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The value of lim_n→∞ [xⁿ / (xⁿ + 1)], where x < - 1 is

1) 1/2 2) – (1/2) 3) 1 4) None of these Solution: (3) 1 \(\begin{array}{l}\begin{array}{l} \lim _{n \rightarrow \infty} \frac{x^{n}}{x^{n}+1}... View Article

If l(x) is the least integer not less than x and g(x) is the greatest integer not greater than x, then lim_x→e+π {l (x) + g (x)} =

1) 9 2) 13 3) 1 4) None of these Solution: (4) None of these \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow e+\pi}\{e(x)+g(x)\}=?... View Article

lim_x→a [log (x – a)] / [log (e^x – e^a)] =

1) 0 2) 1 3) a 4) does not exist Solution: (2) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow a} \frac{\ln (x-a)}{\ln... View Article

If lim_x→a [a^x – x^a] / [x^x – a^a] = – 1, then a =

1) 1 2) 0 3) e 4) (1/e) Solution: (1) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow a} \frac{a^{x}-x^{a}}{x^{x}-a^{a}}=-1 \\ \text {... View Article

lim_x→0 [(√a + x – √a – x) / (4x)] =

1) 1/2√a 2) 4/4√a 3) 1/3√a 4) 2/√a Solution: (2) 4/4√a \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 0}\left(\frac{\sqrt{a+x}-\sqrt{a-x}}{4 x}\right) \\ \text {... View Article

The value of lim_x→0 [e^ax – e^bx] / x =

1) a + b 2) a – b 3) eab 4) 1 Solution: (2) a – b \(\begin{array}{l}\begin{array}{l} \lim _{x... View Article

lim_x→1 [2x² + x – 3] / [3x³ – 3x² + 2x – 2] =

1) 1 2) 2 3) -1 4) -2 Solution: (1) 1 \(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 1} \frac{2 x^{2}+x-3}{3 x^{3}-3 x^{2}+2... View Article

Let [.] denote the greatest integer function and f (x) = [tan² x], then:

1) limx→0 f (x) does not exist 2) f (x) is continuous at x = 0 3) f (x) is... View Article

A double slit interference experiment is carried out in air and the entire arrangement is dipped in water. The fringe width

(a) increases (b) decreases (c) remains unchanged. (d) fringe pattern disappears. Solution: Answer: b Fringe width βwater = βwater/λ λwater... View Article

Resolving power of microscope depends upon

(a) wavelength of light used (directly proportional) (b) wavelength of light used (inversely proportional) (c) frequency of light used (d)... View Article

When an unpolarised light beam is incident from air onto glass (n = 1.5) at the polarising angle.

(a) Reflected beam is polarised completely (b) Reflected and refracted beams are partially polarised (c) Refracted beam is plane polarised... View Article

When a compact disk is illuminated by a source of white light, coloured lines are observed. This is due to

(a) dispersion (b) diffraction (c) interference (d) refraction Solution: Answer: (b) The small ripples on the compact disc split white... View Article

What happens if the monochromatic light used in Young’s double slit experiment is replaced by white light?

(a) No fringes are observed. (b) All bright fringes become while. (c) All bright fringes have colour between violet and... View Article

When exposed to sunlight, thin films of oil on water often exhibit brilliant colours due to the phenomenon of

(a) interference (b) diffraction (c) dispersion (d) polarisation Solution: Answer: (a) interference When a thin film of oil spreads over... View Article

What is the path difference for destructive interference?

(a) nλ (b) n(λ +1) (c) (2n + 1)λ/2 (d) (n +1)λ/2 Solution: Answer: (c) For destructive interference, the path... View Article

According to Huygens’ principle, light is a form of

(a) particle (b) rays (c) wave (d) radiation Solution: Answer: (c) According to Huygens’ principle, light travels in the form... View Article

A laser beam is coherent because it contains

(a) waves of several wavelengths. (b) incoherent waves of a single wavelength. (c) coherent waves of several wavelengths (d) coherent... View Article

Which of the following statements indicates that light waves are transverse

(a) Light waves can travel in vacuum (b) Light waves show interference (c) Light waves can be polarized (d) Light... View Article

The colours on the soap bubble is due to

(a) Interference (b) Polarisation (c) Diffraction (d) Reflection Solution: Answer: (a) Interference The colors of a soap bubble come from... View Article

Why Coherent Sources are Essential for Observable Interference?

Solution: Coherent sources have the same phase so the phase difference between the two sources remains constant.

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