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5651.

Let I1 and l2 be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron.(a) I1 <l2(b) l1=l2(c) l1> l2(d) relation between I1 and l2 depends on the actual shapes of the bodies.

Answer»

(a) I1 < I2 .

Explanation: 

Aluminum has a lower density than iron hence the first body has lesser mass than the second. And if the shapes of the bodies are same the M.I. is directly proportional to the mass. So the first body will have lower M.I. than the second body.

5652.

A uniform solid cylinder of mass 5kg and radius 0.1m is resting on a horizontal platform (parallel to the x-y plane) and is free to rotate about its axis along the y-axis the platform is given a motion in the x direction given by x=0.2 cos (10t) m if there is no slipping then maximum torque acting on the cylinder during its motion isA. `0.2 N-m`B. `2.0 N-m`C. `5.0N-m`D. `10.0N-m`

Answer» Correct Answer - C
`Ialpha = ((MR^(2))/2)xx(a/R)`
`a=(d^(2)x)/dt^(2)= -0.2xx 100cos(10t)=-20cos(10t)`
`alpha=a/R=-200cos(10t)`
`=-(5xx(0.1)^(2))/2 xx200cos(10t)=-5/2xx2xxcos(10t)=-5cos(10t)`
`t_(max)=5Nxxm`
5653.

Waves `y_(1) = Acos(0.5pix - 100pit)` and `y_(2)=Acos(0.46pix - 92pit)` are travelling along x-axis. (Here `x` is in `m` and `t` is in second) (1) Find the number of times intensity is maximum in time interval of `1 sec`.A. 4B. 6C. 8D. 10

Answer» Correct Answer - A
Number of maxima in `1 s` is called the beat frequency.
Hence,
`f_(b) = f_(1) -f_(2)`
=`(100 pi)/(2 pi) -(92 pi)/(2 pi) = 4 Hz`.
5654.

Waves `y_(1) = Acos(0.5pix - 100pit)` and `y_(2)=Acos(0.46pix - 92pit)` are travelling along x-axis. (Here `x` is in `m` and `t` is in second) (2) The wave velocity of louder sound isA. 100 m//sB. 192 m//sC. 200 m//sD. 96 m//s

Answer» Correct Answer - C
Speed of wave,
`v = (omega)/(k)`
`v = (100 pi)/(0.5 pi)` or `(92 pi)/(0.46 pi) = 200 m//s`.
5655.

In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =1. 1 : 32. 3 : 13. 2 : 14. 1 : 2

Answer» Correct Answer - Option 4 : 1 : 2

Concept:

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

 

Calculations:

Given, In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q.

Join AC and BP. 

⇒ \(\angle\)AQP= CQB and \(\angle\)APQ= \(\angle\)CBQ

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent

⇒ \(\rm\triangle APQ ∼ \triangle CBQ\)

⇒ \(\rm \dfrac {AP}{BC}= \rm \dfrac{AQ}{QC}\)

⇒ AD = BC

⇒ \(\rm \dfrac {AP}{BC}= \rm \dfrac{AP}{AD} = \dfrac 1 2\)
 
⇒ \(\rm\rm \dfrac{AQ}{QC} = \dfrac 12\)

 Hence, In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC = 1 : 2

5656.

Akbar founded the Din-i-Ilahi primarily to (a) Establish a national religion which would be acceptable to the Muslims and the Hindus (b) Ensure racial and communal harmony (c) Found a religious institution (d) Put an end to differences between Hindus and Muslims

Answer»

(a) Establish a national religion which would be acceptable to the Muslims and the Hindus

5657.

Number of real solution of the equation sin (ex) = 5x + 5-x is

Answer» Correct Answer - Option 1 : 0

Concept:

-1 ≤ sin x ≤ 1

 

AM, GM, HM Formulas

If A is the arithmetic mean of numbers a and b and is given by ⇔ \({\rm{A}} = \frac{{{\rm{a\;}} + {\rm{\;b}}}}{2}\)

If G is the geometric mean of the numbers a and b and is given by ⇔ \({\rm{G}} = \sqrt {{\rm{ab}}} \)

If H is the Harmonic mean of numbers a and b and is given by ⇔ \({\rm{H}} = \frac{{2{\rm{ab}}}}{{{\rm{a}} + {\rm{b}}}}\)

Relation between AM, GM and HM

  1. G2 = AH
  2. AM  ≥  GM  ≥  HM

 

Calculations:

Given, the equation is sin (ex) = 5x + 5-x 

Consider, LHS = sin (ex)  < 1

As we know AM ≥ GM

\(\rm \Rightarrow \frac{5^x + 5^{-x}}{2} \geq (5^x \times 5^{-x})^{1/2}\)

∴ 5x + 5-x  ≥ 2

RHS = 5x + 5-x  ≥ 2

Here, LHS \(\neq\) RHS

The equations sin (ex) = 5x + 5-x have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction.

Hence, Number of real solution of the equation sin (ex) = 5x + 5-x is zero.

5658.

In Mansabdari system the Commander-in-Chief of the Army was (a) Mansabdar (b) Emperor (c) Prince (d) Dah Hazari

Answer»

In Mansabdari system the Commander-in-Chief of the Army was Emperor.

5659.

The East India Company was founded in India during the reign of (a) Shah Jahan (b) Jahangir (c) Akbar (d) Aurangzeb

Answer»

The East India Company was founded in India during the reign of Akbar.

5660.

Let `agt0, bgt0, cgt0` and `a+b+c=6` then `((ab+1)^(2))/(b^(2))+((bc+1)^(2))/(c^(2))+((ca+1)^(2))/(a^(2))` may beA. `75/4`B. `35`C. `15`D. `10`

Answer» Correct Answer - A::B
A.M. `ge` H.M for `1/a, 1/b, 1/c` we get `(1/a+1/b+1/c)/3 ge 3/6`
`implies 1/a+1/b+1/c ge 3/2`
Now, `((a+1/b)^(2)+(b+1/c)^(2)+(c+1/a)^(2))/3 ge ((a+1/b+b+1/c+c+1/a)/3)^(2) ge ((6+3/2)/3)^(2)`
`(a+1/b)^(2)+(b+1/c)^(2)+(c+1/a)^(2) ge 75/4`
5661.

Mansabdari System was founded by Akbar. The Mansabdars were(a) military commanders (b) provincial governors (c) high civil and military officers (d) all of the above

Answer»

(d) all of the above

5662.

The Mansabdari system introduced by Akbar was borrowed from the system prevalent in (a) Persia (b) Mongolia (c) Afghanistan (d) Turkey

Answer»

The Mansabdari system introduced by Akbar was borrowed from the system prevalent in Mongolia.

5663.

Under the Mughals the Commander-in-Chief of the Army was (a) The crown prince (b) Mansabdar (c) Emperor (d) Zamindar

Answer»

Under the Mughals the Commander-in-Chief of the Army was Emperor.

5664.

Under the Mughals ____ was administered as a department of the household. (a) infantry (b) cavalry (c) artillery (d) navy

Answer»

Under the Mughals artillery was administered as a department of the household.

5665.

The troops provided by the Mansabdars was chiefly (a) cavalry (b) infantry (c) artillery (d) navy

Answer»

The troops provided by the Mansabdars was chiefly artillery.

5666.

Which Rajput dynasty had not surrendered to Akbar? (a) Pratihara (b) Sisodiya (c) Rathor (d) Parmar

Answer»

Sisodiya Rajput dynasty had not surrendered to Akbar.

5667.

The Mughal troops were largely drawn from (a) The Rajput Chiefs (b) Tributary Chiefs (c) Mansabdars (d) Central Contingents

Answer»

(c) Mansabdars

5668.

On the wall of which building built by Shah Jahan, is the following Persian couplet inscribed "if there is paradise on earth, it is this, it is this, it is this"? (a) Jasmine Palace (b) Moti Masjid (c) Diwan-i-Aam, Delhi (d) Diwan-i-Khas, Delhi

Answer»

(d) Diwan-i-Khas, Delhi

5669.

Shah Jahan was kept in prison by Aurangzeb at (a) Ajmer (b) Agra (c) Delhi (d) Daulatabad

Answer»

Shah Jahan was kept in prison by Aurangzeb at Agra.

5670.

Bibi Ka Maqbara was erected by _____ at Aurangabad and is a replica of the Taj Mahal. (a) Jahangir (b) Bahadur Shah Zafar (c) Aurangzeb (d) None of the above

Answer»

(c) Aurangzeb

5671.

In the Battle of Haldighati the Mughal troops were commanded by (a) Asaf khan (b) Raja Man Singh of Amber (c) Qazi Khan (d) Todar Mal 

Answer»

In the Battle of Haldighati the Mughal troops were commanded by Raja Man Singh of Amber.

5672.

Of the following which was not built by Shah Jahan? (a) Moti Masjid (b) Jami Masjid(c) Taj Mahal (d) Fatehpur Sikri 

Answer»

(d) Fatehpur Sikri

5673.

The title of Mahakavi Rai was given by Shah Jahan to (a) Todar Mal (b) Birbal (c) Jagannath (d) Tansen

Answer»

The title of Mahakavi Rai was given by Shah Jahan to Jagannath.

5674.

The garden is located in a radius of 300 Km from Delhi. It was created in the 17th century by architect Nawab Fidai Khan during the early reign of his foster brother Aurangzeb. Now it has been named after one of the rulers of the former princely state of Patiala. How is the garden known as now?

Answer»

PINJORE (YADAVINDRA GARDENS)

5675.

Someone whose job is to design buildings is ______. A) teacher B) architect C) singer D) mailman

Answer»

Correct option is B) architect

5676.

In 1931, Kasturbhai, Narottambhai and Chimanbhai incorporated a venture during the swadeshi movement with an objective to indigenously produce fine and superfine cotton fabrics for the Indian markets. What did they establish?

Answer»

Arvind Mills

5677.

Which Sikh Guru compiled the Granth Sahib?

Answer»

Guru Arjan Dev-the 5th guru

5678.

The construction of Taj Mahal was directed by (a) Ustad Isa (b) Asaf Khan (c) Dara (d) Aurangzeb

Answer»

The construction of Taj Mahal was directed by Ustad Isa.

5679.

Isa Khan Effendi, a world famous architect from Egypt is credited with the design of a famous structure, which one?

Answer»

The Taj Mahal

5680.

which one of the following isa case of wrong matching?A. somatic hybridisation fusion of two diverse cellsB. vector DNA site for RNA sythesisC. Micropropagation -In vitro production of plants in large numbersD. callus unorgainised mass of cells produced in tissue culture

Answer» Correct Answer - B
out of the following the statement is wrong because a vector is a DNA molecule used as a vehicle to transfer foreign genetic material in to desried cell
The RNA is synthsised in the nucleus on a DNA tempelate only 0.25% o ftotal DNA content ocdes for RNA.
5681.

In `DeltaABC`, if `m_(a),m_(b),m_(c)` denote the lengths of the medians drawn to the sides a, b, c respectively and `Delta` is the area of the `DeltaABC` with `a=10, c=6" and "m_(b)=7`thenA. `b=sqrt(76)`B. `Delta=15sqrt(3)`C. `m_(a)=sqrt(76)`D. `m_(c)=sqrt(31)`

Answer» Correct Answer - A
`m_(b)=(1)/(2)sqrt(2a^(2)+2c^(2)-b^(2))`
`b^(2)=76impliesb=sqrt(76)=2sqrt(19),s=(a+b+c)/(2)=8+sqrt(19)`
`Delta=sqrt(s(s-a)(s-b)(s-c))=15sqrt(3)`
`m_(a)=(1)/(2)sqrt(2b^(2)+2c^(2)-a^(2))=sqrt(31)`
`m_(c)=(1)/(2)sqrt(2a^(2)+2b^(2)-c^(2))=sqrt(79).`Ans.
5682.

One mole of `N_(2)` and `3.0` moles of `PCl_(5)` were placedin a 100-liter vessel and heated to `227^(@)C`. The equilibrium pressure was `2.05" atm. "`Assuming ideal behaviour, calculate X. Where `X=1000xxK_(P)` of the reaction at `227^(@)C.`

Answer» Correct Answer - [0205]
`{:("The reaction is",,"PCl"_(5)hArr"PCl"_(3)+"Cl"_(2)),(,,(g)" "(g)" "(g)),("Initial concn.",,3"moles"" "0" "0):}`
Concen. At equilibrium `" "(3-3alpha)" "3alpha" "3alpha` where `alpha` is degree of dissociation of `PCl_(5).`
Total moles of gases in the vessel
`{:(=n=N_(2)(1" mole")+PCl_(5)(3-3alpha)+PCl_(3)(3alpha)+Cl_(2)(3alpha)),(" moles"" moles"" moles"):}`
Or `n=4+3alpha`
Using the ideal gas equation `n=(PV)/(RT)=(2.05xx100)/(0.082xx500K)=5.0" moles "`
Or `4+3alpha=5" or "3alpha=1" or "alpha=1//3=0.333 ("degree of dissociation of" PCl_(5))`
Partial pressure of `PCl_(5)=(2)/(5)xx2.05=0.82" atm."`
Partial pressure of `PCl_(3)=(1)/(5)xx2.05=0.41" atm. "`
Partial pressure of `Cl_(2)=(1)/(5)xx2.05=0.41`
`K_(P)=((0.41" atm")^(2))/((0.82" atm"))=0.205" atm."`
`X=0.205xx1000=205`
5683.

A dishonest shopkeeper sells sugar at Cost price but uses 600 gms in place of 1 kg weight. What is his actual gain percentage?1. 66.67%2. 33.34%3. 25%4. 54%5. 25.67%

Answer» Correct Answer - Option 1 : 66.67%

Given:

A dishonest shopkeeper sells sugar at Cost price but uses 600 gm in place of 1 kg weight.

Formula used:

Profit or Gain % = {(Selling price – Cost price)/Cost price} × 100

Calculation:

Let  be 1 gram = 1 rupees

The cost price of sugar for shopkeeper = Rs. 600            

The selling price of sugar for shopkeeper = Rs. 1000     

⇒ Profit or Gain% = {(1000 – 600)/600} × 100

⇒ (400/600) × 100

⇒ 66.67%

∴ The actual gain percentage of shopkeeper is 66.67%.

5684.

The C60 molecule has(a) 14 pentagons and 18 hexa gons(b) 12 pentagons and 20 hexa gons(c) 10 pentagons and 20 hexa gons(d) 12 pentagons and 18 hexa gons

Answer»

The C60 molecule has 10 pentagons and 20 hexa gons

5685.

Why do Zr and Hf exhibit similar properties ?

Answer»

Due to lanthanide contraction.

5686.

Science and practice of fruit culture isA. SpermologyB. PomologyC. AnthologyD. Dendrology

Answer» Correct Answer - B
Science and practice of fruit culture is pomology.
5687.

Anthesis is a phenomenon which refers to:A. Opening of floral budB. Development of anthersC. Mutaration of anthersD. Reception of pollen by stigma

Answer» Correct Answer - A
Anthesis is opening of floral bud.
5688.

What is effect of increasing pH on K2Cr2O7 solution ?

Answer»

It changes into K2CrO4 solution/orange colour change into yellow colour.

5689.

Ore of chromium is(a) FeCr2 O4(b) K2Cr2O4 (c) PbCrO4 (d) None

Answer»

Ore of chromium is  FeCr2 O4

5690.

What is the effect of pH on the solution of K2Cr2O4 solution ?

Answer»

K2Cr2O4 solution changes into K2Cr2O7/yellow colour changes into orange colour.

5691.

Why Zn, Cd, Hg are soft and have low melting point ?

Answer»

Due to weak interatomic attraction/absence of unpaired electrons.

5692.

Write electronic conflguration of Cu+2 and Co+2.

Answer»

Cu+2 = [Ar] 3d9 4s0
Co+2 = [Ar] 3d7

5693.

Balance the following equations :(a) MnO4- + Fe2+ + H+ →(b) Cr2O7 2-+ Sn2+ + H+ →

Answer»

(a) MnO4 - + Fe2+ + H+  Mn+2 + Fe+3
(b) Cr2O7 2- + Sn2+ + H+ Cr+3 + Sn+4

5694.

Briefly explain why electronic conflguration of lanthanoids are not known with certainty ?

Answer»

4f/5d subshells are very close in energy. +ve electrons can jump from 4f to 5d or vice-versa.

5695.

What is the composition of Permutit (Zeolite) ? How does it works in softening of hard water?

Answer»

Hydrated sodium aluminium silicate / Sodium aluminium silicate.

It exchanges Mg2+ and Ca2+ ions for its Na+ hence soften the hard water.

5696.

A curve describing the equilibrium relationship of sorbed water and vapor pressure (or relative humidity) at a given temperature is a. Isotherm b. Parabola c. Both a. and b. d. None of All

Answer»

a. Isotherm.

5697.

An insect's mechanoreceptors would NOT be sensitive to: a. Body movement b. Sound vibrations c. Wind speed d. Water vapor

Answer»

An insect's mechanoreceptors would NOT be sensitive to Water vapor.

5698.

Who discovered DNA fingerprinting ?(1) Alec Jeffery (2) Jacob Monad (3) Herbert Boyer (4) Stanley Cohen 

Answer»

Correct option: (1) Alec Jeffery

5699.

Mechanoreceptors gives response a. Light b. Humidity c. Body movements d. Pressure 

Answer»

c. Body movements

5700.

Pro-preoreceptros give response a. Light b. Humidity c. Body movement d. Pressure 

Answer»

Pro-preoreceptros give response Pressure.