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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. |
Let, x_(n) = (1-(1)/(3))^(2)(1-(1)/(6))^(2)(1-(1)/(10))^(2)…(1-(1)/((n(n+1))/(2)))^(2), n ge 2 Then the value of underset(n rarr oo)lim _(n) is |
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Answer» `(1)/(3)` |
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| 2. |
A firm manufactures two types of products, A and B, and sells them at a prodit of Rs.5 per unit of type A and Rs.3 per unit of type B.Each product is processed on two machines, M_(1)and M_(2). One unit of type A requires one minute of processing time on M_(1) and one minute on M_(2). Machines M_(1) and M_(2). are respectively available for at most 5 hours and 6 hours in a day. Find out how many units of each type of product the fiem should produce a day in order to maximize the profit. Solve the prolem graphically. |
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| 4. |
The statement P(n): ' '1 xx 1! + 2 xx2! + 3 xx 3! + ... +n xx Xn! = (n + 1)!-1 ' ' is |
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Answer» TRUEFOR all ` N gt 1` |
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| 5. |
If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= a sec theta, y= b tan theta. |
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| 6. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=a (cos theta + theta sin theta),y= a (sin theta- theta cos theta) |
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| 7. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=a (cos t + log "tan" (t)/(2)),y= a sin t |
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| 8. |
If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+4,x+2b],[x+4,x+5,x+2c]| is |
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Answer» 0 |
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| 9. |
If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= a(theta-sin theta), y= a (1+ cos theta). |
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| 10. |
Three objects A, B and C all individually float on top of waater. A and B have identical masses and densities but different shapes while B and C have identical sizes and shapes but C has less mass and density than B. If three identical weights are then tied to the objects and all three are pulled completely beneath the surface of the water, which object will displace the greatest volume of water. ? |
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Answer» object A and C only `V_(A)=B_(B)` `V_(B)=V_(C)` Hence total volume DISPLACED by all 3 is same. |
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| 11. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x = cos theta - cos 2 theta, y= sin theta- sin 2 theta |
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| 12. |
Least Integer Function: We know that any real number x can be expressed as following x= [x] + {x}, where (x) is an integer and 0 le {x} lt 1. We define [x] as the greatest integer less than or equal to x or integral part of x and (x} as the fractional part of x: Suppose for any real number x we write x = (x) - 0, whore (x) Is integer and 0 le (x) < 1. We define (x) as the least integer greater than or equal to x. For example: (2.36) = 3 (-13.11) =-13 (4)=4 Clearly, If xinl, then (x)-{x] if x in l, then (x) = [x] +1. We can also define that xin(n,n+1]rArr(x)=n+1, where ninI. The range of the function f(x)=1/(sqrt((x)-[x])) is |
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Answer» `phi` |
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| 13. |
Least Integer Function: We know that any real number x can be expressed as following x= [x] + {x}, where [x] is an integer and 0 le {x} lt 1. We define [x] as the greatest integer less than or equal to x or integral part of x and (x} as the fractional part of x: Suppose for any real number x we write x = [x]+{x}, where [x] is integer and 0 le {x} < 1. We define (x) as the least integer greater than or equal to x. For example: (2.36) = 3 (-13.11) =-13 (4)=4 Clearly, If x != I, then (x)=x -{x}+1 if x in I, then (x) = [x] +1. We can also define that xin(n,n+1]rArr(x)=n+1, where ninI. The domain of definition of the function f(x)=1/(sqrt(x-{x})) is |
| Answer» ANSWER :D | |
| 14. |
10 persons are sitting around a circle. In how many ways can 2 persons be selected so that they are not adjacent. |
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| 15. |
If alpha, beta , gammaare the roots of 3x^(3) - 5x^(2) - 7x + 1 = 0thent the equation whose roots are -alpha, -beta, - gamma is |
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Answer» `3x^(3) + 5x^(2) - 7x - 1 = 0 ` |
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| 16. |
If y= 500 e^(7x) + 600 e^(-7x), show that (d^(2)y)/(dx^(2))= 49y |
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| 17. |
Find all solutions to aabb = n^(4)- 6n^(3), where a and b are non-zero digits, and n is an integer (a and b are not necessarily distinct). |
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| 18. |
Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) + r_(2) r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r) |
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Answer» STATEMENT I is TRUE, Statement II is True, Statement II is a CORRECT EXPLANATION for Statement I. |
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| 19. |
Find a linear approximation for the functions at the indicated point g (x) = sqrt (x ^(2) + 9), x _(9) =-4 |
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| 20. |
One diagonal of a square is the portion of the line x//97+y//79=1 intercepted between the axes p_(1), p_(2) are the length of the perpendiculars from the vertices of the other diagonal on the axis of y. If p_(2)lt p_(1) then p_(1)//p_(2) is equal to |
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| 21. |
A line is perpendicular to xy-plane Write the angle made by the line with z-axis. |
| Answer» SOLUTION :`SQRT((1+1)^2+(2-2)^2+(Z-)^2=3)rArr4+(z-1)^2=9rArr(z-1)^2=9rArrz-1=_-^+sqrt5rArrz=1_-^+sqrt5` | |
| 22. |
The value of int_(1//e)^(tanx)(tdt)/(1+t^(2))+int_(1+t^(2))^(cotx)(dt)/(1+t^(2)) is equal to |
| Answer» Answer :B | |
| 23. |
Consider the differential equation dy/dx = y/(2ylog y + y -x). Statement - I xy = y^(2) logy + cis a solution of the given differential equation. Statement - II : The differental equation is a linear equation in y and x. |
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Answer» STATEMENT - I is TRUE, Statement - II is True , Statement - II is a CORRECT EXPLANATION for Statement - I |
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| 24. |
Evaluate int_(0)^(2)[x^(2)-x+1]dx where [ ] denotes the GIF |
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| 25. |
For a reaction ............ |
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Answer» <P> `t=0""360""0""0""0` `t=t 360-P" "P""P""P` `P_(t)=360-P+P+P+P` `=360+2P=760` `2P=400` `P=200` `t=2.303/(3.52xx10^(-3)) "LOG" 360/(360-200)` `t=2.303/(3.52xx10^(-3)) "log" 360/160` `=(2.303xx0.352)/(3.52xx10^(-3))=23.03` min |
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| 26. |
For each of the differential equations find solution: (dy)/(dx) +tan x = , y = 0 when x = (pi)/(3) |
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| 27. |
The numberof waysin whichand examinercanassign20 maksto 4questiongivingnot lessthan2 marksto anyquestionis |
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Answer» 280 |
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| 28. |
The probability of throwing 16 in one throw with three dice isa) 1/36b) 1/18c)1/72d)1/9 |
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Answer» `1/36` |
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| 29. |
For all positive values of p, q, r and s ((p^(2)+p+1)(q^(2)+q+1)(r^(2)+r+1)(s^(2)+s+1))/(pqrs) cannot be less than |
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Answer» 81 |
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| 30. |
If 9 squares are choosen at random on a chess board. What is the probability that they form a square of size 3 xx 3 |
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| 31. |
Find the angle between the vectors 2hati-hatj+hatk and 3hati+4hatj-hatk. |
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| 32. |
Let p(n) denotes the number of different ways the positive integer n(ngt1) can be expressed as the sum of 1's and 2's . For example P(5)=8,i-e i.e. 5=1+1+1+1+1 =1+1+1+2=1+1+2+1=1+2+1+1=2+1+1+1 =1+2+2=2+1+2=2+2+1 The value of p(p(6)) is |
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Answer» <P>356 |
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| 33. |
When the origin is shifted to (-1,2) by the translation of axes, find the transformed equation of 2x^2+y^2-4x+4y=0 |
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| 34. |
Let (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)++….+C_(n)x^(n) where C_(r)=""^(n)C_(r) and (C_(0)+C_(1))(C_(1)+C_(2))…..(C_(n-1)+C_(n))=AC_(1)C_(2)…..C_(n) Then for n = 5, A is equal to |
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Answer» `3125/24` |
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| 35. |
A: The equation tha common chord of the two circles x^(2) + y^(2) + 2x + 3y + 1 = 0 , x^(2) + y^(2) + 4x + 3y + 2 = 0 " is " 2x + 1 = 0. |
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Answer» Both A and R are true and R is the correct EXPLANATION of A |
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| 36. |
Find mean of the following probability distribution. |
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| 37. |
Find x, if tan^(-1)4+cot^(-1)x=(pi)/(2). |
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| 39. |
Show that product of lengths of the perpendicular from any point on the hyperbola x^(2)/(16)-y^(2)/(9)=1 to its asymptotes is (144)/(25). |
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| 41. |
Find the equation of the circle passing through the point (1,2) (3,-4)and (5,-6) . |
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| 42. |
Determine the sum of all possible positive integers n, the product of whose digits equals n^2 - 15n- 27 |
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| 43. |
If xy - 4x + 3y - lambda=0 represents the asymptotes of xy - 4x + 3y = 0, then lambda is |
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Answer» 3 |
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| 44. |
If 3 boys and 3 girls are arranged along a row at random. Find the probability that all the girls sit together. |
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| 45. |
Letf(x)=(x^(2)-6x+5)/(x^(2)-5x+6). Then match the expressions/statements in List I with expression /statements in List II. |
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Answer» `a to p, r, s.` If `-1 lt x lt 1, " then "f(x)=((-ve)(-ve))/((-ve)(-ve))= +ve` ` :. f(x) gt 0` ALSO, `f(x)-1=(-x-1)/(x^(2)-5x+6)= -((x+1))/((x-2)(x-3))` For `-1 lt x lt 1, f(x)-1=(-(+ve))/((-ve)(-ve))= -ve` or `f(x) -1 lt 0 or f(x) lt 1` ` :. 0 lt f(x) lt 1` `B to q,s.` If `1 lt x lt 2, " then "f(x)=((-ve)(+ve))/((-ve)(-ve))= -ve` Therefore, `f(x) lt 0 " and, so,"f(x) lt 1.` `c to q,s.` If `3 lt x lt 5,` then `f(x)=((-ve)(+ve))/((+ve)(+ve))= -ve` Therefore, `f(x) lt 0 " and , so, "f(x) lt 1.` `d to p,r,s.` For `x gt 5, f(x) gt 0,` Also, `f(x)-1=(-(x+1))/((x-2)(x-5)) lt 0" for " x gt 5` `orf(x) lt 1,` ` :. 0lt f(x) lt 1` |
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| 46. |
If A=[(6,8,5),(4,2,3),(9,7,1)] is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is |
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Answer» `[(6,6,7),(6,2,5),(7,5,1)]` |
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| 47. |
The plane is passing through the point A(bar(a)) and contais the line bar(r) = bar(b) + lambda bar(c). The length of perpendicular drawn from the origin to this planeis............. |
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Answer» `([bar a barb bar c])/([ bar a XX bar B xx barb xx bar c + BARC xx BARA])` |
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| 48. |
What is wrong with the following application of L'Hopital's rule ? lim_(x to 1) (x^(3) +3 x -4)/(2x^(2) +x -3) |
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| 49. |
Ifh(x) = [ f (x) ] ^(2) + [ g (x) ] ^(2)and(x) = g (x), f''(x) = - f (x) , h (5) = 10 ,find h (10) . |
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