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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. |
LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {{3, 4}} ⊂A |
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| 2. |
If x = log p and y = 1/p then |
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Answer» `(d^2y)/(dx^2) - 2p = 0 ` |
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| 3. |
The sum of first three terms of a G.P is 16 and the sum of the next three terms is 128 Determine the first term, the common ratio and the sum to n terms of the G.P. |
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| 4. |
|{:(x+y,0,0),(0,x-y,0),(0,0,x^(2)+y^(2)):}|= |
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Answer» `x^(4)-y^(4)` |
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| 5. |
If the radius of a sphere ia equal to the height and radius of the cylinder then the ratio of the rates of increases of the volumes of the sphere and cylinder is |
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Answer» `4:3` |
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| 6. |
Find the position vector of two points on the line through P(bar(i)+bar(j)-2bar(k)) at a distance 6 units from P, if the line is parallel to 2bar(i)+2bar(j)+bar(k). |
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| 7. |
sec h^(2)[tan h^(-1)((1)/(2))] + "cosec " h^(2) (cot h^(-1)(3)) = |
| Answer» Answer :C | |
| 8. |
A (3,4,5), C(-1,6,1) are the vetrices of a triangle then Statement-I : The circumcentre of Delta ABC is (1,5,3) Statement -II : The orthocentre of Delta ABC is (2,3,1) |
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Answer» Only I |
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| 9. |
Eccentricity of hyperbola 16y^2-9x^2=144 is ........... |
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| 10. |
A function 'f' well defined AA x , y in R is such that f(1)=2, f(2)=8 and f(x+y)-kxy= f(x)+2y^(2), where 'k' is some constant then f(x) is |
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Answer» `X^(2)` |
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| 11. |
If tan""((theta)/(2))=sqrt([(1-e)/(1+e)]) tan""((alpha)/(2)) thencos alpha= |
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Answer» `(1 - E COS THETA)/(cos theta + e)` |
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| 13. |
Assertion (A): The sum of the distances of a point from two perpendicular lines is 1, then its locus is a square Reason (R): The locus of a point which is at a distance 'p' from the given point is a circle |
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Answer» A TRUE, R true and R is CORRECT explanation of A |
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| 14. |
If (1)/(6) sin theta, cos theta and tan theta are in geometric progression, then the solution set of theta is |
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Answer» `2 N pi PM(pi)/(3)` |
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| 15. |
The negation of the statement 101 is not a multiple of 3" is…. |
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Answer» 101 is a multiple od 3 |
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| 16. |
Solve: sqrt(x + 5) + sqrt(x + 21) = sqrt(6x + 40) |
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Answer» `therefore ` The only root is 4 . |
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| 17. |
The solution set of (5+4Costheta)(2costheta+1)=0 in the interval [0,2pi] is |
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Answer» `{(pi)/(3),(2PI)/(3)}` |
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| 18. |
Let bara =4bari+5barj-bark, barb = bari - 4barj+5bark and c= 3bari +barj-bark. Find the vector which is perpendicular to both bara and barb whose magnitude is twenty one times the magnitude of barc. |
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| 20. |
Evaluate the following limits : Lim_(x to 0 ) (1-cosmx)/(1- cos nx) |
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| 21. |
ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of x + y is |
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Answer» `(2AC)/(a^(2)-b^(2))` |
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| 22. |
If f(theta)=(1-sin2theta+cos2theta)/(2cos2theta) , then value of 8f(11^(0)).f(34^0) is _____ |
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| 23. |
For all value of theta, the lines represented by the equation (2costheta+3sin theta)x+(3costheta-5sintheta)y-(5costheta-2sintheta)=0 |
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Answer» PASS through a fixed POINT |
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| 24. |
If the constant term in expansion of (sqrt(x)-k/(x^(2)))^(10) is 405 then find the value of k . |
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| 25. |
If a+b+c=0 the straight line 2ax+3by+4c=0 passes through the fixed point |
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Answer» `[2,4/3]` |
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| 26. |
If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find B ∩ D |
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| 27. |
Evaluate the following limits in Exercises lim_(xto2)(3x^(2)-x-10)/(x^(2)-4) |
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| 28. |
If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j), then the unit vector in the direction of bar(c) is |
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Answer» `11bar(i)+10bar(J)+2BAR(K)` |
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| 29. |
Function f and g defined on R-{0}rarrRas f(x)=x and g(x)=1/x" then "f.g(x) = ...... . |
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| 30. |
Insert three geometric means between 1 and 256. |
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| 31. |
A line is drawn through the point A(4,-1) and parallel to the line 3x-4y+7=0. Find the coordinates of two points on this line which are at distance of 5 units from A. |
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| 32. |
If theta in [pi/2, (3pi)/2]" then "Sin^(-1)(sintheta)= |
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Answer» `theta` |
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| 33. |
Find the value of ""^6P_1 |
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| 34. |
How many automobiles licence plates can be made if the inscriptions on each contains two different letters followed by three differents digits ? |
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| 36. |
The perpendicular distance from the point (1,-1) to the line x+5y-9=0 is equal to |
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Answer» `SQRT(2/13)` |
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| 37. |
Let a = 6, b = 3 , " and " cos (A - B) = 4/5 Value of sin A is equal to |
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Answer» `1/(2SQRT5)` |
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| 38. |
Evaluate the following limits in Exercises lim_(xto-1)(x^(10)+x^(5)+1)/(x-1) |
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| 39. |
Find the equation of locus of the point whose distance from the coordinate axes are in the ratio 2:3 |
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| 40. |
A and B are events such that P(A) = 0. 42, P(B) = 0. 48and P(A a n d B) = 0. 16. Determine(i) P(not A), (ii) P(not B) and (iii) P(A or B) |
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| 43. |
If the point A(3, -2, 4), B(1, 1, 1) and C(-1, 4, -2) are collinear then (C:AB)= |
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Answer» `1:2` |
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| 44. |
Prove that (1+sec 2 theta) (1+sec 4 theta)........(1+sec 2^(n) theta)=tan 2^(n) theta cot theta |
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| 46. |
Find the acute angle between the diagonals of a parallelogram whose adjacent sides are bar(AB)= 3bari - 2barj +2bark and bar(BC)=-bari-2bark. |
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| 47. |
Write the negation of the following statements: Chenai is the capital of Tamil Nadu. |
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| 48. |
If (2, 5, 1) and (9, 10, 5) are the ends of a diagonal ofa rectangular parallelopiped whose faces are parallel to the coordinate planes, then the lengths of edges are |
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| 49. |
The value of expression (1+ sin 2 alpha)/(cos (2 alpha -2pi) tan (alpha -(3pi)/(4)))- 1/2 sin 2 alpha (cot ""(alpha)/(2) + cot ((3pi)/(2)+(alpha)/(2))) is |
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Answer» 0 |
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