Maths-
General
Easy

Question

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

  1. Statement I is true, statement II true, statement II is the correct explanation for statement II    
  2. Statement I is true, statement II true, statement II is not the correct explanation for statement II    
  3. Statement I is true, statement II is false    
  4. Statement I is false, statement II is true    

The correct answer is: Statement I is true, statement II true, statement II is the correct explanation for statement II


    Put tan x fraction numerator x over denominator 2 end fraction equals t d x equals fraction numerator 2 d r over denominator 1 plus C to the power of 2 end exponent end fraction comma c o s x equals fraction numerator 1 minus r to the power of 2 end exponent over denominator 1 plus C to the power of 2 end exponent end fraction
    S(II): fraction numerator 1 over denominator a end fraction not stretchy integral subscript blank superscript blank fraction numerator 2 over denominator left parenthesis r plus fraction numerator b over denominator a end fraction right parenthesis to the power of 2 end exponent plus fraction numerator a to the power of 2 end exponent minus b to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction end fraction d t
    equals fraction numerator 2 over denominator a end fraction fraction numerator 1 over denominator square root of blank end root a to the power of 2 end exponent minus b to the power of 2 end exponent fraction numerator square root of a to the power of 2 end exponent minus b to the power of 2 end exponent end root over denominator a end fraction 2 end fraction. C a n to the power of negative 1 subscript fraction numerator square root of a to the power of 2 end exponent minus b to the power of 2 end exponent end root over denominator a r a a end fraction end subscript end exponent equals blank over blank C a n to the power of negative 1 end exponent left parenthesis fraction numerator left parenthesis fraction numerator r plus fraction numerator b over denominator a end fraction over denominator blank end fraction right parenthesis b plus n fraction numerator x over denominator 22 end fraction over denominator square root of a to the power of 2 end exponent minus b end root end fraction right parenthesis plus C

    Related Questions to study

    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
    General
    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
    parallel
    General
    Maths-

    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
    II:integral subscript blank superscript blank fraction numerator s e c x over denominator left parenthesis s e c x plus t a n x right parenthesis squared end fraction d x equals fraction numerator 1 over denominator 2 left parenthesis s e c x plus t a n x right parenthesis squared end fraction plus c Which of the following is true

    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
    II:integral subscript blank superscript blank fraction numerator s e c x over denominator left parenthesis s e c x plus t a n x right parenthesis squared end fraction d x equals fraction numerator 1 over denominator 2 left parenthesis s e c x plus t a n x right parenthesis squared end fraction plus c Which of the following is true

    Maths-General
    General
    Maths-

    I:not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 1 plus c o s 2 x end fraction d x equals fraction numerator 1 over denominator 2 end fraction t a n x plus C
    IIcolon integral subscript blank superscript blank fraction numerator 1 plus s i n to the power of 2 subscript chi end exponent over denominator 1 plus c o s 2 x end fraction d x equals t a n x minus 1 half x plus c Which of the following is true

    I:not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 1 plus c o s 2 x end fraction d x equals fraction numerator 1 over denominator 2 end fraction t a n x plus C
    IIcolon integral subscript blank superscript blank fraction numerator 1 plus s i n to the power of 2 subscript chi end exponent over denominator 1 plus c o s 2 x end fraction d x equals t a n x minus 1 half x plus c Which of the following is true

    Maths-General
    General
    Chemistry-

    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?

    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?

    Chemistry-General
    parallel
    General
    Physics-

    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

    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

    Physics-General
    General
    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

    Physics-General
    General
    Physics-

    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
    parallel
    General
    Physics-

    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

    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

    Physics-General
    General
    Physics-

    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
    General
    Physics-

    Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2pil radian. If there is a maximum in direction D the distance XO using n as an integer is given by

    Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2pil radian. If there is a maximum in direction D the distance XO using n as an integer is given by

    Physics-General
    parallel
    General
    Physics-

    Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength lambda passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

    Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength lambda passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

    Physics-General
    General
    Physics-

    A monochromatic beam of light falls on YDSE apparatus at some angle (say theta) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained

    A monochromatic beam of light falls on YDSE apparatus at some angle (say theta) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained

    Physics-General
    General
    Chemistry-

    Given  The number of electrons present in l = 2 is

    Given  The number of electrons present in l = 2 is

    Chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.