Physics-
General
Easy

Question

When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe

  1. 3.8 mm 
  2. 1.6 mm 
  3. 7.6 mm 
  4. 3.2 mm 

The correct answer is: 3.2 mm

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Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio

Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio

Physics-General
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Represent -7 + 3 on number line

When we add something to the given number, we don’t start counting the second number from zero. We count the places from the number itself. Any negative value means we move in left direction. Any positive value means we move in right direction.

Represent -7 + 3 on number line

Maths-General

When we add something to the given number, we don’t start counting the second number from zero. We count the places from the number itself. Any negative value means we move in left direction. Any positive value means we move in right direction.

General
Maths-

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c
Statement-II: If 0<a<b, then integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c
Statement-II: If 0<a<b, then integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c

Maths-General
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General
Maths-

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c
Statement-II: If a>0, a>b, then integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c
Statement-II: If a>0, a>b, then integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c

Maths-General
General
Maths-

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c
Statement-II: If a>b then integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c
Statement-II: If a>b then integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c

Maths-General
General
Maths-

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c
Statement-II: If a<b then integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c

Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c
Statement-II: If a<b then integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c

Maths-General
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Maths-

I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c
II: integral subscript blank superscript blank fraction numerator d x over denominator c o s x minus s i n x end fraction equals fraction numerator 1 over denominator square root of 2 end fraction l o g vertical line t a n left parenthesis x over 2 plus fraction numerator 3 pi over denominator 8 end fraction right parenthesis vertical line plus c Which of the following is true

I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c
II: integral subscript blank superscript blank fraction numerator d x over denominator c o s x minus s i n x end fraction equals fraction numerator 1 over denominator square root of 2 end fraction l o g vertical line t a n left parenthesis x over 2 plus fraction numerator 3 pi over denominator 8 end fraction right parenthesis vertical line plus c Which of the following is true

Maths-General
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I:not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 1 plus x right parenthesis e to the power of x end exponent over denominator s e c to the power of 2 end exponent left parenthesis x e to the power of x end exponent right parenthesis end fraction d x equals blank l o g blank vertical line t a n fraction numerator x over denominator 2 end fraction vertical line plus s e c x plus C
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The probability density plots of 1s and 2s orbitals are given in figure

The density of dots in region represents the probability density of finding electrons in the region. On the basis of above diagram which of the following statements is incor-rect?

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Chemistry-General
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In the set up shown in Fig the two slits, S subscript 1 end subscriptand S subscript 2 end subscript are not equidistant from the slit S. The central fringe at O is then

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Physics-General
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Physics-

In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index mu is placed in front of the slit S subscript 1 end subscript comma then the path difference left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis

In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index mu is placed in front of the slit S subscript 1 end subscript comma then the path difference left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis

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Following figure shows sources S subscript 1 end subscript and S subscript 2 end subscript that emits light of wavelength lambda in all directions. The sources are exactly in phase and are separated by a distance equal to 1.5 lambda. If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along

Following figure shows sources S subscript 1 end subscript and S subscript 2 end subscript that emits light of wavelength lambda in all directions. The sources are exactly in phase and are separated by a distance equal to 1.5 lambda. If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along

Physics-General
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Two coherent sources separated by distance d are radiating in phase having wavelength lambda. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as

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Physics-General
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A beam with wavelength lambda falls on a stack of partially reflecting planes with separation d. The angle theta that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)

A beam with wavelength lambda falls on a stack of partially reflecting planes with separation d. The angle theta that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)

Physics-General
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