If limx→1 [(ax2 + bx + c) / (x – 1)2] = 2, then (a, b, c) =
1) (2, -4, 2) 2) (2, 4, 2) 3) (2, 4, -2) 4) (2, -4, -2) Solution: (1) (2, -4,... View Article
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If f : R → R is defined by f (x) = [x – 3] + |x – 4| for x ϵ R, then limx→3- f (x) =
1) -2 2) -1 3) 0 4) 1 Solution: (3) 0 \(\begin{array}{l}\begin{array}{l} f(x)=[x-3]+|x-4| \\ \lim _{x \rightarrow 3^{-}} f(x)=\lim _{x... View Article
limx→0 (- 1)[x], where [] denotes the greatest integer function =
1) 0 2) 1 3) -1 4) does not exist Solution: (4) does not exist \(\begin{array}{l}\lim _{x \rightarrow 0}(-1)^{[x]}\\ \mathrm{LHL}:... View Article
The value of limx→2 [5] / [√2 – √x] is
1) 10√2 2) + ∞ 3) – ∞ 4) does not exist Solution: (4) does not exist \(\begin{array}{l}\lim _{x \rightarrow... View Article
If f (1) = 1, f’ (1) = 2, then limx→1 [√f (x) – 1] / (√x – 1) =
1) 2 2) 4 3) 1 4) 1/2 5) 3 Solution: (1) 2 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 1} \frac{\sqrt{f(x)-1}}{\sqrt{x}-1} \\... View Article
limx→∞ [(2x – 1) / (√x2 + 2x + 1)] =
1) 2 2) -2 3) 1 4) -1 5) 0 Solution: (2) -2 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty} \frac{2 x-1}{\sqrt{x^{2}+2... View Article
limx→∞ [(x + 2) / (x + 1)]x+3 =
1) 1 2) e 3) e2 4) e3 Solution: (2) e \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty}\left(\frac{x+2}{x+1}\right)^{x+3}\\ \Rightarrow \lim _{x \rightarrow... View Article
If g (x) is a polynomial satisfying g (x) g (y) = g (x) + g (y) + g (xy) – 2 for all real x and y and g (2) = 5, then limx→3 g (x) =
1) 9 2) 10 3) 25 4) 20 Solution: (2) 10 \(\begin{array}{l}\begin{array}{l} g(x) g(y)=g(x)+g(y)+g(x y)-2 \\ \text { For }... View Article
If 0 < a < b, then limn→∞ [(an + bn) / (an – bn)] =
1) 0 2) -1 3) 1 4) does not exist Solution: (2) -1 \(\begin{array}{l}\begin{array}{l} \lim _{n \rightarrow \infty} \frac{a^{n}+b^{n}}{a^{n}-b^{n}} \\... View Article
If f(1) = 2 and f'(1) = 1, then the value of limx→1 [2x – f (x)] / (x – 1) is
1) -1 2) 0 3) 1 4) 2 Solution: (3) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 1} \frac{2 x-f(x)}{x-1} \\ \text... View Article
In Young’s double slit experiment, the ratio of maximum to minimum intensities of the fringe system is 4 :1. The amplitudes of the coherent sources are in the ratio:
(a) 4:1 (b) 3:1 (c) 2:1 (d) 1:1 Solution: (b) Let the amplitude ratio be x/y. Ratio of maximum and... View Article
The maximum number of possible interference maxima for slit separation equal to twice the wavelength is Young’s double-slit experiment, is
(a) Infinite (b) Five (c) Three (d) Zero Solution: (b) In Young’s double slit experiment, the condition for maxima is... View Article
On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If μ =1.5, the thickness of the film is (wavelength of monochromatic light is λ)
(a) 4λ (b) 3λ (c) 2λ (d) λ Solution: (c) Shift in central bright = (μ-1)tD/d Again, λD/d = (μ-1)tD/d... View Article
To demonstrate the phenomenon of interference we require two sources, which emits radiations of
(a) Two sources which emit radiation of same frequency (b) Two sources which emit radiation of nearly same frequency (c)... View Article
In young’s double slit experiment, the ratio of intensities of bright and dark bands is 16 which means:
(a) The ratio of their amplitude is 5. (b) Intensities of individual sources are 25 and 9 units respectively. (c)... View Article
In an interference experiment, the spacing between successive maxima or minima is
(a) μd/D (b) λD/d (c) dD/λμ (d) μλd/4D Answer: (b) Hint: maxima = x = nλD/d and minima = x... View Article
In a Young’s double slit experiment, constructive interference is produced at a certain point P. The intensities of light at P due to the individual sources are 4 and 9 units. The resultant intensity at point P will be
(a) 13 units (b) 25 units (c) √97 units (d) 5 units Solution: Answer: (b) 25 units I1 = 4... View Article
Light of wavelength 6000 A falls on a single slit of width 0.1 mm. The second minimum will be formed for the angle of diffraction of
(a) 0.06 rad (b) 0.05 rad (c) 0.12 rad (d) 0.012 rad Solution: Answer: (d) Wavelength = λ = 6000... View Article
In Young’s double slit experiment, a third slit is made in between the double slits. Then,
(a) fringes of unequal width are formed. (b) contrast between bright and dark fringes is reduced. (c) intensity of fringes... View Article
If the fringe width is 0.4mm, the distance between the fifth bright and third dark band on the same side is.
(a) 1mm (b) 2mm (c) 3mm (d) 4mm Solution: Answer: (a) 1mm Position of nth bright fringe from central maxima... View Article
