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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 polar of three points with respect to a given circle are concurrent, then the three points |
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Answer» are the VERTICES of an EQUILATERAL triangle |
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| 2. |
The major axis of an ellipse is y =x and one vertex is at origin , the other axis of the ellipse , if the length of semi-major axis be 10, can be |
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Answer» ` x+y= 10 ` |
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| 3. |
Discuss the relative position of the fol- lowing pair of circles. x^(2)+y^(2) - 4x- 6y - 12 = 0 x^(2) + y^(2) + 6 x+ 18 y + 26 = 0. |
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| 5. |
From the first 20 natural numbers, find the number of ways of selecting two numbers which are not consecutive |
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| 6. |
Differentiate cos sqrt(x) w.r.t.x |
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| 7. |
The value of f(0), so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(243+5x)^(1//5)),(xne0) is continuous at x=0, is given by |
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Answer» `(2)/(3)` `f(0) = underset(xrarr0)lim f (x) = underset(xrarr0)lim ((27-2x)^(1//3)-3)/(9-3(243+5x)^(1//5))` `("from"(0)/(0))` `=underset(xrarr0)lim((1)/(3)(27-2x)^(-2//3)(-2))/(-(3)/(5)(243+_5x)^(-4//5)(5))=2` |
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| 8. |
Let A be a square matrix of order 2 such that A-1 =AA^(T) (where I is an identity matrix of order 2), then which one of the following is INCORRECT statement (where |A| represents determinant value of matrix A) |
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Answer» |A|=1 TAKE TRANSPOSE both the SIDES `A^(T) - I =AA^(T)`………..(2) from (1) and (2) `A=A^(T)` `rArr A-I =A^(2)` `rArr |A| = 1, adj (A) = A^(-1)` Trace of (A) =1 |
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| 9. |
If 4 people are chosen at random, then find the probability that no two of them were born on the same day of the week. |
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Answer» <P> |
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| 10. |
If e and e^1 are the eccentricities of the ellipse 5x^(2)+9y^(2)=45 and the hyperbola 5x^(2)-4y^(2)=45" then "e e^(1)= |
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Answer» 9 |
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| 11. |
If If {{:(,(72^(x)-9^(x)-8^(x)+1)/(sqrt2-sqrt(1+cosx)),x ne 0),(,k log 2 log 3, x=0):}is a continuous function then k is equal to |
| Answer» ANSWER :D | |
| 12. |
Find (dy)/(dx) when x and y are connected by the relation given: sec(x+ y) = xy |
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| 13. |
If bar(a)=(-3,1,0) and bar(b)=(1,-1,-1) then "Comp"_(bar(a))bar(b) …………. |
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Answer» `(4)/(sqrt(10))` |
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| 14. |
Evaluate: int(cos2x - cos2alpha)/(cosx - cos alpha) dx |
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| 16. |
If the product of the intercepts make by the straight line xtan alpha+y sec alpha=1, (0 le alpha lt (pi)/2), on the co-ordinates axes is equal to sin alpha, find alpha. |
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Answer» |
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| 17. |
int(dx)/(sqrt(2x-x^(2)))=.... |
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Answer» `COS^(-1)(x-1)+c` |
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| 18. |
If x=1+(3)/(1!)xx(1)/(6)+(3xx7)/(2!)((1)/(6))^(2)+(3xx7xx11)/(3!)((1)/(6))^(3)+.... "then"x^(4) equals |
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Answer» 81 |
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| 19. |
Construct truth tables for the following and indicate which of these are tautologiesp ^^ q rarr P vv q. |
Answer» SOLUTION :
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| 20. |
If I is the identity matrix of order 2 and A = [{:(1,1),(0,1):}], then for n ge1, mathematical induction gives, |
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Answer» `A^(N) = NA -(n -1)1` |
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| 21. |
Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)(200sinx+100cosx)/(sinx+cos)dx=.......... |
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Answer» `5PI` |
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| 22. |
By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],[b,c,0]|=0 |
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Answer» Solution :`|[0,a ,-b],[-a,0,-C],[b,c,0]|=0 [because[[0,a ,-b],[-a,0,-c],[b,c,0]]`is a skew-symmetricmatrixof order 3 DETERMINANT of a skew-symmetric MATRIX of ODD order is zero. |
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| 24. |
The sum of all 4 digit numbers of different digits formed with the digits 1, 2, 5 and 6 is |
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Answer» 93324 |
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| 25. |
IfA =[{:( a,x,y),( x,b,z),( y,z,c) :}] : a,b,c,x,y,z, "in"(1,2,3,4,5,6)a,b,c,x,y,z, are distinct then number of matrices A with trace equal to 10 are |
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Answer» `3(3L)^(2) ` |
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| 26. |
IfX is a discrete random variable P(X gta) is equal to |
| Answer» Answer :A | |
| 27. |
If x_(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n))), then x_(1), x_(2), x_(3)....oo is equal to |
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Answer» `(1+isqrt3)/(2)` |
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| 28. |
If sin^(3) xsin 3x = sum_(m=0)^(n)C_m cos^(m)x " where " C_0,C_1..........., C_n are constant and C_n ne 0 , then n= |
| Answer» Answer :D | |
| 30. |
Let f(x) = lim_( n to oo)( x^(2n-1)+ax^(2)+bx)/(x^(2n+1)), if f(x) is continuousforall x inR.then thevalueof a+ 8b i s______. |
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| 31. |
If int(dx)/(1+3sqrt(x+1))=(3)/(2)(x+1)^(2//3)-3(x+1)^(1//3) + f(x) + C then f(x) is equal to |
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Answer» `log|1+3sqrt(x+1)|` |
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| 32. |
Write the equation of the plane passing through the point (1,2,3), the direction ratios of the normal to the plane being langle3,5,7rangle |
| Answer» SOLUTION :GIVEN EQUATION of the PLANE is `x+y+2z=1rArrx/1+y/1+z/((1/2))=1` | |
| 34. |
State and prove a multinomial Theorem. |
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Answer» SOLUTION :Multinomial THEOREM : `(p_1+p_2+ .... + P_m)^n` `sum (n!)/((n_1)!(n_2)!...(n_m)!) p_1^(n_1) p_2^(n_2) ... p_m^(n_m)` where `n_1+n_2+ ... + n_m` = n The PROOF of this theorem is beyond of the syllabus. |
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| 35. |
Let x be the elements of the set A={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120} and x_(1),x_(2),x_(3) be positive integers and d be the number of integral solutions of x_(1),x_(2),x_(3)=x, then d is |
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Answer» 100 |
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| 36. |
Find the values of a,b,c,and d from the following equation : [{:(2a+b,a-2b),(5c-d,4c+3d):}]=[{:(4,-3),(11,24):}] |
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| 37. |
State which of the following statements are true (T) or false(F) The line (x+5)/(-2)=(y-3)/1=(z-2)/3 lies on the plane x-y+z+1=0. |
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| 38. |
Define bijective function. |
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| 39. |
The numberof rectangleswhichare notsquaresformedin achessboard is |
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| 40. |
Find the area bounded by y=sinxand y=cosxbetween any two consecutive points of intersection. |
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| 41. |
Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) which are reflexive ans symmetric but not transitive is |
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Answer» 1 |
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| 42. |
If a matrix has 8 elements, what are the possible orders it can have? |
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| 43. |
The sum of three numbers is 6 . When second number is subtracted from thrice thesum of first and third numbers, we get number 10 . Four times of third number issubtracted from five times the sum of firstand second numbers , the result is 3 . Using above informations , find these three numbers by matrix method . |
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| 44. |
The tangents at an extremity (in the first quadrant )of latus rectum of the hyperbola (x^(2))/( 4) - ( y^(2))/( 5)=1meets x-axis and y- axis at A and B respectively . Then(OA)^(2) - (OB) ^(2) , where O is the origin , equals |
| Answer» Answer :A | |
| 45. |
Ifalpha , beta , gammaare the rootsofx^3 + px^2 + qx+ r=0 formthe equationwhoserootsarealphabeta , betagamma, gammaalpha |
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| 47. |
In the given figure, AB is the diameter of the circle, centered at O. If angleCOA = 60^(@), AB = 2r, AC = d, and CD = l, then l is equal to |
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Answer» `d sqrt3`  `AC = d, OA = OB r, CD = BD = I, angleCOA = (pi)/(3)` CLEARLY `DeltaAOC` is equilateral `:. d = r` Also, `angleBOD = angleCOD = (2pi)/(3xx2) = (pi)/(3)` or `TAN.(pi)/(3) = (BD)/(OB) = (l)/(r) RARR l = r sqrt3 = d sqrt3` |
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| 48. |
If [{:(x+3,z+4,2y-7),(-6,a-1,0),(b-3,-21,0):}]=[{:(0,6,3y-2),(-6,-3,2c+2),(2b+4,-21,0):}] Find the values of a,b,c,x,y and z. |
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| 49. |
ABCD is a tetrahedron. A_(1), B_(1), C_(1), D_(1) are the centroids of the triangles BCD, ACD, ABD and ABC ,A A_(1), B B_(1), C C_(1), D D_(1) divide one another in the ration : |
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Answer» `1:1` |
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| 50. |
IF a andb are naturalnumberssuchthata^2-b^2isprimenumberthena^2 -b^2 equals |
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Answer» `a+b` |
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