100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	What is the smallest prime number
Answer» 2 is the smallest prime number.

Discussion

2.	The sides of two similar triangles are in the ratio `2: 3`, then the areas of these triangles are in the ratio ________.
Answer» Correct Answer - `4 : 9`

Discussion

3.	`Delta PQR` is right angled isosceles triangle, right angled at R. Find value of `sin` P.
Answer» `Sin P = 1//sqrt2`

Discussion

4.	If 12P5 + 5. 12P4 = 13Pr , find r.
Answer» We have ^(n–1)P_r + r. ^(n–1)P_(r–1) = ⁿP_r and r ≤ n ¹²P₅ + 5.¹²P₄ = ¹³P₅ = ¹³P_r (given) ⇒ r = 5

4.

If 12P5 + 5. 12P4 = 13Pr , find r.

Answer»

We have ^(n–1)P_r + r. ^(n–1)P_(r–1) = ⁿP_r and r ≤ n

¹²P₅ + 5.¹²P₄ = ¹³P₅ = ¹³P_r (given) ⇒ r = 5

Discussion

5.	The number of real roots of `x^(8) - x^(5) + x^(2) - x + 1 = 0` is
Answer» Correct Answer - `0` `(1)` when `x lt 0 rArr` expression `gt 0` `(2)` when `x = 0 rArr` expression `= 1 gt 0` `(3)` when `0 lt x lt x^(8) + x^(2) (1 - x^(3)) + (1 - x) gt 0` `(4) x = 1, 1-1 + 1 - 1 + 1 gt 0` `(5) x gt 1, x^(5)(x^(3) - 1) + x( x - 1) + 1 gt 0` so `x^(8) - x^(5) + x^(2) - x + 1 gt 0, cancelAAx in R` so on real roots

Discussion

6.	If `x^(2) - 3x + 2` is factor of `x^(4) - px^(2) + q` then `2q - p` is equal to
Answer» Correct Answer - `3` `x^(2) - 3x + 2 = 0` `(x - 2)(x - 1) = 0 rArr x = 1 , 2` so `1 - p + q = 0 rArr p = +5` `16 - 4p + q = 0` `2q - p = 8 -5 = 3`

Discussion

7.	Let `a,bepsilonR^+` for which `60^a=3` and `60^b=5` then `12^((1-a-b)/(2(1-b)))` is equal to
Answer» Correct Answer - `2` `60^(a) = 3 rArr a = log_(60)3` `60^(b) = 5 rArr b = b = log_(60)5` `(1 - a - b)/(2(1 - b)) = (1 - log_(60) 3 - log_(60) 5)/(2(1 - log_(60)5)) = log_(60)((60)/(3 xx 5))/(2log_(60)((60)/(5)))` `(log_(60)(4))/(2log_(60)(12)) = (log_(60)2)/(log_(60)12) = log_(12)2` `:. (12)^(log_(12)2 = 2`

Discussion

8.	Polynomial `P(x)` contains only terms of aodd degree. when `P(x)` is divided by `(x - 3)`, the ramainder is `6`. If `P(x)` is divided by `(x^(2) - 9)` then remainder is `g(x)`. Then find the value of `g(2)`.
Answer» Correct Answer - `4` As `P(x)` has only add degree terms `:. P(-x) = -P(x)` `rArr P(-3) = -P(3) = -6` Let `P(x) = Q(x^(2) - 9) + g(x)` where `Q` is quetient and `g(x)` is remainder `g(x) = ax + b` `P(x) = Q(x^(2)- 9) + ax + b` `x = 3, P(3) = 3a + b = 6 ….(i)` `x = -3, P(-3) = -3a + b = -6 ....(ii)` `b = 0` and `a = 2` `:. g(x) = 2x` `:. g(2) = 4`

Discussion

9.	If `a,b,c in R - {0}` and `a^(2) = bc` and `a + b +c = abc` then the least possible value of `a^(2)` is
Answer» Correct Answer - `3` Given `bc = a^(2) …(i)` `b + c = abc - a` `b + c = a^(3) - a…..(ii)` `:.` equation `x^(2) - (b + c)x + bc = 0overset(b)underset(c)(lt)` `x^(2) - (a^(3) - a) x + a^(2) = 0` has two roots `b` and `c`. `b` and `c` are equal so `D ge 0` `(a^(3) - a)^(2) - 4a^(2) ge 0` `a^(2)(a^(4) -2a^(2) - 3) ge 0` `a^(2)(a^(2) - 3)(a^(2) + 1) ge 0` `a^(2) - 3 ge 0` `:. a^(2) ge 3` `:. (a^(2))_(min) = 3`

Discussion

10.	Range of \(\cfrac{x^2}{x^4+1}\).
Answer» f(x) = \(\cfrac{x^2}{x^4+1}\) = \(\cfrac{1}{x^2+\cfrac1{x^2}}\) = \(\cfrac{1}{\left(x+\cfrac1{x}\right)^2-2}\) \(\because\) \({\left(x+\cfrac1{x}\right)^2}\) \(\geq\) 2² or \({\left(x+\cfrac1{x}\right)^2}\) \(\geq\) 4 = \({\left(x+\cfrac1{x}\right)^2}\) - 2 \(\geq\) 4 - 2 = \({\left(x+\cfrac1{x}\right)^2}\) - 2 \(\geq\) 2 = \(\cfrac{1}{\left(x+\cfrac{1}{x}\right)^2-2}\) \(\leq\) \(\cfrac12\) = \(\cfrac{x^2}{x^4+1}\) \(\leq\) \(\cfrac12\)....(i) Also, x² \(\geq\) 0 and x⁴ + 1 \(\geq\) 1 = \(\cfrac{x^2}{x^4+1}\) \(\geq\) 0 ...(ii) (\(\because\) Division of two positive numbers be always positive) Then from (i) and (ii),we obtain 0 \(\leq\) \(\cfrac{x^2}{x^4+1}\) \(\leq\) \(\cfrac12\) \(\therefore\) Range of f(x) = \(\cfrac{x^2}{x^4+1}\) is [0,\(\cfrac12\)].

10.

Range of \(\cfrac{x^2}{x^4+1}\).

Answer»

f(x) = \(\cfrac{x^2}{x^4+1}\) = \(\cfrac{1}{x^2+\cfrac1{x^2}}\)

= \(\cfrac{1}{\left(x+\cfrac1{x}\right)^2-2}\)

\(\because\) \({\left(x+\cfrac1{x}\right)^2}\) \(\geq\) 2² or \({\left(x+\cfrac1{x}\right)^2}\) \(\geq\) 4

= \({\left(x+\cfrac1{x}\right)^2}\) - 2 \(\geq\) 4 - 2

= \({\left(x+\cfrac1{x}\right)^2}\) - 2 \(\geq\) 2

= \(\cfrac{1}{\left(x+\cfrac{1}{x}\right)^2-2}\) \(\leq\) \(\cfrac12\)

= \(\cfrac{x^2}{x^4+1}\) \(\leq\) \(\cfrac12\)....(i)

Also, x² \(\geq\) 0 and x⁴ + 1 \(\geq\) 1

= \(\cfrac{x^2}{x^4+1}\) \(\geq\) 0 ...(ii)

(\(\because\) Division of two positive numbers be always positive)

Then from (i) and (ii),we obtain

0 \(\leq\) \(\cfrac{x^2}{x^4+1}\) \(\leq\) \(\cfrac12\)

\(\therefore\) Range of f(x) = \(\cfrac{x^2}{x^4+1}\) is [0,\(\cfrac12\)].

Discussion

11.	In a ` A B C`if `b+c=3a ,t h e ncotB/2dotcotC/2`has the value equalto:``4b. 3 c. 2d. 1A. `4`B. `3`C. `2`D. `1`
Answer» Correct Answer - C In `a Delta ABC if b + c = 3a` ………… `cot.(B)/(2).cot.(C )/(2)=(s(s-b))/(Delta)(s(s-c))/(Delta)((s-a))/(s-a) = (s)/(s-a)` `= (2s)/(2s-2a)` but `a+b+c = 4a implies 2s = 4a` Hence `cot. (B)/(2). cot. (C )/(2)` `= (4a)/(2a) = 2I`

Discussion

12.	Show that the square to `(sqrt(26-15))//(5sqrt(2)-sqrt(38-5sqrt(3)))`is a rational number.
Answer» Correct Answer - `3` `5sqrt(2) - sqrt(38 + 5sqrt(3)) = 5sqrt(2) - (1)/(sqrt(2)) sqrt(76 + 2 sqrt(75))` `= 5sqrt(2) - (1)/(sqrt(2)) -(sqrt(75) + 1) = (sqrt(3)(3sqrt(3) - 5))/(sqrt(2))` `:. (sqrt(26 - 15sqrt(3)))/(5sqrt(2) - sqrt(38 + 5 sqrt(3))) = (sqrt(52 - 30sqrt(3)))/(sqrt(3)(3sqrt(3) - 5))` `= (3sqrt(3) - 6)/(sqrt(3)(3sqrt(3)-5)) = (1)/(sqrt(3))` so `p = 1 q = 3`

Discussion

13.	In the expansion of `(x+x^(2)+x^(3)+…….) (1+x+x^(2)+x^(3)) (x^(2)+x^(3)+x^(4)+……+x^(10))` the coefficient of `x^(6)` isA. `10`B. `18`C. `30`D. `12`
Answer» Correct Answer - A In the expansion ……….. `(x+x^(2)+…….)………` Coefficient of `x^(6)` in the expansion `(x+x^(2)+…..)` `(1+x+x^(2)+x^(3))(x^(2)+…….+x^(10))` = Coefficient of `x^(6)` in the expension `x^(3)(1+x+x^(2)+……) (1+x+x^(2)+x^(3))(1+x+x^(2)+....+x^(8))` = Coefficient of `x^(3)` in the expansion `(1-x^(4))(1-x^(9))(1-x)^(-3)` = Coefficient of `x^(3)` in the expansion `(1-x)^(-3) = ^(5)C_(3) = 10`

Discussion

14.	A={a,b,c} B={1,2,3,4}. Then number of elements in set C= {f:A-->B 2€f(A) and f is not one one}
Answer» C = {f : A → B 2 ∈ f(A) and f is not one-one} Case-I : If f(x) = 2 ∀ x∈ A, then number of function = 1 Case-II : If f(x) = 2 for exactly two elements then total number of many-one function = ³C₂³C₁ = 9 Case -III : If f(x) = 2 for exactly one element then total number of many-one function = ³C₁³C1 = 9 Total = 19

14.

A={a,b,c} B={1,2,3,4}. Then number of elements in set C= {f:A-->B 2€f(A) and f is not one one}

Answer»

C = {f : A → B 2 ∈ f(A) and f is not one-one}

Case-I : If f(x) = 2 ∀ x∈ A, then number of function = 1

Case-II : If f(x) = 2 for exactly two elements then total number of many-one function

= ³C₂³C₁ = 9

Case -III : If f(x) = 2 for exactly one element then total number of many-one function

= ³C₁³C1 = 9

Total = 19

Discussion

15.	\( y=\sqrt{4 x-x^{3}} \)
Answer» What we have to find, range, domain or what?

Discussion

16.	If three vertices of a parallelogram taken in order are `(-1, 0), (3, 2) and (2, 3)` then area of the parallelogram isA. `12`B. `(21)/(2)`C. `6`D. `3`
Answer» Correct Answer - C If the vertices of ……….. `A(-1, 0), (B(3, 2), C(2, 3), then D is (-2, 1)` `:.` area (parallelogram ABCD) = 6

Discussion

17.	If `m` is the slope of the straight line through the point `(1, 2)`, whose distance from the point `(13, 1)` has the greatest value, then `(2)/(3) m` is equal toA. `2`B. `4`C. `8`D. `12`
Answer» Correct Answer - C If `m` is the stope………… Stope of the joining `(1, 2)` and `(13, 1)` is `(1)/(12)` `:.` slope of the equired line is `12` `:. (2)/(3) m = 8`

Discussion

18.	If `x = 13 + 2sqrt(42)`, then `sqrt(x) + (1)/(sqrt(x))` is equal to `asqrt(b)` then find the value of `b - a` ?
Answer» Correct Answer - `5` Given `x = 13 + 2sqrt(42)` `x = 7 + 6 + 2sqrt(6 xx 7)` `x = (sqrt(7) + sqrt(6))^(2)` `:. sqrt(x) = sqrt(7) + sqrt(6)` `(1)/(sqrt(x)) = (1)/(sqrt(7) + sqrt(6)) xx (sqrt(7) - sqrt(6))/(sqrt(7) - sqrt(6)) = (sqrt(7) - sqrt(6))/(7 - 6)` `(1)/(sqrt(x)) = sqrt(7) - sqrt(6)` `:. sqrt(x) + (1)/(sqrt(x)) = 2sqrt(7) = asqrt(b)` `b = 7, a = 2` `rArr b - a = 5`

Discussion

19.	Both the roots of the equation `(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0`are alwaysa. positive b. realc. negative d. noneof theseA. positiveB. negativeC. realD. real and equal
Answer» Correct Answer - C `(x-b)(x-c) + (x-a)(x-c) + (x-a)(x-b) = 0` `rArr 3x^(2) - 2 (a + b + c)x + (ab + bc + ca) = 0` Now `D = 4 (a + b+ c)^(2) - 12(ab + bc + ca)` `= 4(a^(2) + b^(2) + c^(2) - ab - bc - ca)` `= 2[(a - b)^(2) + (b - c)^(2) + (c - a)^(2)]` which is always positive or zero so roots are real

Discussion

20.	If `alpha,beta`are the roots of the equation `x^2-2x+3=0`obtain the equation whose roots are `alpha^3-3alpha^2+5alpha-2`and `beta^3-beta^2+beta=5`A. `x^(2) + 3x + 2 = 0`B. `x^(2) - 3x + 2 = 0`C. `x^(2) - 3x - 2 = 0`D. none of these
Answer» Correct Answer - B Given `x^(2) - 2x + 3 = 0overset(alpha)underset(beta)(lt)` `alpha + beta = 2` and `alphabeta = 3` `:. alpha^(2) - 2alpha + 3 = 0 rArr alpha^(2) = 2alpha - 3` `alpha^(3) = 2alpha^(2) - 3alpha` Similarly `beta^(3) = 2beta^(2) - 3beta` Now `P = alpha^(3) - 3alpha^(2) + 5alpha - 2` `=2alpha^(2) - 3alpha - 3alpha^(2) + 5alpha - 2 = -alpha^(2) + 2alpha - 2` `= 3 - 2 = 1` `:. Q = beta^(2) - beta^(2) + beta + 5` `= (2beta^(2) - 3beta) - beta^(2) + beta + 5 = beta^(2) - beta + 5` `= -3 + 5 = 2` `:.` Sum of roots `= P + Q = 1 + 2 = 3` `:.` Product `PQ = 2` `:.` Required equation `x^(2) - 3x + 2 = 0`.

Discussion

21.	If `x=2` is a real root of cubic equation f (x) = `3x^(3)+bx^(2)+bx+3=0`. Then the value of lim_(xrarr(1)/(2)) (e^(f(x)-1)/(2x-1))`A. `(27)/(4)`B. `-(27)/(4)`C. `-(27)/(8)`D. `(27)/(8)`
Answer» Correct Answer - C `3x^(3)+bx^(2)+bx+3=3(x^(3)+1)+bx(x+1)=0` has roots `- 1,2,(1)/(2)` so, `underset(xrarr(1)/(2))(lim)((3x^(3)+bx^(2)+bx+3)/(2x-1))=(3(x-1)(x-2)(x-(1)/(2)))/(2(x-(1)/(2)))` `(3)/(2).(3)/(2).(-3)/(2)=-(27)/(8)`

Discussion

22.	The number of common tangent(s) to the circles `x^2+y^2+2x+8y-23=0`and `x^2+y^2-4x-10 y-19=0`is1 (b) 2(c) 3 (d)4A. `1`B. `2`C. `3`D. `4`
Answer» Correct Answer - C the number ber of ………… `x^(2)+y^(2)+2x+8y-23= 0` ………..(1) `x^(2)+y^(2)-4x-10y+19 = 0` ………..(2) `c_(1) -= (-1, -4)` , `r_(1) = sqrt(1+16+23) = 2sqrt(10)` `c_(2)-= (2, 5)` , `r_(2)= sqrt(4+25-19) = sqrt(10)` Here `c_(1)c_(2) = sqrt(9+81), r_(1)+r_(2)= 3sqrt(10)` Hence circles touch each other externally So there are 3 common tangent

Discussion

23.	`F(x)=x^(5)+log,(x+sqrt(1+x^(2)))`, Then for all `alpha, beta in R` such that `alpha+beta gt 0`A. `F(alpha)+F(beta)lt0`B. `F(alpha)+F(beta)gt0`C. `F(alpha+7)+F(beta)lt0`D. `F(alpha)+F(beta+1)=0`
Answer» Correct Answer - B `F(x)` is an odd function so ` F(alpha)+F(-alpha)=0` `F(x)` is uarr function so is `alpha+beta gt implies alpha gt -beta implies F(alpha)+F(beta)gt0`

Discussion

24.	The digits, from `0 to 9` are written on `10` slips of paper (one digit on each slip) and placed in a box. If three of the slips are drawn and arranged, then the number of possible different arrangements isA. `1000`B. `720`C. `810`D. None of these
Answer» Correct Answer - B The digits, from 0 to 9 …….. `.^(10)P_(3) = 720`

Discussion

25.	If equation `(cos^(-1)x)^(4)-8(cos^(-1)x)^(3) + a (cos^(-1)x)^(2)+b (cos^(-1)x)+16=0` has four positive real roots, where a, b epsilon R then `[x]` = (Where [.] G.I.F.)A. `1`B. `0`C. `-1`D. `2`
Answer» Correct Answer - C All th roots of given equation are equal therefore `cos^(-1) x=2` `therefore x = cos 2` `[x]=[cos 2] =-1`

Discussion

26.	If `(a+(1)/(a))^(2)= 3`, then `a^(3)+(1)/(a^(3))` equalsA. `6 sqrt(3)`B. `3 sqrt(3)`C. `0`D. `7 sqrt(7)`
Answer» Correct Answer - C If `(a+(1)/(a))^(2) = 3` ………… `a^(3)+(1)/(a^(3)) = (a+(1)/(a)) ((a+(1)/(a))^(2)-3)` `= (a+(1)/(a)) (3-3) = 0`

Discussion

27.	If `alpha, beta` are roots of `x^(2)-2x-1=0`, then value of `5alpha^(4)+12beta^(3)` isA. 153B. 169C. 183D. None of these
Answer» Correct Answer - C `2x^(3)y dy+(1-y^(2))(x^(2)y^(2)+y^(2)-1)dx=0` `implies ((2y)/(1-y^(2)))(dy)/(dx)+(x^(2)y^(2)+y^(2)-1)/(x^(3))=0` `implies ((2y)/(1-y^(2)))(dy)/(dx)+(y^(2))/(x)=(1-y^(2))/(x^(3))` `implies (2y)/((1-y^(2))^(2))(dy)/(dx)+(1)/(x)((y^(2))/(1-y^(2)))=(1)/(x^(3))` `(dt)/(dx)+(1)/(x)t=(1)/(x^(3))("where " t = (y^(2))/(1-y^(2)))` `x(dt)/(dx)+t=(1)/(x^(2))implies (d)/(dx)(tx)=(1)/(x^(2))` `tx=-(1)/(x)+C` `(x^(2)y^(2))/(1-y^(2))=(Cx-1)impliesx^(2)y^(2)=(Cx-1)(1-y^(2))`

Discussion

28.	Let `vec(p),vec(q),vec(r)` be three unit vectors such that `vec(p)xxvec(q)=vec(r)`. If `vec(a)` is any vector such that `[vec(a)vec(q)vec(r )]=1,[vec(a)vec(r)vec(p )]=2`, and `[vec(a)vec(p)vec(q )]=3`, then `vec(a)=`A. `vec(p)+3q+vec(r )`B. `vec(3p)+vec(2q)+vec(r )`C. vec(p)-vec(2q)-vec(3r)`D. `vec(p)+vec(2q)+vec(3q)`
Answer» Correct Answer - D Given that `vec(p)xxvec(q)=vec(r )` `implies (vec(p)xxvec(q)).vec(r )=\|vec(r )\|^(2)implies[vec(p)vec(q)vec(r )]=1` Let `(a)=xvec(p)+yvec(q)+zvec(r)....(1)` Take dot product in equation (1)both sides with `vec(p)xxvec(q), vec(q)xxvec(r)` and `vec(r )xxvec(p)` we get `x=1, y=2, z=3.`

Discussion

29.	If one root of the equation `x^(2)+px+q=0` is `2+sqrt(3)` where `p, q epsilon I` and roots of the equation `rx^(2)+x+q=0` are `tan 268^(@)` and `cot 88^(@)` then value of `p+q+r` is :A. `-1`B. `-2`C. `-3`D. `-4`
Answer» Correct Answer - B If one root of ………… `x^(2)+px+q=0` has one root `2+sqrt(3)` then other root `= 2 - sqrt(3)` "sum" of roots `= - (P)/(1)= 2+sqrt(3)+2-sqrt(3)` `implies P = -4` product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))` `implies q = 1` …..(i) product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))` `implies q=1` ....(ii) now `rx^(2)+x+q=0` roots are tan `(268^(@)) tan (180^(@)+88^(@)) = tan 88^(@)` and `cot 88^(@)` `:.` Product of roots `= tan 88^(@) .cot 88^(@) = (q)/(r )` `implies 1 = (q)/(r ) implies q = r` ....(iii) `:. p+q+r= -4+1+1= -2`

Discussion

30.	Let `R` be the relation defined on power set of A such that `ARB hArr n(P(A)) = n(P(B))` can be : (where `P(A)` denotes power set of `(A)`A. ReflexiveB. SymmetricC. TransitiveD. Equiivalence
Answer» Correct Answer - A::B::C::D Let `R` be the ……….. `(A.B) in R implies n(P(A)) = n(P(B))` `implies 2^(n(A)) = 2^(n(B))` Now, `n(A)=n(A) implies (A,A)in R AA A` `implies R` is reflexive Let `(A,B) in R implies n(A) = n(B) implies n(B)= n(A) implies (B,A) in R` `:.` symmetric Let `(A,B) in R implies n(A)=n(B)` Let `(B,C)in R implies n(B) = n(C )` `implies n(A) = n(C )` `implies (A,C)in R :.` transitive `:.` equivalence

Discussion

31.	Let `P_(1)=x+y+z+1=0, P_(2)=x-y+2z+1=0,P_(3)=3x+y+4z+7=0` be three planes. Find the distance of line of intersection of planes `P_(1)=0` and `P_(2) =0` from the plane `P_(3) =0.`A. `(2)/sqrt(26)`B. `(4)/sqrt(26)`C. `sqrt((1)/(26))`D. `(7)/sqrt(26)`
Answer» Correct Answer - B Let direction ratios of line are a,b,c Now `a+b+c=0` `a-b+2c=0` `(a)/(3)=(b)/(-1)=(c )/(-2)` So direction ratios of line are `(3,-1,-2)` `x+y+z+1+0….(1)` `x-y+2z+1=0….(2)` Put z=0, we get `x=1, y=0` Equation of line of intersection of `P_(1)=0 P_(2)=0` is parallel to the plane `P_(3)=0`. Sodistance of point `(-1,0,0)` from `P_(3)=0` is `\|(-3+7)/sqrt(9+1+16)\| = (4)/sqrt(26)`

Discussion

32.	Figure of merit γ is a. Ratio of output signal to noise ratio to input signal to noiseratio b. Ratio of input signal to noise ratio to output signal to noiseratio c. Ratio of output signal to input signal to a system d. Ratio of input signal to output signal to a system
Answer» a. Ratio of output signal to noise ratio to input signal to noiseratio

Discussion

33.	`Let sec ^(2)((pi)/(9))+sec^(2)((2pi)/(9))+sec_(2)((4pi)/(9))=S` and `Sigma_(k-1)^(89) cos^(6)(k^(o))=(a)/(b)` ,where a,b are coprime, then which of the following is/are correct?A. Number of positive divisors of a+b + S is 4B. Number of positive divisors of a+b + S is 8C. S is a perfect squareD. a+b is a prime number
Answer» Correct Answer - A::C::D `sec^(2)((pi)/(9))+sec^(2)((2pi)/(9))+sec^(2)((4pi)/(9))` `=((cos.(2pi)/(9))^(2)(cos.(4pi)/(9))^(2) +(cos.(4pi)/(9))^(2)(cos.(pi)/(9))^(2)+cos^(2)((pi)/(9))cos^(2)((2pi)/(9)))/(cos.(pi)/(9)cos.(2pi)/(9)cos.(4pi)/(9))^(2)` Using CD formulas `=(1)/(4)([(cos.(2pi)/(3)+cos.(2pi)/(9))^(2)+(cos.(5pi)/(9)+cos.(pi)/(3))^(2)+(cos.(pi)/(3)+cos.(pi)/(9))^(2)])/(((1)/(64)))` `= 16 ((3)/(4)+cos^(2).(pi)/(9)+cos^(2).(2pi)/(9)+cos^(2).(4pi)/(9)+cos.(pi)/(9)-cos^(2).(2pi)/(9)-cos.(4pi)/(9))` `=16((3)/(9)+(3)/(2))` `therefore cos .(pi)/(9)-cos^(2).(2pi)/(9)-cos.(4pi)/(9)=0 =36` `underset(k=1)overset(89)Sigmacos^(6)(k^(@))= underset(k=1)overset(89)Sigmasin^(6)(k^(@))=(1)/(2)underset(k=1)overset(89)sum(sin^(6)(k^(@))+cos^(6)(k^(@)))` `(1)/(2)(underset(k=1)overset(89)Sigma(1-(3)/(4)sin^(2)(2k^(@))))=(89)/(2)-(3)/(8)underset(k=1)overset(89)Sigma(2k)^(@)` `=(89)/(2)-(3)/(8)xx45` `(a)/(b)=(221)/(8)` `a221,b=8`

Discussion

34.	Consider the equation `sectheta+ cottheta = 31/12` On the basis of above, answer the following Number of values of theta where `theta in ((pi)/(2),(3pi)/(2))` is equal toA. `0`B. `1`C. `2`D. `3`
Answer» Correct Answer - B 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

35.	For what purposes transformer ratio meter can be used?
Answer» Transformer ratio meter can be used for, a. To find the ratio of a transformer. b. To find the phase angle deviation of primary and secondary voltage of transformer. c. To find the magnitude of magnetizing currents.

35.

For what purposes transformer ratio meter can be used?

Answer»

Transformer ratio meter can be used for,

a. To find the ratio of a transformer.

b. To find the phase angle deviation of primary and secondary voltage of transformer.

c. To find the magnitude of magnetizing currents.

Discussion

36.	What do you understand by tan delta for a insulating material?
Answer» Tan delta measurement is done to find the qualities of insulating material. Tan delta is angle between current due to surface leakage or current due to capacitance and the capacitive current. That is Tan δ = Ir / Ic.

Discussion

37.	What are the design objectives of Electrical System?
Answer» a. To evacuate generated electrical power. b. To provide required power to SUT, UT, DG, UPS, and CUPS. c. To provide required emergency power from onsite DG, UPS & CUPS. d. To provide Fast transfer in event of Class IV failure. Emergency transfer in events of Class III and Class II failure. e. Load shedding in event of one DG available. f. To provide un-interruptible or few milli seconds interrupted power supply by UPS and un-interruptible power supply by CUPS. g. To provide operational flexibility by providing required qualities of requirement. h. To provide isolation, Alarms, indication, protection of the system. i. To provide fire protection. j. To provide surge and lightning protection. k. To provide adequate lighting. l. To provide equipment earthing, system earthing, and personnel protection. m. To provide necessary electrical and physical isolation of electrical equipments.

37.

What are the design objectives of Electrical System?

Answer»

a. To evacuate generated electrical power.

b. To provide required power to SUT, UT, DG, UPS, and CUPS.

c. To provide required emergency power from onsite DG, UPS & CUPS.

d. To provide Fast transfer in event of Class IV failure. Emergency transfer in events of Class III and Class II failure.

e. Load shedding in event of one DG available.

f. To provide un-interruptible or few milli seconds interrupted power supply by UPS and un-interruptible power supply by CUPS.

g. To provide operational flexibility by providing required qualities of requirement.

h. To provide isolation, Alarms, indication, protection of the system.

i. To provide fire protection.

j. To provide surge and lightning protection.

k. To provide adequate lighting.

l. To provide equipment earthing, system earthing, and personnel protection.

m. To provide necessary electrical and physical isolation of electrical equipments.

Discussion

38.	What is the range of resistances that can be measured using following.
Answer» The range of resistances that can be measured using are. a. Wheatstone bridge – 1 milli Ω to 11 MΩ. b. Kelvins double bridge – 0.2 micro Ω to 11 Ω. c. Megger – Insulation resistances more than 100 kΩ

38.

What is the range of resistances that can be measured using following.

Answer»

The range of resistances that can be measured using are.

a. Wheatstone bridge – 1 milli Ω to 11 MΩ.

b. Kelvins double bridge – 0.2 micro Ω to 11 Ω.

c. Megger – Insulation resistances more than 100 kΩ

Discussion

39.	What is the difference in action of lock out pressure signal on 6.6 kV and 220 kV breakers?
Answer» When lock out signal comes to 6.6 kV breakers the breaker will trip. Where as in case of 220 kV breakers the breaker will not trip. If the breaker is open it will be open only and can not be closed. If it is in closed condition it will be closed.

Discussion

40.	What type breakers are provided in 6.6 kV buses?
Answer» ABB. Make, SF6 gas, 1250A and 2000A capacity circuit breakers are provided in 6.6 kV buses.

Discussion

41.	List some important loads to 6.6 kV buses.
Answer» a. Auxiliary transformers. b. PHT motors. c. BFP motors. d. CEP motors. e. CCW motors. f. Chiller motors. g. Pressuring pump motors.

41.

List some important loads to 6.6 kV buses.

Answer»

a. Auxiliary transformers.

b. PHT motors.

c. BFP motors.

d. CEP motors.

e. CCW motors.

f. Chiller motors.

g. Pressuring pump motors.

Discussion

42.	What is the purpose of CVT (capacitance voltage transformer)?
Answer» Purposes of CVT are. a. To indicate if line is charged or not. b. To synchronize grid with generator. c. For power line communication and carrier tripping.

42.

What is the purpose of CVT (capacitance voltage transformer)?

Answer»

Purposes of CVT are.

a. To indicate if line is charged or not.

b. To synchronize grid with generator.

c. For power line communication and carrier tripping.

Discussion

43.	What are three types of secondary instruments?
Answer» The three types of secondary instruments are, a. Indicating type: It only indicates the electrical quantity measured. Example: Ammeter, Voltmeter, Frequency meter etc. b. Integrating type: It integrates (sums up) the quantity being measured. Example: Energy meter. c. Recording meter: It records as well as indicates the electrical quantity being measured. Example: 3 pen graphical recorder.

43.

What are three types of secondary instruments?

Answer»

The three types of secondary instruments are,

a. Indicating type: It only indicates the electrical quantity measured. Example: Ammeter, Voltmeter, Frequency meter etc.

b. Integrating type: It integrates (sums up) the quantity being measured. Example: Energy meter.

c. Recording meter: It records as well as indicates the electrical quantity being measured. Example: 3 pen graphical recorder.

Discussion

44.	What are the advantages of digital instruments over analog instruments?
Answer» The advantages of digital instruments over analog instrument are. a. Human errors are avoided (comparative error) because the output is displayed in form of numbers. b. Power consumption of digital meters are low as compared to analog meters.

44.

What are the advantages of digital instruments over analog instruments?

Answer»

The advantages of digital instruments over analog instrument are.

a. Human errors are avoided (comparative error) because the output is displayed in form of numbers.

b. Power consumption of digital meters are low as compared to analog meters.

Discussion

45.	Give three operating forces acting on indicating instruments.
Answer» a. Deflecting force. b. Controlling force. c. Damping force.

45.

Give three operating forces acting on indicating instruments.

Answer»

a. Deflecting force.

b. Controlling force.

c. Damping force.

Discussion

46.	Why earth switches are provided in 220 kV bays?
Answer» When bay CB trips, both end (station and grid) CB will trip. The earth switches are provided because the grid will always be alive so to prevent any shocks to the operator or maintenance personnel who is working on the line or bay due to accidental energizing of the bus.

Discussion

47.	What are the two main classifications of analog instruments?
Answer» The two main classifications of instruments are, a. Absolute instruments. Example tangent galvanometer. b. Secondary instruments. Example ammeter, voltmeter. Analog instruments are classified according to their electrical quantity they measure. Example frequency meter, voltmeter, etc. Principles they work are moving coil, induction.

47.

What are the two main classifications of analog instruments?

Answer»

The two main classifications of instruments are,

a. Absolute instruments. Example tangent galvanometer.

b. Secondary instruments. Example ammeter, voltmeter. Analog instruments are classified according to their electrical quantity they measure. Example frequency meter, voltmeter, etc. Principles they work are moving coil, induction.

Discussion

48.	List out the components of station output system.
Answer» Main generator, Generator transformer, PT, CT, CVT, lightning arrestor, wave trap, main 220 kV bus, transfer bus, SF6 circuit breakers and isolators, line protection scheme, GT and Generator protection scheme, bus bar protection scheme etc.

Discussion

49.	For how long 220 V DC batteries can supply power UPS?
Answer» 220 V DC batteries can supply Power UPS for 30 minutes. Within this time class III power supply should be restored by DG’s.

Discussion

50.	What are the main sources of power supply to 6.6 kV buses?
Answer» The main sources of power supply to 6.6 kV buses are. a. Unit transformer which steps down the generated voltage to 6.6 kV from the generator. b. Start up transformer, which steps down the grid voltage to 6.6 kV.

50.

What are the main sources of power supply to 6.6 kV buses?

Answer»

The main sources of power supply to 6.6 kV buses are.

a. Unit transformer which steps down the generated voltage to 6.6 kV from the generator.

b. Start up transformer, which steps down the grid voltage to 6.6 kV.

Discussion

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For what purposes transformer ratio meter can be used?

What do you understand by tan delta for a insulating material?

What are the design objectives of Electrical System?

What is the range of resistances that can be measured using following.

What is the difference in action of lock out pressure signal on 6.6 kV and 220 kV breakers?

What type breakers are provided in 6.6 kV buses?

List some important loads to 6.6 kV buses.

What is the purpose of CVT (capacitance voltage transformer)?

What are three types of secondary instruments?

What are the advantages of digital instruments over analog instruments?

Give three operating forces acting on indicating instruments.

Why earth switches are provided in 220 kV bays?

What are the two main classifications of analog instruments?

List out the components of station output system.

For how long 220 V DC batteries can supply power UPS?

What are the main sources of power supply to 6.6 kV buses?