Given first term, a = 1 Let Sn denote the sum of n terms of an A.P.... View Article
The 100th term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4,… is (a) 12 (b) 13 (c) 14 (d) 15 Solution: Given series 1, 2, 2, 3, 3, 3, 4, 4, 4, 4,... 1st term = 1 2nd term = 2... View Article
The 20th terms of the series 2 + 3 + 5 + 9 + 16 +…….is (a) 950 (b) 975 (c) 990 (d) 1010 Solution: Let S1 = 2 + 3 + 5 + 9 + 16 +...............xn (i) S1 = 2 + 3 + 5 + 9 +... View Article
If a, b, c are the sides of a triangle, then the minimum value of [a/(b+c-a)] + [b/(c+a-b)] + [c/(a+b-c)] is equal to (a) 3 (b) 6 (c) 9 (d) 12 Solution: a, b, c > 0 Let A = [a/(b+c-a)] + [b/(c+a-b)] + [c/(a+b-c)] Multiply... View Article
a, b, c are three distinct real numbers and they are in a G.P. if a + b + c = xb, then (a) x ≤ -1 or x ≥ 3 (b) x < -1 or x > 3 (c) x ≤ -1 or x > 3 (d) x < -3 or x > 2 Solution: Let b =... View Article
A series is such that its every even term is ‘a’ times the term before it and every odd term is c times the term before it. The sum of 2n term of the series is (the first term is unity) (a) (1 - cn)(1 - an)/(1 - ac) (b) (1 + a)(1 - cnan)/(1 - ac) (c) (1 + cn)(1 + an)/(1 - ac) (d) (1 + a)(1 + cnan)/(1 + ac) Solution: The... View Article
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 = 10 t2 = 6+7 = 13... View Article
Mercury vapour lamp gives 1) continuous spectrum 2) line spectrum 3) band spectrum 4) absorption spectrum Answer: 2) line spectrum Solution: Mercury... 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 all 4) all Fraunhofer lines changed... 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 first excitation of sodium is... 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 Solution: Number of emitted spectral lines N=n(n−1)/2 When, N=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 rn ∝ n2 r1/r3 = n12/n22 r/r3= 1/(3)2 r3 = 9r... 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 ⇒ n2 = n = 4 Number of lines =... 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... 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 + 10x3 +........ (i) Multiply by x xS = x +... View Article
