100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 1983 InterviewSolution

99101.	The founder of Aligarh Movement (A) Muhammad Iqbal (B) Sir Syed Ahmad Khan (C) M.A.Ansari
Answer» Correct option is (B) Sir Syed Ahmad Khan

Discussion

99102.	The establishment of the Asiatic Society of Bengal and the introduction of English education are examples for two kinds of policies adopted by Britain to establish their domination in India. What are these policies?
Answer» An in depth understanding of the social cultural life of the Indians. It will help strengthen their rule. To get the support of a fraction of Indian society through English education.

Discussion

99103.	The founder of ‘Asiatic Society of Bengal’ (A) William Jones (B) Jonathan Duncan (C) Warren Hastings
Answer» Correct option is (A) William Jones

Discussion

99104.	A ray light from a liquid `(mu=sqrt(3))` is incident on a system of two right angled prism of refractive indices `sqrt(3) and sqrt(2)` as shown. The ray suffers zero deviation when emerges into air from CD. The angle of incidence I is A. `45^(@)`B. `35^(@)`C. `20^(@)`D. `10^(@)`
Answer» Correct Answer - A

Discussion

99105.	Write down two characteristics of fuse wire.
Answer» (i) Low resistance, (ii) Low melting point.

Discussion

99106.	What is the material of optical fibre core?
Answer» Glass or Quartz.

Discussion

99107.	Write down the expression of fringe width in interference.
Answer» The expression of fringe width in interference is β = λd/d.

Discussion

99108.	What is inductive reactance?
Answer» Inductive reactance X_L= ωL.

Discussion

99109.	Capacitor `C_3` in the circuit is a variable capacitor (its capacitance can be varied). `C_1 and C_2` are of fixed values. Graph is plotted between potential difference `V_1` (across capacitor `C_1)` versus `C_3`. Electric potential `V_1` approches on asymptote of 10 V as `C_3 prop oo`. , When `V_1 = 4V`m then `C_3` is equal toA. `5C_2//2`B. `5C_1//3`C. `5C_2//3`D. none of these
Answer» Correct Answer - D When `C_(3)toinfty` it means distance between the plates of `C_(3)` is zero or both plates will be at the same potential then `C_(2)` will be shorted entire pontential V will ber across `C_(1)` hence `V=V_(1)=10V` From graphs when `C_(3)=0,V_(1)=2V. So C_(3)` will act like open switch `C_(1)` and `C_(2)` will be in series potential different across `C_(2)` is `V_(2)=10-V_(1)` `=8V` `q=C_(1)V_(1)=C_(2)V_(2)` or `C_(12)=C_(28)` or `C_(1)=4C_(2)` `V_(1)=4V,V_(2)=10-4=6V` `q=C_(1)V_(1)=(C_(2)+C_(3))V_(2)` or `C_(14)=(C_(2)+C_(3))6` or `16C_(2)=6C_(2)+6C_(3)` or `C_(3)=5C_(2//3)`

Discussion

99110.	Capacitor `C_3` in the circuit is a variable capacitor (its capacitance can be varied). `C_1 and C_2` are of fixed values. Graph is plotted between potential difference `V_1` (across capacitor `C_1)` versus `C_3`. Electric potential `V_1` approches on asymptote of 10 V as `C_3 prop oo`. , Relation between `C_1and C_2` isA. `C_1 = C_2`B. `C_1 = 4C_2`C. `4C_1 = C_2`D. any relation
Answer» Correct Answer - C When `C_(3)toinfty` it means distance between the plates of `C_(3)` is zero or both plates will be at the same potential then `C_(2)` will be shorted entire pontential V will ber across `C_(1)` hence `V=V_(1)=10V` From graphs when `C_(3)=0,V_(1)=2V. So C_(3)` will act like open switch `C_(1)` and `C_(2)` will be in series potential different across `C_(2)` is `V_(2)=10-V_(1)` `=8V` `q=C_(1)V_(1)=C_(2)V_(2)` or `C_(12)=C_(28)` or `C_(1)=4C_(2)` `V_(1)=4V,V_(2)=10-4=6V` `q=C_(1)V_(1)=(C_(2)+C_(3))V_(2)` or `C_(14)=(C_(2)+C_(3))6` or `16C_(2)=6C_(2)+6C_(3)` or `C_(3)=5C_(2//3)`

Discussion

99111.	A gang capacitor is a variable capacitor in which capacitance is varied by changing theA. Dielectric B. Number of plates C. Distance between plates D. Plate Area
Answer» A gang capacitor is a variable capacitor in which capacitance is varied by changing the Plate Area.

Discussion

99112.	A uniform rod of mass m, hinged at its upper end, is released from rest from a horizontal position. When it passes through the vertical position, the force on the hinge is (a) 3/2 mg (b) 2mg (c) 5/2 mg (d) 3mg
Answer» Correct Answer is: (c) 5/2 mg mg. l/2 = 1/2 Iω² = 1/2. ml²/3 ω². or ω² = 3g/l. Now, N - mg = mω² l/2 = m. 3g/l . l/2 = 3/2 mg or N = 5/2 mg.

99112.

A uniform rod of mass m, hinged at its upper end, is released from rest from a horizontal position. When it passes through the vertical position, the force on the hinge is (a) 3/2 mg (b) 2mg (c) 5/2 mg (d) 3mg

Answer»

Correct Answer is: (c) 5/2 mg

mg. l/2 = 1/2 Iω² = 1/2. ml²/3 ω².

or ω² = 3g/l.

Now, N - mg = mω² l/2 = m. 3g/l . l/2 = 3/2 mg

or N = 5/2 mg.

Discussion

99113.	One end of a uniform rod of length l and mass m is hinged at A. It is released from rest from horizontal position AB as shown in figure. The force exerted by the rod on the hinge when it becomes vertical is A. `(3)/(2)mg`B. `(5)/(2)mg`C. 3mgD. 5mg
Answer» Correct Answer - B `U_(1)=(1)/(2)QE` `U_(2)=QE` `U_(1),U_(2)=1 : 2` Note : Energy dissipated as heat `=U_(2)-U_(1)=(1)/(2)QE`

Discussion

99114.	A car `A` going north-east at `80km//h` and another car `B` is going south-east at `60km//h.` The direction of the velocity of `A` relative to `B` makes an angle with the north equal to:A. `tan^(-1)((2)/(7))`B. `tan^(-1)((7)/(2))`C. `tan^(-1)(7)`D. `tan^(-1)((1)/(7))`
Answer» Correct Answer - B `intvec(B).dl=mu_(0)Sigmai=4pixx10^(-7)(-1+5-3)=4pixx10^(-7)Tm`

Discussion

99115.	There are two vectors of same magnitude 5 and addition of them have magnitude `5sqrt(3)` then what is magntude of their differenceA. 5B. 0C. 10D. g
Answer» `\|vecA+vecB\|=2(5)cos(theta)/(2)=5sqrt(3)` `theta=60^(@)` `\|vecA-vecB\|=2(5)sin(60)/(2)=5`

Discussion

99116.	X- component of `vec(a)` is twice of its Y- component. If the magnitude of the vector is `5sqrt(2)` and it makes an angle of `135^(@)` with z-axis then the components of vector is:A. `2sqrt(3), sqrt(3), -3`B. `2sqrt(6), sqrt(6), -6`C. `2sqrt(5), sqrt(5), -5`D. None of these
Answer» Correct Answer - C `a_(x)=2a_(y), cos gamma=a_(z)/a=cos 135^(@)=-1/sqrt(2)` `rArr a_(z)=-a/sqrt(2)=-(5sqrt(2))/sqrt(2)=-5` Now `a_(x)^(2)+a_(y)^(2)=50 rArr 4a_(y)^(2)+a_(y)^(2)+25=50` `rArr a_(y)^(2)=5 rArr a_(y)= +- sqrt(5) rArr a_(x)= +- 2sqrt(5)`

Discussion

99117.	The input to a coherent detector is DSB-SC signal plus noise. The noise at the detector outputis (a) the in-phase component (b) the quadrature-component (c) zero (d) the envelope
Answer» (a) the in-phase component The coherent detector rejects the quadrature component of noise therefore noise at the output has in phase component only.

99117.

The input to a coherent detector is DSB-SC signal plus noise. The noise at the detector outputis (a) the in-phase component (b) the quadrature-component (c) zero (d) the envelope

Answer»

(a) the in-phase component

The coherent detector rejects the quadrature component of noise therefore noise at the output has in phase component only.

Discussion

99118.	Consider the equation `sectheta+ cottheta = 31/12` On the basis of above, answer the following If `0 lt theta lt (pi)/(2)`, then minimum value of `[tan theta]` is equal to (where [ ] is G.I.F)A. `0`B. `1`C. `2`D. `3`
Answer» Correct Answer - A Let `t =tan,(theta)/(2)` `implies (1+t^(2))/(1-t^(2))+(1-t^(2))/(2t)=(31)/(12)` `implies6t^(4)+43t^(3)-12t^(2)-19t+6=0` `implies(3t-1)(2t^(3)+15t^(2)+t-6)=0` `implies t=(1)/(3),alpha,beta,gamma` where `alpha in(-8,-7)implies(theta)/(2)in((pi)/(2),(3pi)/(4))` `beta in (-1,(-1)/(2))implies(theta)/(2) in ((3pi)/(4),(7pi)/(8))` `gamma in((1)/(2),1)implies(theta)/(2)in(0,(pi)/(4))` (i) if `0lttheta lt (pi)/(2)` then `t=(1)/(3)` or `t in ((1)/(2),1)` `implies tan theta =(3)/(4) "or if" tan. (theta)/(2)in((1)/(2),1)implies "tan" theta in ((4)/(3),oo)` `implies"Min value of" [tan theta] =0` (ii)No. of values of `theta in ((pi)/(2),(3pi)/(2))` will be 1

Discussion

99119.	Consider the equation `sectheta+ cottheta = 31/12` On the basis of above, answer the following Number of values of theta where `theta in [0,5pi]` is equal toA. `4`B. `6`C. `8`D. `10`
Answer» Correct Answer - D Let `t =tan,(theta)/(2)` `implies (1+t^(2))/(1-t^(2))+(1-t^(2))/(2t)=(31)/(12)` `implies6t^(4)+43t^(3)-12t^(2)-19t+6=0` `implies(3t-1)(2t^(3)+15t^(2)+t-6)=0` `implies t=(1)/(3),alpha,beta,gamma` where `alpha in(-8,-7)implies(theta)/(2)in((pi)/(2),(3pi)/(4))` `beta in (-1,(-1)/(2))implies(theta)/(2) in ((3pi)/(4),(7pi)/(8))` `gamma in((1)/(2),1)implies(theta)/(2)in(0,(pi)/(4))` (i) if `0lttheta lt (pi)/(2)` then `t=(1)/(3)` or `t in ((1)/(2),1)` `implies tan theta =(3)/(4) "or if" tan. (theta)/(2)in((1)/(2),1)implies "tan" theta in ((4)/(3),oo)` `implies"Min value of" [tan theta] =0` (ii)No. of values of `theta in ((pi)/(2),(3pi)/(2))` will be 1

Discussion

99120.	Signum function sgn(f), for f>0, f=0 and f<0, has the values: a. -1 to +1 b. +1, 0, -1 respectively c. -∞ to + ∞ d. 0 always
Answer» b. +1, 0, -1 respectively The sgn(f) is a signum function that is defined in the frequency domain as sgn(f) = 1, f> 0 = 0, f = 0 = -1, f< 0 Mathematically, the sign function or signum function is an odd mathematical function which extracts the sign of a real number and is often represented as sgn

99120.

Signum function sgn(f), for f>0, f=0 and f<0, has the values: a. -1 to +1 b. +1, 0, -1 respectively c. -∞ to + ∞ d. 0 always

Answer»

b. +1, 0, -1 respectively

The sgn(f) is a signum function that is defined in the frequency domain as sgn(f) = 1, f> 0

= 0, f = 0 = -1, f< 0

Mathematically, the sign function or signum function is an odd mathematical function which extracts the sign of a real number and is often represented as sgn

Discussion

99121.	Area of the triangle formed by the pair of tangents drawn form (1,1) to `x^(2)+2x-y+7=0` and its chord of contact is `Delta` then `(Delta)/(9)` is equal to
Answer» Area of the traingle is `\|(S_(1).^(3//2))/(2a)\|`

Discussion

99122.	Two lines are drawn at right angles one being a tangent to `y^(2) = 12x` and the other to `x^(2) = 111116y`. If the locus of their point of intersection is `(x^(2)+y^(2))(lx+my)+(nx-3y)^(2)=0` then `l+n-m` is equal to
Answer» Correct Answer - C Tangets on both the parabolas `y = mx +(3)/(m),y = mx-4m^(2)` `m^(2)x- my +3=0,4m^(2)-mx+y=0` eliminating m we get the locus

Discussion

99123.	Let `(alpha,beta)` be the focus of `x^(2) + 2xy +1 -y^(2) then 12beta + 4alpha` is equal to
Answer» Let parabola be `(x+y-k)^(2)=lambda(y-x+p)` comparing the above equation with parabola `x^(2)+2xy=2x+1-y^(2)`, we get lambda, k and p`

Discussion

99124.	The number of integers satisfying the inequation `\|x-1\|le[(sqrt(2)+1)^(6)+(sqrt(2)-1)^(6)]` where `[.]` denotes greatest integer function is greater than and equal to :A. `198`B. `396`C. `397`D. `398`
Answer» Correct Answer - A::B::C The number of ……….. Using binomial theorem, `(sqrt(2)+1)^(6)+(sqrt(2)-1)^(6) = 198` Hence `\|x-1\|le198` `implies x-1 epsilon [-198, 198]` `implies x epsilon [-197, 199]` , `:. 397`

Discussion

99125.	The number of integral solution of the equation `(sgn((x-1)(x-5)))^(x)=1` lying in the interval `[-10, 10]` is not equal to :A. `11`B. `16`C. `17`D. `18`
Answer» Correct Answer - A::B::C The number of ……….. `(f(x))^(g(x)) = 1` is possible when Case - I `f(x)=1, g(x) in R` Case - II `f(x) in R - {0}, g(x) = 0` Case - III `f(x)= -1, g(x) =` even Case - I `sgn((x-1)(x-5)) = 1` `implies (x-1) (x-5) gt 0` `implies x in (-oo, 1) uu (5, oo)` Also `x in [-10, 10]` `:. x = {-10, -9, -8, ..... -1,0}uu{6,7,8,9,10}` `:. 16` values Case - II `g(x) = 0` and `f(x) != 0` `x = 0` and `sgn{(x-1) (x-5)}!= 0` i.e. already considered in Case - I Case - III `f(x)= -1, g(x) =` even `implies sgn ((x-1) (x-5)) = -1` and `x =` even `implies x in (1,5)` and `x =` even `implies x = {2, 4} implies 2` more values `:. 16+12=18`

Discussion

99126.	With the increase of temperature, the resistance of a semiconductor(a) increases(b) decrease(c) sometimes increases and sometimes decreases (d) remains unchanged.
Answer» (b) decreases

Discussion

99127.	The input impedance of a diff amp equals re' times a. 0 b. RC c. RE d. 2 times Beta
Answer» (d) 2 times Beta

Discussion

99128.	Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite direction with same speed. Water comes to rest relative to wall after striking. Treating A as cross-section of jet and density of water as `rho` Select the correct alternative(s)A. force exerted on the wall is `2rhoAv^(2)`B. force exerted on the wall is `4rhoAv^(2)`C. rate of change of kinetic energy of water jet striking the wall is `8rhoAv^(3)`D. rate of change of kinetic energy of water jet striking the wall is zero.
Answer» Correct Answer - B::D mass rate of strike `(dm)/(dt) = A(2v)rho` Change in velocity during strike `=Deltav=vec(v)_(f)-vec(v)_(i)=(-v)-(v)=-2v` Thrust force on jet `=Deltav (dm)/(dt)=(dm)/(dt)(-2v)=-4rhoAv^(2)` Thrust force on wall =-Thrust force on jet `=4rhoAv^(2)` `(d(KE))/(dt)=1/2 (dm)/(dt) (v_(f)^(2))-1/2(dm)/(dt)(v_(i)^(2))=1/2(dm)/(dt)[(-v)^(2)-v^(2)]=0`

Discussion

99129.	Two particles of a medium disturbed by the wave propagtion are at `x_(1)=0` and `x_(2)=1` cm The wave is propagating in positive x-direction The displacement of the particles is given by the equation: `y_(1)=(2sin3pit)` cm and `y_(2)=2sin(3pit-pi//8)` cm (t is in seconds)A. The frequency of wave is `1.5` HzB. Wavelength of the wave can be 16 cmC. Velocity of the wave can be 24 cm//sD. Wave equation can be `y=(2)sin[(2pi)/16(24t-x)]` cm.
Answer» Correct Answer - A::B::C::D As the motions of particles are simple harmonic, amplitude =2 cm `omega` (Angular frequency) `=3pirad//sec` As the phase difference of particles separated by 1 cm is `pi//8` `lambda=8/pixx2pi=16` cm Hence, wave velocity `=omega/(2pi)xxlambda=24` cm//s `y=(2)sin[(2pi)/16(24t-x)]` cm

Discussion

99130.	Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite with same speed. Water come to rest relative to wall after striking. Treating A as cross-section of jet and density of water as `rho`. Select the correct alternative(s)A. force exerted on the wall is `2rhoAv^(2)`B. force exerted on the wall is `4rhoAv^(2)`C. rate of change of kinetic energy of water jet striking the wall is `8 rhoAv^(3)`D. rate of change of kinetic energy of water jet striking the wall is zero
Answer» Correct Answer - B::D

Discussion

99131.	Which of the following acts as a circuit protecting device? (1) Conductor (2) Inductor (3) Switch (4) Fuse
Answer» The correct option is (4) Fuse. Explanation: Fuse wire has less melting point so when excess current flows, due to heat produced in it, it melts.

99131.

Which of the following acts as a circuit protecting device? (1) Conductor (2) Inductor (3) Switch (4) Fuse

Answer»

The correct option is (4) Fuse.

Explanation:

Fuse wire has less melting point so when excess current flows, due to heat produced in it, it melts.

Discussion

99132.	Two particles of of a medium disturbed by the wave propagation are at `x_(1) = 0` and `x_(2) = 1 cm`. The wave is propagating in positive x-direction. The displacement of the particles is given by the equation : `y_(1) = (2sin3pit)cm` and `y_(2) = 2sin(3pit- pi//8)cm` (t is in secondA. The frequency of wave is `1.5` HzB. wavelength of the wave can be `16` cm.C. Velocity of the wave can be `24 cm//s`D. Wave equation can by `y = (2) sin [(2pi)/(16)(24t-x)]cm`.
Answer» Correct Answer - A::B::C::D

Discussion

99133.	Don’t you think it is significant _______? A) in case he fails B) that he has been re-elected C) how comfortable is it D) if we had been offered the job
Answer» Correct option is B) that he has been re-elected

Discussion

99134.	The working of dynamo is based on the principle of(a) heating effect of current(b) electromagnetic induction(c) magnetic induct(d) electric induction
Answer» (b) electromagnetic induction

Discussion

99135.	For an arithmetic sequence 22, 26, 30, ………….. a. What is the common difference? b. Will 50 be a term of this sequence? Why? c. Can the difference between any two terms of this sequence be 50? Justify your answer?
Answer» a. Common differenced = 26 – 22 = 4 b. \(\frac{50-22}{4}=7\) So, 50 is a term of this sequence, c. 50 is not a multiple of 4. So, 50 is cannot be a difference of two terms.

99135.

For an arithmetic sequence 22, 26, 30, ………….. a. What is the common difference? b. Will 50 be a term of this sequence? Why? c. Can the difference between any two terms of this sequence be 50? Justify your answer?

Answer»

a. Common differenced = 26 – 22 = 4

b. \(\frac{50-22}{4}=7\)

So, 50 is a term of this sequence,

c. 50 is not a multiple of 4. So, 50 is cannot be a difference of two terms.

Discussion

99136.	Water is a compound _______ molecule consists of two atoms of hydrogen and one atom of oxygen. A) which B) whom C) whose D) of which
Answer» Correct option is C) whose

Discussion

99137.	Find the smallest 3 digit number which is the multiple of 6. Find the sum of all the three-digit numbers which are the multiple of six.
Answer» Smallest 3 digit number which is the multiple of 6 = 102, Highest = 996 Common difference = 6 Arithmetic series : 102, 108, …………….. 996 Number of three digit numbers = \(\frac{996-102}{6}+1=150\) Sum = \(\frac{150}{2}(102+996)=82350\)

99137.

Find the smallest 3 digit number which is the multiple of 6. Find the sum of all the three-digit numbers which are the multiple of six.

Answer»

Smallest 3 digit number which is the multiple of 6 = 102,

Highest = 996

Common difference = 6

Arithmetic series : 102, 108, …………….. 996

Number of three digit numbers

= \(\frac{996-102}{6}+1=150\)

Sum = \(\frac{150}{2}(102+996)=82350\)

Discussion

99138.	A dynamo is a machine _______ is used for producing electricity. A) who B) which C) whom D) of which
Answer» Correct option is B) which

Discussion

99139.	I’ll leave him a note ________ he’ll know where we are. A) so that B) that C) in order D) for
Answer» Correct option is A) so that

Discussion

99140.	The student couldn’t remember the year _______ Hitler was born. A) when B) which C) at which D) where
Answer» Correct option is A) when

Discussion

99141.	That’s the hotel ________ last year. A) which we stayed B) at which we stayed at C) where we stayed at D) where we stayed
Answer» Correct option is D) where we stayed

Discussion

99142.	Write the sequence formed by the number of diagonals from a vertex of a triangle, a quadrilateral, a pentagon etc. What is its algebra?
Answer» Diagonal drawn from one vertex of a triangle = 0 = 3 – 3 = 0 Diagonal drawn from one vertex of a quadrilateral = 4 – 3 = 1 Diagonal drawn from one vertex of a pentagon = 5 – 3 = 2 Diagonal drawn from one vertex of a n sided polygon = n – 3 Sequence of number of diagonals 0, 1, 2, 3, 4, ………. Algebraic expression x_n= n – 3

99142.

Write the sequence formed by the number of diagonals from a vertex of a triangle, a quadrilateral, a pentagon etc. What is its algebra?

Answer»

Diagonal drawn from one vertex of a triangle = 0 = 3 – 3 = 0

Diagonal drawn from one vertex of a quadrilateral = 4 – 3 = 1

Diagonal drawn from one vertex of a pentagon = 5 – 3 = 2

Diagonal drawn from one vertex of a n sided polygon = n – 3

Sequence of number of diagonals 0, 1, 2, 3, 4, ……….

Algebraic expression x_n= n – 3

Discussion

99143.	Prove that the squares of the sequence 1, 3, 5,……..belongs to that sequence itself.
Answer» Odd-numbered arithmetic sequence will be 1, 3, 5, … Here the arithmetic sequence have common difference 2. Their squares are also odd numbers. Therefore the squares of the sequence 1, 3, 5, … belongs to that sequence itself. nth term = 2n – 1.

99143.

Prove that the squares of the sequence 1, 3, 5,……..belongs to that sequence itself.

Answer»

Odd-numbered arithmetic sequence will be 1, 3, 5, … Here the arithmetic sequence have common difference 2.

Their squares are also odd numbers.

Therefore the squares of the sequence 1, 3, 5, … belongs to that sequence itself. nth term = 2n – 1.

Discussion

99144.	Write the sequence of the number of diagonals in a quadrilateral, pentagon, hexagon etc. What is its algebra?
Answer» The number of diagonals in a quadilateral = \(\frac{4\times(4-3)}{2}=2\) The number of diagonals in a pentagon = \(\frac{5\times(5-3)}{2}=5\) The number of diagonals in a hexagon = \(\frac{6\,\times\,3}{2}=9\) The number of diagonals in a n sided = \(\frac{7\,\times\,4}{2}=14\) The number of diagonals in a n sided polygon = \(\frac{n\times(n-3)}{2}=\frac{n(n-3)}{2}\)

99144.

Write the sequence of the number of diagonals in a quadrilateral, pentagon, hexagon etc. What is its algebra?

Answer»

The number of diagonals in a quadilateral = \(\frac{4\times(4-3)}{2}=2\)

The number of diagonals in a pentagon = \(\frac{5\times(5-3)}{2}=5\)

The number of diagonals in a hexagon = \(\frac{6\,\times\,3}{2}=9\)

The number of diagonals in a n sided = \(\frac{7\,\times\,4}{2}=14\)

The number of diagonals in a n sided polygon = \(\frac{n\times(n-3)}{2}=\frac{n(n-3)}{2}\)

Discussion

99145.	Write the sequence of the squares of all odd numbers. What is its algebra?
Answer» Odd numbers = 1, 3, 5, 7, 9, 11, ……… f = l, d = 3 – 1 = 2, f – d = 1 – 2 = – 1 Algebraic form of odd numbers x_n = dn + (f – d) = 2n – 1 The sequence of the squares of all odd numbers = 1, 9, 2 5, 49,………. Algebraic form = (2n -1 )²

99145.

Write the sequence of the squares of all odd numbers. What is its algebra?

Answer»

Odd numbers = 1, 3, 5, 7, 9, 11, ………

f = l, d = 3 – 1 = 2, f – d = 1 – 2 = – 1

Algebraic form of odd numbers x_n = dn + (f – d) = 2n – 1

The sequence of the squares of all odd numbers = 1, 9, 2 5, 49,……….

Algebraic form = (2n -1 )²

Discussion

99146.	That is the hotel _______ I stayed at. A) where B) which C) that D) whose
Answer» Correct option is B) which

Discussion

99147.	Write the sequence of the perimeters of the equilateral triangles having sides 1cm, 2cm, 3cm. a. Write the sequence of area b. Write the sequence of sum of angles.
Answer» ’If we Increase 1 cm of sides of an equilateral triangle having sides 1cm, 2cm, 3cm. a. Area =1 cm², Area after increasing sides by 1 cm \(\frac{\sqrt{3}\times2^2}{4}=\sqrt{3}\) cm² Area after increasing the length of side 2cm by V³x3² = 9V³ , 1cm = \(\frac{\sqrt{3}\times3^2}{4}=\frac{9\sqrt{3}}{4}\) cm2 Area after increasing thelength of side 3cm by 1cm = \(\frac{\sqrt{3}\times4^2}{4}=\frac{16\sqrt{3}}{4}=4\sqrt{3}\) cm² Sequence of area = \(\sqrt{3},\frac{9\sqrt{3}}{4},4\sqrt{3}\) c. The sum of angles of a triangle will be 180° always for any measures of sides. Sequence of sum of angles 180, 180, 180,……..

99147.

Write the sequence of the perimeters of the equilateral triangles having sides 1cm, 2cm, 3cm. a. Write the sequence of area b. Write the sequence of sum of angles.

Answer»

’If we Increase 1 cm of sides of an equilateral triangle having sides 1cm, 2cm, 3cm.

a. Area =1 cm², Area after increasing sides by 1 cm \(\frac{\sqrt{3}\times2^2}{4}=\sqrt{3}\) cm²

Area after increasing the length of side 2cm by V³x3² = 9V³ ,

1cm = \(\frac{\sqrt{3}\times3^2}{4}=\frac{9\sqrt{3}}{4}\) cm2

Area after increasing thelength of side 3cm by

1cm = \(\frac{\sqrt{3}\times4^2}{4}=\frac{16\sqrt{3}}{4}=4\sqrt{3}\) cm²

Sequence of area = \(\sqrt{3},\frac{9\sqrt{3}}{4},4\sqrt{3}\)

c. The sum of angles of a triangle will be 180° always for any measures of sides. Sequence of sum of angles 180, 180, 180,……..

Discussion

99148.	Hydrogen is an element _______ atomic number is 1 and _______ atomic weight is 1.008. A) whose / whose B) of which / whose C) which / of which D) which / which
Answer» Correct option is A) whose / whose

Discussion

99149.	Write the sequence starting from 60 and 0 is added subsequently
Answer» Answer is 60, 60, 60,…………..

Discussion

99150.	Write the sequence starting from 1/2 and 3/4 is added subsequently
Answer» \(\frac{1}{2},1\frac{1}{2},2,2\frac{3}{4},3\frac{1}{2},4\frac{1}{4},5,.....\)

Discussion

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