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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. |
If the mean deviation of the number 1, 1+d, 1+2d,….,1+100 d from their means is 255, then the d is equal to |
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Answer» `20.0` |
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| 2. |
Find the slope of the normal to the curve x=1 -a sin theta , y = b cos^(2) thetaat theta= (pi)/(2) . |
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| 3. |
Function 'f:RrarrR,f(x)=3x-5' is : |
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Answer» ONE to one |
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| 4. |
Evaluate the following lim_(xto2) (x^2 +3x -9)/(x+1) |
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Answer» SOLUTION :`lim_(xto2) (x^2 +3X -9)/(x+1)` `=(2^2+3cdot2-9)/(2+1)=1/3` |
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| 5. |
Find (dy)/(dx) in the following: y= sec^(-1) ((x^(2) + 1)/(x^(2)-1)) |
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| 6. |
Consider the relation 4l^(2)-5m^(2)+6l+1=0 , where l,m in R Tangents PA and PB are drawn to the above fixed circle from the points P on the line x+y-1=0 . Then the chord of contact AP passes through the fixed point. |
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Answer» `(1//2,-5//2)` `X^(2)+y^(2)+2gx+2fy+c=0`(1) The line `lx +my+1=0` will touch circle (1) if the length of perpendicular from the center `( -g, -f)` of the circle on the line is equal to its radius, i.e., `(|-g l =mf +1|)/(sqrt(l^(2)+m^(2)))=sqrt(g^(2)+f^(2)-c)` `(gl+mf-1)^(2)= (l^(2)+m^(2))(g^(2)+f^(2)-c)` or `(c-f^(2))l^(2)+(c-g^(2))m^(2)-2gl-2fm+2fglm+1=0`(2) But the given condition is `4l^(2)-5m^(2)+6l+1=0`(3) Comparing (ii) and (iii), we GET `c-f^(2)=4,c-g^(2)= -5, -2g = 6, -2f =0, 2gf=0` Solving, we get `f=0, g= -3, c=4` Substituting these values in (1) , the equation of the circle is `x^(2)+y^(2)-6x+4=0`. Any point on the ling `x+y-1=0` is `(t, 1-t) , t in R`. The chord of contact w.r.t. this point of circle is `TX +y(1-t) -3(t+x) +4 =0` or `t ( x-y-3) + (-3x+y+4)=0`, which is concurrent at the point of intersection of the lines `x-y-3=0` and `-3x+y+4=0` for all values of t. Hence, the lines are concurrent at `(1//2, -5//2)`. Also point (2,-3) lies outside the circle from which TWO tangents can be drawn. |
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| 7. |
Consider the planes p_1: 2x+y+z+4=0, p_2: y-z+4=0 and p_3: 3x+2y+z+8=0 Let L_1, L_2, L_3 be the lines of intersection of the planes p_2 and p_3, p_3 and p_1, p_1 and p_2 respectively. Then. |
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Answer» at LEAST two of the line `L_1, L_2 and L_3` are non parallel. |
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| 8. |
If forafunctionf :R to Rf (x +y ) =F(x )+ f(y)for allx andy thenf(0)is |
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Answer» t |
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| 10. |
Consider three sets A = {1, 2, 3}, B = {3, 4, 5, 6}, C = {6, 7, 8, 9}. R_(1) is defined from A to B such that R_(1) = {(x, y) : 4x lt y, x in A, y in B}. Similarly R_(2) is defined from B to C such that R_(2) = {(x, y) : 2x le y, x in B and y in C} then R_(1)oR_(2)^(-1) is |
| Answer» ANSWER :D | |
| 11. |
The slope of a curve at any point on it is the reciprocal of twice of ordinate at that point. If the curve passes through (4,3) then the equation is |
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Answer» `y^(2) = x+4` |
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| 12. |
The normal to x^(2)=4y passing through (1, 2) has equation ………. |
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Answer» `x+y=3` |
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| 13. |
If f: R to R" is definedby f(x)"=[x-3]+[x-4]"for "x in R"then " underset(x to 3-)"Lt"f(x)= |
| Answer» Answer :C | |
| 14. |
Let Q be a point on the circle B : x ^(2) + y ^(2)=a ^(2) and p(h,k) be a fixed point. If the locus of the point which divides the join of P and Q in the ratio p:q is a circle C, then the centre of C is |
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Answer» <P>`((p+q)/(P), (p+q)/(q))` |
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| 15. |
Prove that : log_ea-log_eb=2[(a-b)/(a+b)+1/3((a-b)/(a+b))^3+1/5((a-b)/(a+b))^5+...],a > b |
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Answer» 7 Solution :LET`(a-b)/(a+b)=a` in the R.H.S.`thereforeR.H.S.=2[x+x^2/3+x^5/5+...]=log((1+x)/(1-x))=log(1+(1-b)/(a+b)/1-(a-b)/(a+b))=log((2A)/(AB))=loga-logb=L.H.S` |
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| 16. |
The value of lim_(ntooo){(sqrt(3)+1)^(2n)} is……..(where {.} denotes fractional part of x). |
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| 17. |
The number of ways in which 7 pencils, 6 books and 5 pens be disposed off is |
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Answer» 336 |
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| 18. |
Evaluate : (i) Find the value a such int_(0)^(a)(1)/(e^(x)+4e^(x)+5)dx = ln 3sqrt(2). (ii) Find the value of int_(0)^((pi//2)^(1//2))x^(5).sinx^(3)dx |
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| 19. |
Prove that the portion of the tangent intercepted between the point of contact and the directrix of the parabola y^(2) =4ax subtends a right angle at its focus. |
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| 20. |
Let A = {1,2,3},B = {4,5,6,7} and let f={(1,4),(2,5),(3,6)} be a function from A to B. Show that f is one - one. |
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| 21. |
The time T of oscillation of a simple pendulum of length L is governed by T=2pisqrt(L/g), where g is a constant. The percentage by which the length be changed in order to correct an error of loss equal to 2 minutes of time per day is |
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Answer» `-5/18` |
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| 22. |
For the process : H_(2)O (l, 1 atm, 373 K) rArr H_(2)O(g, 1 atm, 373 K) [Given normal boiling point of water = 373 K at 1 atm pressure.] The correct set of thermodynamic parameter is : |
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Answer» `DeltaG = 0, Delta U lt 0, Delta H lt 0` |
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| 23. |
Solve the following systems of linear inequalities graphically : x - 2y + 2 lt 0 , x gt 0 |
Answer» SOLUTION :
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| 25. |
Show that the lines joining the origin with the points of intersection of the curve 7x^2-4xy+8y^2+2x-4y-8=0 with the line 3x-y=2 are mutually perpendicular. |
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| 26. |
Mother,Father and Son line up at random for a family picture.E : son on one end, F:Father in middle. Find P(E/F). |
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Answer» Solution :SUPPOSE A,B,C denote the mother, the father and the son respectively. Then S ={ABC,ACB,BAC,BCA,CAB,CBA} `rArr` n(S) = 6 E = {CAB,CBA,ABC,BAC}, F={ABC,CAB} `rArr` n(F)=2 Also,`EnnF`={ABC,CAB}`rArr` n`(EnnF)` = 2 therefore`P(EnnF)`=2/6 and P(F) =2/6 `rArr` P(E/F) = `(P(EnnF))/P(F))`=1 |
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| 27. |
If f(a)=2, f'(a)=1, g(a)=3, g'(a)=-1, then underset(x to a)lim (f(a)g(x)-f(x)g(a))/(x-a) is equal to |
| Answer» ANSWER :D | |
| 28. |
If p + q = 12 and pq = 35, then 1/p + 1/q = |
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Answer» `1//5` |
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| 29. |
Extend the function f(x)=x^2 + x defined on the interval (0,3) onto the interval(-3, 3) in an even and an odd way. |
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Answer» An odd EXTENSIONS defines the function `PSI(x) ={{:(,f(x)=x^(2)+x" for "0 le x le 3),(,-f(x)=-x^(2)+x" for "-3 le x lt 0):}` |
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| 30. |
The probability for a randomly chosen month to have its 10^(th) day as Sunday is |
| Answer» Answer :A | |
| 31. |
If Delta ne 0 then the system is ............... . |
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Answer» CONSISTENT and has UNIQUE solution |
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| 32. |
Differentiate w.r.t.x the function in Exercises 1 to 11. (sin x- cos x)^( sin x - cos x), (pi)/(4) ltx lt (3pi)/(4). |
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| 33. |
Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (logx)^(x)+ x^(log x). |
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| 34. |
A ball is thrown upward with such a velocity v that it returns to the thrower after 3 s. Take g = 10 ms^(-2). Find the value of v :- |
| Answer» Answer :A | |
| 35. |
If A and B are two independent events, then the probability of occurrence of atleast one of A and B is given by |
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Answer» <P>`1-P(A).P(B)` |
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| 36. |
If is the sum of the n^(th)powers , p is the sumof the products of m together of the n quantities a_(1),a_(2),……a_(n) eachof whichis greater than1 , show that (n-1) !s gt (n-m) ! …m! p |
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Answer» <P> |
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| 37. |
The volume of a cube is increasing at the rate of increasing at the instant when the length of an edge of the cube is 24 cm? |
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| 38. |
intsinx.log (sinx) dx. = |
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Answer» `-`COSX.LOG (sinx) + log `|tan""(x)/(2)|` + cos x + C |
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| 39. |
One limiting point of the coaxal system of circles containingx^(2) + y^(2) - -6x - 6y + 4 = 0 " and " x^(2) + y^(2) - 2x - 4y + 3 = 0is |
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Answer» (-1,1) |
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| 40. |
Using differentials, find the approximate value of(25)^(1/3). |
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| 41. |
The shortest distance the lines (x-3)/(3) = (y-8)/(-1) = (z-3)/(1) and (x+3)/(-3) = (y + 7)/(2) = (z-6)/(4) is.......... |
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Answer» `SQRT(30)` |
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| 42. |
A fair coin is tossed n times. Let x be random variable denoting the number of heads tossed. If P(x=4), P(x=5),P(x=6) are in A.P. then n = |
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Answer» 7 |
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| 43. |
Aline in 3 dimensional space makes an angletheta (0 lt theta le pi//2)with both the x and y axex . Then the set of all values ofthetais the interval |
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Answer» `(0, (PI)/(4))` |
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| 44. |
Prove the following : cot22(1/2)^@=sqrt2+1 |
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Answer» SOLUTION :`COT(45^@/2)=(1+cos45^@)/(SIN45^@)=(1+1/sqrt2)/(1/sqrt2)` `sqrt2+1` |
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| 45. |
A tower of height b subtends an angle alpha at a point on the same level as the food of the tower .At a second point , b meters above the first , the angle of depression of the foot pole and the finds that the elevation is now 2 theta.The value of cot thetais |
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Answer» B COT `alpha "TAN " beta `  In triangle ABD. `h=x tan alpha` In triangle BCE. `X= b cot beta` from (1) and (2) we get `thereforeh=b tan alpha cot beta` |
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| 47. |
integrate the following inte^(2x+7)dx |
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Answer» Solution :`inte^(2x+7)DX` [put 2x+7=t 2dx=dt or dx=(1/2)dt] `inte^tcdot (1/2)dt =(1/2)e^t+C =(1/2)e^(2x+7)+C` |
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| 48. |
Find the area bounded by the parabola y=x^(2),the x -axis and the lines x=-1, x=2 . |
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| 49. |
Consider the binary operation ** on the set A= {1,2,3,4,5} given by the following multiplication table Compute (2**3)**4 and 2**(3**4) |
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Answer» SOLUTION :`(2**3)**4=1**4=1` `2**(3**4)=2**1-1` |
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