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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The vector equation of the plane which is at a distance of 3//sqrt(14) from the origin and the normal from the origin is 2hati-3hatj+hatk is |
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Answer» 1)`VECR.(2hati-3hatj+hatk)=3` |
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| 2. |
If n(U) = 25, n(A) = 12, n(B)=11, n(A cap B) =4, where U is the universal set, A and B are sub-sets of U, then n((A cup B)') is equal to |
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Answer» 3 |
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| 3. |
The mid point of a chord of the ellipse x^(2)+4y^(2)-2x+20y=0 is (2,-4). The equation of the chord is |
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Answer» x-6y=26 |
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| 4. |
For any four points O(0,0,0),P(1,2,1),Q(2,3,0),R(0,1,-1), the angle between the planes OPQ and PQR is |
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Answer» `cos^(-1)((5)/(sqrt(28)))` |
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| 5. |
Find the focus of the parabola (x-3)^2 +8(y+1)=0 |
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| 6. |
Find the focus of the parabola x^2-4x-5y-1=0 |
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| 7. |
Find the latus rectum of the parabola y^2+4x+2y=11 |
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| 10. |
If |{:(6i , -3i , 1) , (4 , 3i, -1) , (20 , 3 , i):}| = x +iy show that x = y = 0 |
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Answer» `x = 3 , y= 1` |
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| 11. |
If f : R to R is defined by f(x)=[(x)/(5)] for x in R, where [y] denotes the greatest integer not exceeding y, then {f(x):|x|lt 71} is equal to |
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Answer» `{-14,-13,…0,….,13,14}` |
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| 12. |
Consider the circuit If the probability that a circuit is closed is p and the probability that current flows from A to B is 4/9, then value of p is |
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Answer» `1/2` |
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| 13. |
If a _(1) , a _(2), a _(3),a _(4), a _(5) are in A.P. with common differennce ne 0, then find the value of sum _( I =1) ^(5) a _(1), when a _(5) = 2. |
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Answer» |
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| 14. |
A: IF InaDelta ABC, c cos^2""A/2+a cos^2""C/2=(3b)/2 then a,b,c are In A.P. R: In a Delta ABC,a cos C+ c cos A=b |
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Answer» A is TRUE, R is true and R is correct explanation of A |
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| 15. |
If p and q are the coefficients of x^n in (1+x)^(2n) and (1-4x)^(-1//2), |x| lt (1)/(4), then |
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Answer» `p=q` |
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| 16. |
cos^(2)x(dy)/(dx) + y = tan x (o le x le (pi)/(2)) |
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Answer» |
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| 17. |
Vascularized bags present in Terrestrial animals helps in :- |
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Answer» PULMONARY respiration |
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| 18. |
A water tank has the shape of an inverted right-circular cone with its axis vertical and vertex lower most. Its semi-vertical angle is tan^(-1)((1)/(2)). Water is poured into it at a constant rate of 5 cubic meter per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10 m. |
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| 19. |
The value of int_(-20pi)^(20 pi) [ sin x + cos x] dxis(where [.] denotes greatest integer function) |
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Answer» `10 pi` `=20XX[(pi)/(2)-pi+(3pi)/(4)-2xx(3pi)/(2)+2pi-(7pi)/(4)+(3pi)/(2)]=20xx-pi=-20pi` |
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| 20. |
Find the equation of lines joining the points. (2,1,3) and (4,-2,5). |
| Answer» SOLUTION :Equation of the line JOINING the POINTS (2,1,3) and (4.-2,5) is `(x-2)/(4-2)=(y-1)/(-2-1)=(z-3)/(5-3)` or `(x-2)/2=(y-1)/(-3)=(z-3)/2` | |
| 21. |
The solution of y'' = y' tan x = sin x is |
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Answer» `y =(1)/(2) (sin x) + ALOG (SEC x + tan x) + b` |
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| 22. |
Find the area bounded by the curves x = |y^(2)-1| and y = x- 5 |
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| 23. |
If a=lambdahati+2hatj-3hatk, b=2hati+lambdahatj-hatk, c=hati+2hatj+hatk and [abc]=6, then lambda is equal to |
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Answer» `-8 or 3` On applying `C_(1) to C_(1)-C_(3)`, we get `=|(lambda+3, 2 , -3),(3, lambda, -1),(0,2,1)|` `(lambda+3)(lambda+2)-3(2+6)=0` `RARR lambda^(2)+5lambda - 24=0` `rArr lambda =- 8 or 3 ` |
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| 24. |
Let P=-(1,7,sqrt(2)) be a point and line L is 2sqrt(2)(x-1)=y-2,z=0. If PQ is the distance of plane sqrt(2)x+y-z=1 from point P measured along a line inclined at an angle of 45^(@) with the line L and is minimum then the value of PQis |
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Answer» 3 This line L MAKES an ANGLE of `45^(@)` with the PLANE `SQRT(2)x+y-z=1` `therefore` Required distance PQ is PREPENDICULAR distance of plane from P I.e., `PQ=(|sqrt(2)+7-sqrt(2)-1|)/sqrt(2+1+1)=3` |
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| 25. |
Let f _(n) x+ f _(n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-{0}. where n in N and g (x) = max { f_(2) (x), f _(3) (x),(1)/(2)} AA x in R - {0} The number of value of sum _(k =1) ^(oo) f _(2k) (cosec theta ) + sum _(k =1)^(oo) f _(2k) (sec theta ), where theta ne (kpi)/(2), k in I is: |
| Answer» ANSWER :B | |
| 26. |
A company produces soft drinksthat has a contract which requires that a minimum of 80 units of the chemicalA and 60 units of the chemical B go into each bottle of the drink. The chemicalsare available in prepared mix packets from two different suppliers. SupplierS had a packet of mix of 4 units of A and 2 units of B that costs Rs.10. The supplier T has a packet ofmix of 1 unit of A and 1 unitof B costs Rs.4. How many packets of mixedfrom S and T should the companypurchase to honour the contract requirement and yet minimize cost? Make a LPPand solve graphically. |
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| 27. |
(d)/(dx) (sin^(3)x)= ……. |
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Answer» `3 sin^(2)x` |
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| 28. |
Let N be the set of non-negative integers, I the set of integers, N_(p) the set of non-positive integers, E the set of even integers and P the set of prime numbers. Then |
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Answer» <P>`I-N=N_(p)` |
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| 29. |
Differentiate sqrtxsinx |
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Answer» SOLUTION :LET `y=sqrtxsinx` Then `dy/dx=SQRTX.d/dx(SINX)+d/dx(sqrtx)sinx` `=sqrtx CDOT cosx+1/(2sqrtx)sinx` |
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| 30. |
The solution of (dy)/(dx) = cos(x+y) is |
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Answer» `TAN((x+y)/(2)) = x+c` |
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| 31. |
A survey shows that in a certain village 2 out of every 100 men and 1 out of every 100 women have strength ulcers. A person selected at random from the village is found to have stomach ulcer. Find the probability that the person is a male, given that the probability of selecting a male from the village is 0.55. |
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| 32. |
Assertion (A) : In the (1+x)^50, the sum of the coefficients of odd powers of x is 2^49 Reason ( R) : The sum of coefficients of odd powers of x in (1+x)^n is 2^(n-1) |
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Answer» A and R are TRUE , R is correct explanation of A |
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| 33. |
If y=x^(4)-10 and if x change from 2 to 1.99, what is the change in y ………. |
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Answer» `0.32` |
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| 34. |
Let A={(x,y)//y=e^(x),x in R},B={(x,y)//y=e^(-x),x in R}, then |
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Answer» `A NN B=phi` |
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| 35. |
intsqrt( ( cos x - cos^(3) x)/( 1 - cos^(3) x)) dx = ........+ C. ( where x in R - { (kpi)/( 2)//k in Z} ) |
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Answer» `(2)/(3) cos^(-1) ( sin^(3/2) X)` |
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| 36. |
Find the scalar and vector components of the vector with initial point (2,1) and terminal point (-5,7). |
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| 37. |
if f(x)cos pi (|x|+[x]), where[.]denotesthegreatestinteger, functionthen whichis not true ? |
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Answer» continuousat x=1/2 |
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| 38. |
If R _(1) and R _(2) are equivalence rrelations in a set A show that R _(1) nn R _(2) is also an equivalence relation. |
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| 39. |
Translate "If you do not work hard, then you will repent" propositions into symbolic form , stating the prime components. |
| Answer» Solution :Let p : You work hard, Q : you will REPENT. Then the GIVEN STATEMENT is `~~p rarr q`. | |
| 40. |
Find inverse of[{:(1,2,1),(3,2,3),(1,1,2):}] |
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| 41. |
If sinx+cosy=a and cosx+siny = b, then tan""(x-y)/(2) is equal to : |
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Answer» a+b |
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| 42. |
Evaluate the limit . underset(n to 00)("lim") [(1)/(n+1)+(1)/(n+2)+…………… +(1)/(6n)] |
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| 44. |
By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin^(5/2)xdx)/(sin^(5/2)x+cos^(5/2)x) |
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| 45. |
Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)gtx^xy^yz^zgt[(x+y+z)/(3)]^(x+y+z)(x,y,zgt0) |
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Answer» SOLUTION :Let `TAN^(2) ALPHA = x` and `tan^(2) beta = y` `:. (sec^(4) alpha)/(tan^(2) beta) + (sec^(4) beta)/(tan^(2) alpha) = ((x + 1)^(2))/(y) + ((y + 1)^(2))/(x)` `= (x^(2))/(y) + (y^(2))/(x) + (1)/(x) + (1)/(y) + 2 (x)/(y) + 2 (y)/(x)` Now, USING A.M `ge` G.M we get ltbegt `((x^(2))/(y) + (y^(2))/(x) + (1)/(x) + (1)/(y) + (x)/(y) + (x)/(y) + (y)/(x) + (y)/(x))/(8) ge ((x^(2))/(y). (y^(2))/(x).(1)/(x).(1)/(y).(1)/(y).(x)/(y).(x)/(y).(y)/(x).(y)/(x))^((1)/(8))` `IMPLIES (x^(2))/(y) + (y^(2))/(x) + (1)/(x) + (1)/(y) + (X)/(y) + (x)/(y) + (y)/(x) + (y)/(x) ge 8` `:. (sec^(4) alpha)/(tan^(2) beta) + (sec(4) beta)/(tan^(2) alpha) ge 8` |
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| 46. |
Consider, f(x) =((x^(2)-1)(x^(2)-4))/( g(x)), x in R- {a,b} , where g(X)is apolynomial ofdegree le4. f(x)hasa removabletype ofdiscontinuity at x=and x=b. Alsoit is known that (i)lim_ (x to pmoo) f(X) =+oo (ii) lim_( x to -1) f(x) =6 (iii) lim_( x to -2)f(x) = a non -zero finite number LEt L andM denote the numberof points ofdiscontiuityandthe numberof pointsof non - derivatively repectively of nay functionin R.(R is the of real numbers )Numberof points where|f(x)| is non- differentiablein itsdomainis |
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Answer» 2 |
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| 47. |
Consider, f(x) =((x^(2)-1)(x^(2)-4))/( g(x)), x in R- {a,b} , where g(X)is apolynomial ofdegree le4. f(x)hasa removabletype ofdiscontinuity at x=and x=b. Alsoit is known that (i)lim_( x to +_oo) f(X) =+oo (ii) lim_( x to -1) f(x) =6 (iii)lim_( x to -2)f(x) = a non -zero finite number LEt L andM denote the numberof points ofdiscontiuityandthe numberof pointsof non - derivatively repectively of nay functionin R.(R is the of real numbers )Number of pointswhere f(-|x|)is non- differentiablein its domain is |
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Answer» 0 |
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| 48. |
Consider, f(x) =((x^(2)-1)(x^(2)-4))/( g(x)), x in R- {a,b} , where g(X)is apolynomial ofdegree le4. f(x)hasa removabletype ofdiscontinuity at x=and x=b. Alsoit is known that (i)lim_( x to +-oo) f(X) =+oo (ii) lim_( x to -1) f(x) =6 (iii)lim_( x to -2) f(x) = a non -zero finite number LEt L andM denote the numberof points ofdiscontiuityandthe numberof pointsof non - derivatively repectively of nay functionin R.(R is the of real numbers )Number of pointswhere f(|x|)is non- differentiablein its domain is |
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Answer» 2 |
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| 49. |
A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5) are vertices of a triangle ABC. The vector along the bisector angleA is ………….. |
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Answer» `hati+hatj+hatk` |
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