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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. |
Y overset(200^(@)C)(larr)CaSO_(4). 2H_(2)O overset(120^(@)C)(rarr)X. X and Y are respectively:- |
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Answer» Plaster of paris, DEAD burnt plaster |
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| 2. |
The smallest value of x^(2) - 3x + 3 in the interval [-3, (3)/(2)] is |
| Answer» Answer :A | |
| 3. |
If (x+1)^(2)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)+1) " then "Sin^(-1)(A/C)= |
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Answer» `pi/6` |
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| 4. |
A town has total population of 25,000 out of which 13,000 read ''The Times of India'' and 10,500 read ''The Hindustan Times''. 2,500 read both papers. The percentage of population who read neither of these newspapers is |
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Answer» 16 |
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| 5. |
A bag contains 2 white and 3 black balls and another bag contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Find the probability that the colour of the ball is white. |
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| 7. |
For a gt 1, b gt 1, the value of int_(0)^(oo) (a^(-x)-b^(-x))dx= |
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Answer» `LN(AB)` |
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| 8. |
If int((1)/(sin^(2)x))log(cosx+cos2x)dx=cotxlog(cosx+sqrt(cos2x)+P(cosec^(2)x-2)^(t)-Q(x+cotx)+c, then |
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Answer» `t=P+(Q)/(2)` |
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| 9. |
Integration using rigonometric identities : int tanx*sec^(2)x sqrt(1-tan^(2)x)dx=.... |
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Answer» `-(1)/(3)(1-tan^(2)x)^((3)/(2))+C` |
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| 10. |
If [[2" "1" "3][{:(-1,0,-1),(-1,1,0),(0,0,1):}]*[{:(1),(0),(-1):}]=A find A. |
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| 11. |
Find the derivative of tan^(-1) "" (sqrt(1 + x^(2)) - 1)/( x) with respectto tan^(-1) ( 2 x sqrt( 1 - x^(2)))/(1 - 2 x ^(2))at x = 0 |
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| 12. |
If A = [( 1, cos theta , 1),( - cos theta ,1,cos theta ),( -1 , - cos theta ,1)]where0 lethetale2 pithen ….. |
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Answer» DET (A)=0 |
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| 13. |
Find a vector of magnitude 6, which is perpendicualr to both the vectors 2bar(i)-bar(j)+2bar(k) and 4bar(i)-bar(j)+3bar(k). |
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| 14. |
Jack is putting together gift boxes at a rate of 3 per hour in the first hour. Then jill comes over and yells, ''Work faster!'' jack, now nervous, works at the rate of only 2 gift boxes per hour for the next 2 hours. Then Alexandra comes to Jack and whispers. ''The steadiest hand is capable of the divine. Jack, calmer, then puts together 5 gift boxes in the fourth hour. What is the average rate at which Jack puts together gift boxes over the entire period? |
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| 15. |
A cannon ball is fired at an angle theta, 0 lt theta lt pi//2, with the horizontal. If v is the initial velocity of the cannon ball, the height h of the ball at time t, ignoring the air resistance, is given by : h=(v sin theta) t-4.9t^(2). The value of theta so that the horizontal range of the ball is maximum is : |
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Answer» `pi//6` |
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| 16. |
Let the product of all the divisors of 1440 be P . If P is divisible by 24^(x) , then the maximum value of x is : |
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Answer» 28 |
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| 17. |
Consider : Statement-1 : (p^^~q)^^(~p^^q) is a fallacy. Statement-2 : (pimpliesq)iff(~qimplies~p) is a tautology. |
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| 18. |
int (dx)/(x^(2) sqrt(4 - x^(2)))= |
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Answer» `(1)/(4) (sqrt(4 - x^(2))/(x))` + c |
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| 19. |
Differentiate the following w.r.t.x log(logx),xgt1 |
| Answer» SOLUTION :`d/dx[LOG(LOGX)]=1/(logx)d/dx(logx)=1/(logx)xx1/x=1/(XLOGX)` | |
| 20. |
Two dice are thrown. Find the conditional probability that two fives occur, if it is known that the total is divisible by 5. |
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Answer» |
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| 21. |
int_(0)^(1//2)(dx)/((1+x^(2))sqrt(1-x^(2))) is equal to |
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Answer» `1/sqrt2 TAN^(-1)SQRT(2/3)` |
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| 22. |
If a, b, c are in G.P. and x, y are the arithmetic mean of a, b and b, c respectively, then 1/x + 1/y is equal to |
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Answer» `2/b` |
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| 23. |
Find the sum of the n terms of the series whose nth term is (i) n(n+2) (ii) 3^n -2^n. |
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Answer» SOLUTION :(i) `(1)/(6)n(n+1)(2n+7)`, (II) `1//2(3^(n+1)+1)-2^(n+1)` |
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| 24. |
lim_(x rarr oo) ( sqrt(x + sqrt(x + sqrt(x))) - sqrt(x)) is equal to : |
| Answer» ANSWER :D | |
| 25. |
Prove that{:|( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)|:}=a^(3) |
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| 26. |
Let a and b be positivenumber not equal to 1 and (3pi)/(2) lt theta lt 2pi if a^(tan theta)gt b^(tan theta)gt1 then which one of the followingis always TRUE? |
| Answer» Answer :B | |
| 27. |
vec(AB) = 3hati - hatj + 4hatk and vec(CD) =- 3 hati + 2 hatj + 4 hatk two vectors. The position vectors of the points A and C areA (6 hati + 7 hatj + 4 hatk) and c (2 hati -2 hatj + 11 hatk) respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such thatvec(PQ) si perpendicular to vec(AB) and vec (CD) both. |
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| 28. |
Show that the points bari-barj+3bark and 3(bari +barj+bark) are equidistant from the plane barr.(5bari+2barj-7bark)+9=0 and lies on opposite side of it. |
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| 29. |
Two element X (at. Mass = 75) and Y (at. Mass = 16) combine to give a compound having 75.8% of X. the formula of the compound is :- |
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Answer» XY |
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| 30. |
The solution of (dy)/(dx) + y cot x = 4x cosec x, given that y = 0, x = (pi)/(2) is |
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Answer» `y SIN X = 2X^(2) - (pi)/(3)` |
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| 31. |
If ((x- 1)^(2))/((x^(2) +1)^(2)) dx = tan^(-1) x + g (x) + c then g (x) = |
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Answer» `tan^(-1)"" (x)/(2) ` |
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| 32. |
int_(0)^(1) (x^(6))/(sqrt(1-x^(2)))dx= |
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Answer» `(5pi)/(32)` |
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| 33. |
Find the number of ways of permuting the letters of the word PICTURE so that all vowels come together |
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| 34. |
If ""^(n)C_(4),""^(n)C_(5),""^(n)C_(6) are in A.P., then the value of n is |
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Answer» 11 |
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| 35. |
Evaluate the following:""^(20)C_(1)= |
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| 37. |
Let vec(OA) = hat(i)+2hat(j)+2hat(k). In the plane of vec(OA) and hat(i), rotate vec(OA) through 90^(@) about the origin O such that the new position of vec(OA) makes an acute angle with the positive x-axis. The new position of vec(OA)is |
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Answer» `(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))` Let new position of `vec(OA) " is " vec(R)=ahat(i)+bhat(j)+chat(k)` `because vec(OA),vec(r) " and " hat(i) " are coplaner" =|(1,2,2),(a,b,c),(1,0,0)| = 0 IMPLIES b = c` `because vec(r)_|_vec(OA) implies a+2b+2c=0impliesa=-4b{because b=c}` `therefore vec(r)=-4bhat(j)+bhat(j)+bhat(k)=-b(4hat(i)-hat(j)-hat(k))` Also `|vec(r)|=|vec(OA)|impliesb=pm(1)/(sqrt(2))impliesvec(r)=pm(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))` `because vec(r)` makes acute angle withpositive x-axis `implies vec(r)=(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))` |
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| 38. |
A variable line passes through the fixed point (alpha, beta). The locus of the foot of the perpendicular from the origin on the line is |
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Answer» `x^(2) + y^(2) - alpha x -BETA y=0` |
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| 39. |
Statement-1: A function is given by g(x)=ln""(x^(2)+1)/(x^(2)-1) because Statement-2 : int(dx)/(x^(7)-x^(11))=(-1)/(6x^(6))-(1)/(2x^(2))-(1)/(4)g(x) |
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Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 |
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| 40. |
Let S_(1) " and " S_(2) be the foci of a rectangular hyperbola, which has the centre at Q , then for and point P on the hyperbola S_(1) Pequals to |
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Answer» `S_(1)S_(2)^(2)` |
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| 41. |
D, E, F are three points on the sides BC, CA, AB, respectively, such that angleADB = angle BEC = angle CFA= theta. A', B', C' are the points of intersections of the lines AD, BE, CF inside the triangle. Show that area of Delta A'B'C' = 4 Delta cos^(2) theta, where Delta is the area of Delta ABC |
Answer» SOLUTION :From `Delta AB'C (AB')/(sin(pi-(A + theta))) = (AC)/(sin(pi - B))`  `rArr AB' = 2R sin (A + theta)` From `Delta AC'B, (AC')/(sin (theta - A)) = (AB)/(sin (pi - C))` `rArr AC' = 2R sin (theta - A)` `:. B'C' = 2R (sin (A + theta) - sin (theta - A))` `= 4R cos theta sin A = 2a cos theta` Similarly, `C'A' = 2b cos theta` `:. " Area of " Delta A'B'C' = (1)/(2) (B'C') (A'C') sin angleB'C'A'` `= (1)/(2) (2 a cos theta) (2b cos theta) sin C` `= 4 cos^(2) theta XX Delta` |
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| 43. |
Which of the following wil rotate the plane of polarised light in the polarimeter tube experiment ? |
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| 44. |
If mean and standard deviation of 5 observations x_1,x_2,x_3,x_4 are 10 and 3 respectively , then the variance of 6 observation x_1,x_2,…..x_5 and -50is equal to: |
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Answer» `582.5` |
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| 45. |
Let f and g functions such that f+g is a continuous function then |
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Answer» f and G are CONTINUOUS function |
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| 47. |
6 boys and 5 girls are arranged in a random order. The probability of arranging the girls as neighbours in specified order is |
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Answer» `(/_6)/(/_11) |
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| 48. |
Consider the curvey = tan^(-1) x " anda point "A ( 1 , pi/4) on it. If the variable pointP_(i)(x_(i) , y_(i)) moves on the curve fori = 1,2,3 , …. N ( n in N) " such that" y_(r) =Sigma_(m=1)^(r) tan ^(-1) ( 1/( 2 m^(2)))and B ( x,y) be the limiting position of variable point P_(n) " as " n to infty,then the value of reciprocal of the slope of AB will be |
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| 49. |
Which of the following sentences are propositions and which are not ? Write with reason : x is greater than 100. |
| Answer» SOLUTION :"x is GREATER than 100" is not a statement as x is not DEFINED | |
| 50. |
Without any trouble you are safely travelling towards your desination. It is just then that you come across a cave, in Nepal.The owl says that the cave is a short-cut, but the journey would be difficult, with many obstacles along the way. Brilliant as you all are, you decide to take the challenge. The cave is dark. One of you switches a flashlight on, and leads the way. Soon, you encounter a room with many book shelves. A door is on the other end of the room. As you observe the books, you notice that one book is very old, but the others are new. You realize that the old book may have the key for the door! You open the book and look through the pages. In the middle of the book, you see an odd figure, like the one below. You think of a theory, and start solving the puzzle. The lines originating from the centre, divide each pentagon into 10 equal parts or wedges. The part between two immediate pentagons is a ring. Remaining letters must be filled in such that: 1.Each ring must contain all the letters of the word “TOUCHLINES” 2.Every two adjacent wedges together must contain all letters of the word “TOUCHLINES”. The above puzzle has four boxes. Starting from the outermost ring and going inwards, note the letters and compare with the options given below. Which of the following is the correct answer? |
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Answer» NEST You can take the following QUESTION as a PENTAGON Sudoku. Therefore, after COMPLETING the task the pentagon look something like this:  The letters in the boxes starting from OUTER ring are E,T,C,H. hence the answer is ETCH. |
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