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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. |
Statement - I : If f(x) =sin^ (2)x+sin^(2)(x+(pi)/(3))+cos(x+(pi)/(3)),then f'(9x) = 0Statement - II : The differentiation of constant function with respectto x is zero |
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Answer» STATEMENT -I : f(x) = sin x then f' `(PI)`= f'`(3pi)` |
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| 2. |
Cl_(2)+underset("(hot and conc.)")(NaOH)toA+B Find the sum of oxidation state of Cl in A and B. |
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Answer» Algebraic sum of oxidation stateof Cl in A and B `=-1+5=+4` |
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| 3. |
Let C* = C - {0}, the set of non-zero complex number. Define a relation i? on C* as follows: z_(1), z_(2)in C^(*), z_(1)Rz_(2) if (z_(1)-z_(2))/(z_(1) + z_(2)) is a real numbers then |
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Answer» R is REFLEXIVE and SYMMETRIC only |
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| 4. |
If Aand Baresymmetricmatricesof sameorder, thenAB+BAis a …… |
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Answer» skewsymetricmatrix |
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| 5. |
Find the number of ways by which 4 green, 3 red and 2 white balls can be arranged in a row such that no two balls of the same colour are together. All balls of the same colour are identical. |
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Answer» |
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| 6. |
Evaluation of definite integrals by subsitiution and properties of its : int_(-pi)^(pi)(2x(1+sinx))/(1+cos^(2)x)dx=......... |
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Answer» `(pi^(2))/(4)` |
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| 7. |
If cos alpha , cos beta, cos gamma are the direction-cosines of a line, then the value of sin^2alpha + sin^2 beta + sin^2gamma = |
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| 8. |
For what values of natural numbers n can the product of the numbers n n + 1, n + 2, n +4, n + 5 be equal to the product of remaining ones? |
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| 9. |
Ifa = 2 hati + 3 hatj+ hatk, b = hati - hatj + 2 hatk "and" c= 2hati + hatj + hatk are three vecotrs , then|(a xx b) xx c | = |
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Answer» A.`|a XX (B xx C) |` |
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| 10. |
In the given figure, what is the radius of the inscribed semicircle having base on AB ? |
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Answer» `3//2` `rArr (5.r)/(2) + (3.r)/(2) = (4.3)/(2)` `rArr 8r = 12` `rArr r= 3//2` 
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| 11. |
If P(A) = 0.3, P(B) = 0.4, then the value of P(AuuB) where A and B are independent events a)0.48 b)0.51 c)0.52 d)0.58 |
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Answer» 0.48 |
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| 12. |
Intergrate the following: intsinx cos4xdx |
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Answer» SOLUTION :`intsinx cos4xdx` =`1/2 int2sinx.cox4xdx` = 1/2 {-1/5cos5x+1/3 COS3X}+C =1/6cos3x-1/10cos5x+C |
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| 13. |
Define a continuity of a function at a point. Find all the points of discontinuity of f defined by f(x) = |x| - |x - 1|. |
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| 14. |
A pair of four dice is thrown indepandently three times . The probability ofgetting a score of exactly 9 twice is : |
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Answer» `8//9` |
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| 15. |
A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total unmber of posts of each kind in all the offices taken together, |
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Answer» taluka respectively and O, H, C, Cl , T and P for office SUPERINTENDENT, Head clerk, Cashier, Clerk, Typist and Peon respectively. Then the number of offices can be arranged as elements of a row matrix A and the composition of staffin various offices can be areanged in a `3xx6` matrix B (say). `{:(Div,Dis,Tal):}` `therefore A = [[5,30,200]]` and `B=[[1,1,1,2+1,1,1+1],[0,1,1,1+1,0,1+1],[0,1,1,1,0,1]]` or `B= [[1,1,1,3,1,2],[0,1,1,2,0,2],[0,1,1,1,0,1]]` The basic monthly salarise of various types of EMPLOYEES of these offies correspond to the elements of the column matrix C. `thereforeC={:[O],[H],[C],[Cl],[T],[P]:}[[500],[200],[175],[150],[150],[100]]` Total number of Posts = AB `{:(O,H,C,Cl,T,P):}` `{:(,"Div","Dis","Tal"),("[",5,30,200" ]"):}xx =[{:(,1,1,1,3,1,2),(,0,1,1,2,0,2),(,0,1,1,1,0,1):}]` `{:( ,O,H,C,Cl,T,P),(=,"["5,235,235,275,5,270"]"):}` i.e. Required number of posta in all the offices taken together are 5 office Suprintendents, 235 Head Clareks, 235 Cashiers, 275 Clerks, 5 Typists and 270 Peons. |
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| 16. |
Statement I : A fair coin is tossed 100 times . The probability of getting tails an odd number of times is 1/2 . Statement II : A fair coin is tossed 99 times . The probability of getting tails an odd number of times is 1/2 Then which of the above statements are true . |
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Answer» only I |
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| 17. |
A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of all the offices taken together. |
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Answer» taluka RESPECTIVELY and O, H, C, CL , T and P for office superintendent, Head clerk, Cashier, Clerk, Typist and Peon respectively. Then the number of offices can be arranged as elements of a row matrix A and the composition of staffin various offices can be areanged in a `3xx6` matrix B (say). `{:(Div,Dis,Tal):}` `therefore A = [[5,30,200]]` and` B=[[1,1,1,2+1,1,1+1],[0,1,1,1+1,0,1+1],[0,1,1,1,0,1]]` or `B= [[1,1,1,3,1,2],[0,1,1,2,0,2],[0,1,1,1,0,1]]` The basic monthly salarise of various types of employees of these offies correspond to the elements of the COLUMN matrix C. `thereforeC={:[O],[H],[C],[Cl],[T],[P]:}[[500],[200],[175],[150],[150],[100]]` The total basic monthly salary bill of all the offices taken together `= A BC = A(BC)` `= [ (5,30,200)]xx[[1675],[875],[625]]` `[5xx1675+30xx865+200xx625]` `= [159625]` Hence, total basic monthly salary bill of all the offices taken together is Rs 159625. |
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| 18. |
Evaluate the following integrals int_1^2(3^(x+2))dx |
| Answer» SOLUTION :`int_1^2 3^(x+2)DX=[3^(x+2)/(IN3)]_1^2=72/(In3)` | |
| 19. |
The ratio by which the line 2x + 5y- 7 = 0 divides the straight line joining the points (-4, 7) and (6, -5) is |
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Answer» 1 : 4 |
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| 20. |
If(1+ x ) ^(15)= a _ 0+ a _1 x+ … + a _(15) , thensum _(r = 1 ) ^(15)r(a _ r )/(a _ (r-1))is equalto |
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Answer» 110 `thereforea _ 0= ""^(15) C_0, a _ 1= ""^(15) C_1a _ 2= ""^(15) C_2, … ` ` a_(15)= ""^(15) C_(15) ` `thereforer (a_r)/( a_(R-1 ))= r. (""^(15) C_r ) /(""^(15)C _ (r - 1 )) ` `= r (15 - r + 1 )/(r ) "" [ because(""^N C _ r)/(""^nC_(r- 1)) = (n - r + 1 )/(r) ] ` ` =15 -r + 1` `thereforesum_(r = 1 ) ^(15)r . (a_r)/(a _ (r- 1 ))=sum _ ( r = 1 ) ^(15 )r(""^(15) C_r ) /(""^(15) C_(r-1)) ` `=15+14+13 +... +1` `=(15 (16))/(2) ` ` [ because1 +2+...+n =( n ( n + 1 ) ) /(2) ] ` ` = 120` |
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| 21. |
Find the area of the region bounded by x^(2)=8y, x-axis and the line x= 4 |
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| 22. |
Let A and B be two sets, and P(A) denotes the power set of A, then which of the following is true? |
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Answer» <P>`P(A) cup P(B) = P(A cup B)` |
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| 23. |
Draw the rough sketch and find the area of the region: {(x,y): 4x^(2) + y ^(2) le 4,2x + y ge 2} |
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| 24. |
If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k = |
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Answer» 2 |
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| 25. |
Find the direction cosines of a line which makes equal angles with the coordinate axes. |
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| 26. |
Find the distance between the parallel planesvecr.(2hati-3hatj+6hatk)=5 and vecr.(6hati-9hatj+18hatk)+20=0 |
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| 27. |
If y= x ^(3) Sin ^(-1) x + (x ^(2) + 2 ) sqrt(1- x ^(2)), then dy //dx = |
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Answer» `Sin ^(-1)X` |
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| 28. |
Find the equation of circle passing through each of the following three points. (1,2),(3,-4),(5,-6) |
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| 29. |
Ifthecoefficientsofx ^(9), x ^( 10) , x ^ ( 11 )intheexpansion of(1 +x ) ^nareinarithmeticprogressionthenn^ 2-41 n= |
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Answer» `398` `therefore""^n c _9,""^n c _ (10),""^nc _(11)` arein `A.P` `therefore2 (nc _ (10)) =nc _ 9 +nc _ (11)` ` rArr2= (nc _9 ) /(nc _ (10))+(nc _(11))/(nc _ (10)) ` ` rArr 2= (10)/(n - 10+1 ) +(n - 11+ 1 )/(11)[ because(nc _r )/(nc _ (R - 1 ))= (n -r + 1 )/(r ) ] ` ` rArr 2=(10)/(n - 9)+(n - 10)/(11)` `rArr2-(10)/(n-9 )=(n -10)/(11)` ` rArr(2n -28)/(n -9 ) = (n -10)/(11)` ` rArr11 (2n- 28) =(n - 9 )(n - 10) ` `rArr22n- 308=n ^ 2-19n +90 ` `thereforen^ 2 - 41 n+398=0 ` |
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| 30. |
Random variable X takes integer values from 1 to n with equal probabilities then E(X) = ……….. |
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Answer» `(N)/(2)` |
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| 31. |
If f(x)=(e^(x))/(1+e^(x)),I_(1)=int_(f(-a))^(f(a))xg{x(1-x)}dx andI_(2)=int_(f(-a))^(f(a))g{x(1-x)}dx, then the value of (I_(2))/(I_(1)) is - |
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Answer» -1 |
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| 32. |
""^11C_0^2 - ""^11C_1^2 + ""^11C_2^2 - ""^11C_3^2 + ……- "^11C_11^2 = |
| Answer» Answer :A | |
| 33. |
Determine order and degree (if defined) of the following differential equations . (y''')^2 + (y'')^3 + (y')^4 + y^5 = 0 |
| Answer» Solution :The HIGHEST order derivative in the differential EQUATION is y... and its DEGREE is 2. `therefore` The order and the degree of the differential equation are 3 and 2 RESPECTIVELY. | |
| 34. |
If in a moderately skewed distribution, the values of mode and mean are 6 lambda and 9 lambda respectively, then value of median is |
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Answer» `8 lambda` |
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| 35. |
Let T_(n) denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If T_(n+1)-T_(n)=28 Then n = |
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Answer» 4 |
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| 36. |
If p(theta)is a pointon the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtb)then find its coresponding point |
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| 38. |
(1+cos 56^(@)+cos58^(@)-cos66^(@))/(cos28^(@)cos29^(@)sin33^(@))=kcos(A/2)cos(B/2)sin(c/2) then k=? |
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Answer» 0 |
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| 39. |
If P(A) = 0.1, P(B) = 0.2and P(A cup B)= 0.25 then P(A' | B')= ………… |
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Answer» `(1)/(6)` |
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| 40. |
If a, b, c are real if ax^(2)+ bx + c = 0 has two real roots alpha, betawhere a lt -1, beta gt 1 then |
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Answer» `1+ (C) /(a)+ |(b)/(a)| LT 0` |
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| 41. |
If the matrix A is both symmetric and skew suymmetric, then |
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Answer» A is a DIAGONAL matrix |
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| 42. |
Can you generalize this situation? If a fair coin is tossed six times, find the probability of getting exactly 2 heads. |
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Answer» SOLUTION :A fair coin is tossed 6 times, Let A be the event of getting EXACTLY 2 heads. `THEREFORE absA= ^6C_2=15 therefore P(A)=15/2^6` Yes we can GENERALIZE the SITUATION, i.e., if a fair coin is tossed n-times, then probability of getting exactly 2 heads= `("^nC_2)/2^n`= `("^6C_2)/2_6` |
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| 43. |
Integration by partial fraction : If int (2x^(2)+3*dx)/((x^(2)-1)(x^(2)-4))=log((x-2)/(x+2))^(a)((x+1)/(x-1))^(b)+c then the value of a and b are ...... Respectively. |
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Answer» `(11)/(12),(5)/(6)` |
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| 44. |
Statement-I If a=3hat(i)-3hat(j)+hat(k), b=-hat(i)+2hat(j)+hat(k) and c=hat(i)+hat(j)+hat(k) and d=2hat(i)-hat(j), then there exist real numbers alpha, beta, gamma such that a=alphab+betac+gammad Statement-II a, b, c, d are four vectors in a 3-dimensional space. If b, c, d are non-coplanar, then there exist real numbers alpha, beta, gamma such that a=alphab+betac+gammad. |
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Answer» BothStatement-I and Statement-II are CORRECT and Statement-II is the correct EXPLANATION of Statement-I |
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| 45. |
For the inverse cosine function function |
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Answer» `y=cos^(-1)x,-1lexle1` |
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| 47. |
A and B are seeking admission into I.I.T. If the probability for A to be selected is 0.5 and that both to be selected is 0.3. Is it possible that the probability of B to be selected is 0.9? |
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Answer» <P> |
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| 48. |
A circle passes thorugh A(2,1) and touches y-axis then the locus of its centre is |
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Answer» `(y+1)^(2)=4(x+1)` |
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| 49. |
Find the unit vector in the direction of vector overline(PQ), where P and Q are the points P=(1,2,3).Q=(4,5,6) respectively. |
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