Maths-
General
Easy

Question

The area bounded by y=cos x, y=x+1 and y=0 in the second quadrant is

  1. 3/2 sq units    
  2. 2 sq units    
  3. 1 sq unit    
  4. 1/2 sq units    

The correct answer is: 1/2 sq units

Related Questions to study

General
physics-

A Tjoint is formed by two identical rods A and Beach of mass m and length L in the X Yplane as shown. Its moment of inertia about axis coinciding with A is

I equals I subscript x end subscript plus I subscript y end subscript equals fraction numerator m L to the power of 2 end exponent over denominator 12 end fraction plus fraction numerator m L to the power of 2 end exponent over denominator 12 end fraction equals fraction numerator m L to the power of 2 end exponent over denominator 6 end fraction

A Tjoint is formed by two identical rods A and Beach of mass m and length L in the X Yplane as shown. Its moment of inertia about axis coinciding with A is

physics-General
I equals I subscript x end subscript plus I subscript y end subscript equals fraction numerator m L to the power of 2 end exponent over denominator 12 end fraction plus fraction numerator m L to the power of 2 end exponent over denominator 12 end fraction equals fraction numerator m L to the power of 2 end exponent over denominator 6 end fraction
General
Maths-

The area bounded by the parabolablank x to the power of 2 end exponent=4ay, x-axis and the straight-line y=2a is

The area bounded by the parabolablank x to the power of 2 end exponent=4ay, x-axis and the straight-line y=2a is

Maths-General
General
physics-

Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?

Moment of inertia of the system about the centre of plane is given by
I equals open square brackets fraction numerator 2 over denominator 5 end fraction cross times 1 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 1 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 2 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 2 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 3 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 3 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 4 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 4 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
equals 1.004 plus 2.008 plus 3.012 plus 4.016
equals 10.04 blank k g minus m to the power of 2 end exponent

Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?

physics-General
Moment of inertia of the system about the centre of plane is given by
I equals open square brackets fraction numerator 2 over denominator 5 end fraction cross times 1 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 1 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 2 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 2 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 3 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 3 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 4 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 4 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
equals 1.004 plus 2.008 plus 3.012 plus 4.016
equals 10.04 blank k g minus m to the power of 2 end exponent
parallel
General
physics-

For the given uniform square lamina A B C D, whose centre is O

Let the each side of square lamina is d.
So, I subscript E F end subscript equals I subscript G H end subscript (due to symmetry)
And I subscript A C end subscript equals I subscript B D end subscript (due to symmetry)
Now, according to theorem of perpendicular axis,

I subscript A C end subscript plus I subscript B D end subscript equals I subscript 0 end subscript
rightwards double arrow 2 I subscript A C end subscript equals I subscript 0 end subscript (i)
and I subscript E F end subscript plus I subscript G H end subscript equals I subscript 0 end subscript
rightwards double arrow 2 I subscript E F end subscript equals I subscript 0 end subscript (ii)
From Eqs. (i) and (ii), we get
I subscript A C end subscript equals I subscript E F end subscript
therefore I subscript A D end subscript equals I subscript E F end subscript plus fraction numerator m d to the power of 2 end exponent over denominator 4 end fraction
equals fraction numerator m d to the power of 2 end exponent over denominator 12 end fraction plus fraction numerator m d to the power of 2 end exponent over denominator 4 end fraction open parentheses a s I subscript E F end subscript equals fraction numerator m d to the power of 2 end exponent over denominator 12 end fraction close parentheses
So, I subscript A D end subscript equals fraction numerator m d to the power of 2 end exponent over denominator 3 end fraction equals 4 I subscript E F end subscript

For the given uniform square lamina A B C D, whose centre is O

physics-General
Let the each side of square lamina is d.
So, I subscript E F end subscript equals I subscript G H end subscript (due to symmetry)
And I subscript A C end subscript equals I subscript B D end subscript (due to symmetry)
Now, according to theorem of perpendicular axis,

I subscript A C end subscript plus I subscript B D end subscript equals I subscript 0 end subscript
rightwards double arrow 2 I subscript A C end subscript equals I subscript 0 end subscript (i)
and I subscript E F end subscript plus I subscript G H end subscript equals I subscript 0 end subscript
rightwards double arrow 2 I subscript E F end subscript equals I subscript 0 end subscript (ii)
From Eqs. (i) and (ii), we get
I subscript A C end subscript equals I subscript E F end subscript
therefore I subscript A D end subscript equals I subscript E F end subscript plus fraction numerator m d to the power of 2 end exponent over denominator 4 end fraction
equals fraction numerator m d to the power of 2 end exponent over denominator 12 end fraction plus fraction numerator m d to the power of 2 end exponent over denominator 4 end fraction open parentheses a s I subscript E F end subscript equals fraction numerator m d to the power of 2 end exponent over denominator 12 end fraction close parentheses
So, I subscript A D end subscript equals fraction numerator m d to the power of 2 end exponent over denominator 3 end fraction equals 4 I subscript E F end subscript
General
chemistry-

Which is correct about the change given below

Which is correct about the change given below

chemistry-General
General
chemistry-

Identify Z in the reaction 

Which undergoes Cannizaro’s reaction to give Z

Identify Z in the reaction 

chemistry-General
Which undergoes Cannizaro’s reaction to give Z
parallel
General
chemistry-

 X and Y are respectively

 X and Y are respectively

chemistry-General
General
chemistry-

 The product A is

 The product A is

chemistry-General
General
chemistry-

 Y is

 Y is

chemistry-General
parallel
General
chemistry-

For which of the following molecule significant m ¹ 0
I)
II)
III)
IV)

-OH and -SH groups do not cancel their dipole moment

For which of the following molecule significant m ¹ 0
I)
II)
III)
IV)

chemistry-General
-OH and -SH groups do not cancel their dipole moment
General
chemistry-

Which one of the following will be the major product when

Is treated with dilute H2SO4 in the presence of HgSO4

Which one of the following will be the major product when

Is treated with dilute H2SO4 in the presence of HgSO4

chemistry-General
General
chemistry-

The appropriate reagent (s) for the transformation
is / are

Transformation of C = O group into CH2 in the presence of Zn + Hg is called Clemmensen’s reduction and in the presence of NH2 - NH2/OH- is called Wolf-Kishner Reduction

The appropriate reagent (s) for the transformation
is / are

chemistry-General
Transformation of C = O group into CH2 in the presence of Zn + Hg is called Clemmensen’s reduction and in the presence of NH2 - NH2/OH- is called Wolf-Kishner Reduction
parallel
General
chemistry-

The most suitable reagent of r the conversion of RCH2OH → RCHO is

Refer to Comprehensive Review

The most suitable reagent of r the conversion of RCH2OH → RCHO is

chemistry-General
Refer to Comprehensive Review
General
chemistry-

Which alkali metal floats over cold water without any reaction?

4, Na, k all are less denses them water among these first group Li is very less reactive

Which alkali metal floats over cold water without any reaction?

chemistry-General
4, Na, k all are less denses them water among these first group Li is very less reactive
General
physics-

The radius of germanium (G e) nuclide is measured to be twice the radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript. The number of nucleons in Ge are

Let radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript nucleus be r. Then radius of germanium (Ge) nucleus will be2 r.
Radius ofnucleus is given by
R equals R subscript 0 end subscript A to the power of 1 divided by 3 end exponent
therefore fraction numerator R subscript 1 end subscript over denominator R subscript 2 end subscript end fraction equals open parentheses fraction numerator A subscript 1 end subscript over denominator A subscript 2 end subscript end fraction close parentheses to the power of 1 divided by 3 end exponent
rightwards double arrow fraction numerator r over denominator 2 r end fraction equals open parentheses fraction numerator 9 over denominator A to the power of 2 end exponent end fraction close parentheses to the power of 1 divided by 3 end exponent left parenthesis because A subscript 1 end subscript equals 9 right parenthesis
rightwards double arrow blank open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 3 end exponent equals fraction numerator 9 over denominator A to the power of 2 end exponent end fraction
Hence,A subscript 2 end subscript equals 9 blank cross times blank open parentheses 2 close parentheses to the power of 3 end exponent blank equals 9 cross times 8 equals 72
Thus, in germanium (G e) nucleus number of nucleons is 72.

The radius of germanium (G e) nuclide is measured to be twice the radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript. The number of nucleons in Ge are

physics-General
Let radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript nucleus be r. Then radius of germanium (Ge) nucleus will be2 r.
Radius ofnucleus is given by
R equals R subscript 0 end subscript A to the power of 1 divided by 3 end exponent
therefore fraction numerator R subscript 1 end subscript over denominator R subscript 2 end subscript end fraction equals open parentheses fraction numerator A subscript 1 end subscript over denominator A subscript 2 end subscript end fraction close parentheses to the power of 1 divided by 3 end exponent
rightwards double arrow fraction numerator r over denominator 2 r end fraction equals open parentheses fraction numerator 9 over denominator A to the power of 2 end exponent end fraction close parentheses to the power of 1 divided by 3 end exponent left parenthesis because A subscript 1 end subscript equals 9 right parenthesis
rightwards double arrow blank open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 3 end exponent equals fraction numerator 9 over denominator A to the power of 2 end exponent end fraction
Hence,A subscript 2 end subscript equals 9 blank cross times blank open parentheses 2 close parentheses to the power of 3 end exponent blank equals 9 cross times 8 equals 72
Thus, in germanium (G e) nucleus number of nucleons is 72.
parallel

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