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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. |
theta is said to be well behaved if it lies in interval [0,(pi)/(2)]. They are intelligent if they make domain of f +g and g equal. The vlaue of theta for which h (theta) is defined are handosome. Let f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49), h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)], where theta isin radians. Complete set of vlaues of theta which are well behaved as well as intellignent is: |
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Answer» `[(3)/(4),(pi)/(2)]` |
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| 2. |
theta is said to be well behaved if it lies in interval [0,(pi)/(2)]. They are intelligent if they make domain of f +g and g equal. The vlaue of theta for which h (theta) is defined are handosome. Let f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49), h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)], where theta isin radians. Complete set of values of theta which are well behaved, intelligent adn handsome is : |
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Answer» `(0, (PI)/(2)]` |
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| 3. |
Differentiate the functions givenw.r.t. x. (logx)^(x)+ x^(log x). |
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| 4. |
Find all the points of discontinuity of the greatest integer function defined by f(x)= [x], where [x] denotes the greatest integer less than or equal to x. |
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| 5. |
Three machines A, B and C produce respectively 30%, 50% and 20% of the total number of items of a factory. The percentage of defective output of these machines are 1%, 4% and 3% respectively. If an item is selected at random, find the probability that the item is non-defective. |
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Answer» 0.963 |
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| 6. |
Show that the common tangent of the ellipse 3x^(2) +13y^(2) =78 and the circle x^(2) + y^(2) =16 is inclined at 45^(@) with the major axis. |
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| 7. |
Prove that |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=(a-b)(b-c)(c-a)(a+b+c) |
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| 9. |
Find the angle between the line (x+1)/(2)= (y)/(3)= (z-3)/(6) and the plane 10x+2y-11z=3 |
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| 10. |
A factory can shell 'x' items per week at price of Rs (20-(x)/(1000)) each. If the cost price of one item is Rs (5+(2000)/(x)), find the number of items, the factory should produce every week for maximum profit. If price is reduced, how it will effect the sale? Give reasons. (ii) Profit function of a company is given as : P(x)=(24x)/(5)-(x^(2))/(100)-500. where 'x' is the number of units produced. What is the maximum profit of the company? |
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Answer» (ii) Max. profit = RS 76 when x = 240. |
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| 11. |
If f(x) = (|log x|)/(x^(2)), " then " int_(1//e)^(e ) f(x) = dx= |
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Answer» E |
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| 13. |
The ratio of the wavelength of a proton & alpha-particle will be 1:2 if their |
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Answer» Velocity of proton to velocity of `ALPHA` is in RATIO 1:8 |
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| 14. |
If A=[(a,b,c),(b,c,a),(c,ab)], abc=1, A^(T)A=l, then the maximum value of a^(3)+b^(3)+c^(3) can be : |
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Answer» 2 As `A^(T)=A` `rArr A^(2)=I` `rArr a^(2)+b^(2)+C^(2)=1 and ab+bc+ca=0` As `(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2(ab+bc+ca)` `rArr (a+b+c)=pm1` Now `a^(3)+b^(3)+c^(3)-3ABC=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)` `rArr a^(3)+b^(3)+c^(3)-3=(a+b+c)` `rArr a^(3)+b^(3)+c^(3)=3pm1` `rArr a^(3)+b^(3)+c^(3)=4, 2` |
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| 15. |
Find the ratio in which the straight line 2x+3y-5=0 divides the line joining the points (0,0) and (-2,1). |
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| 17. |
Evalute the following integrals int (2x^(2) + x + 1)/((x+3)(x-2)^(2)) dx |
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| 18. |
The rank of the matrix [[2,-1,2,4],[3,1,4,-1],[5,0,6,3]] is : |
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Answer» 1 |
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| 19. |
if an equilateral triangle ABC with vertices at z_1, z_2 and z_3 be inscribed in the circle |z|=2 and againa circle isinscribed in the triangle ABC touching the sides AB, BC and CA at D(z_4) , E(z_5) and F(z_6) respectively |
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Answer» <P>`{:(P, Q, R, S),(4, 1, 2, 3):}` |
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| 20. |
Observe the following statements :Statement -I : In the expansion of (1+x)^50, the sum of the coefficients of odd powers of x is 2^50.Statement -II : The coefficient of x^4 in the expansion of (x/2 - (3)/(x^2))^10 is equal to 504/259 . Then the true statements are: |
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Answer» only I |
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| 21. |
Solve the following linear programming problem graphically: Maximize :z=x+2y Subject to: x-yle2 x+yle4 xge0 yge0 |
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| 23. |
The normal at the point (1,1) on the curve 2y + x^(2) = 3 is |
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Answer» x+y=0 |
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| 24. |
If the chord joining t_(1) and t_(2) on the parabola y^(2) = 4ax is a focal chord then |
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Answer» `t_(1)t_(2)=-1` |
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| 25. |
If the set A and B are as follows : A={1,2,3,4},B={3,4,5,6}, then |
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Answer» `A-B={1,2}` |
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| 26. |
n different things are arranged along a circle. In how many ways can '3' objects be selected such that no two of the selected objects are consecutive. |
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| 27. |
For linear programming x+2y ge 10, 3x+4y le 24" and "x ge 0, y ge 0 ……… is not the corner point of feasible region. |
| Answer» ANSWER :C | |
| 28. |
A set B contain 2007 elements. Let C be the set consisting of subsets of B which contain at most 1003 elements. The number of elements is C is |
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Answer» `2^(2005)` |
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| 29. |
The two circles (x-a)^(2)+y^2=c and (y-b)^(2)+x^(2)=4c have only one real common tangent then |
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Answer» `a^(2)+B^(2)=C` |
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| 30. |
Iff(x) ={{:(x+2,xlt0),(-x^(2)-2,0le xlt1),( x, xge1):} thenthe numberof pointsof discontinuity of|f(x)|is |
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Answer» 1 |
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| 31. |
The table above shows the relative investment in alternative energy sources in the United States by type. One column shows the relative investment in 2007 of $75 million total invested in alternative energy. The other column shows the projected relative investment in alternative energy in 2017 is $254 million. Suppose that a new source of alternative energy, Cold Fusion,is perfected. It is projected that by 2017 that $57 million will be invested in Cold fusion in the United states, without any corresponding reduction in investment for any other form of alternative energy. What portion of the total investment of alternative energy in the United states will be spent on biofuels? |
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Answer» 0.18 |
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| 32. |
If ABCDEFis a regular hexagon with centre O , then P.T bar(AB)+bar(AC)+bar(AD)+bar(AE)+bar(AF)=3bar(AD)=6bar(AO) |
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| 33. |
Probability of solving specific problem independently by A and B are (1)/(2) and (1)/(3) respectively. If both try to solve the problem independently, find the probability that : (i) the problem is solved (ii) exactly one of them solves the problem. |
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| 34. |
If iz^(3)+z^(2)-z+i=0, then absz equals |
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Answer» 2 |
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| 35. |
Let f(x+1)=2x -3,then find f^-1(x) |
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| 36. |
If Delta ABC is such that angle A=90^0, angle B ne angle C, then (b^2+c^2)/(b^2-c^2) sin (B-C)= . |
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Answer» `(1)/(3)` |
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| 37. |
Solve 5x-3 lt 7, when (i) x is an integer. (ii) x is a real number. |
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| 38. |
If the circles x^2 + y^2 + 2ax + cy + a =0 and x^2 + y^2 - 3ax + dy - 1 = 0 intersect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for |
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Answer» EXACTLY ONE value of 'a' |
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| 39. |
Solve graphically 7x - 4y lt 14 |
Answer» SOLUTION :
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| 40. |
Find the area enclosed with in the curve y=sin 2x , y=sqrt(3) sin x , x=0 ,x=(pi)/(6) |
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| 41. |
Show that the most general orthogonal matrix or order two is of the form [{:( cos theta , sin theta ),( +-sin theta , +-cos theta ):}] |
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| 42. |
x sin x |
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Answer» Solution :` =x INTSIN x DX- int {(d)/(dx)x int sin x dx }dx` (TAKING x as first fucntions) =x(-cos x) - `int 1. ` (-cos x) dx =- cos x+c `int cos ` x dx =- x cosx+ sin x+C |
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| 43. |
Evaluate int(e^(x)(1+x))/(cos^(2)(xe^(x)))dx |
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Answer» `-cot(EX^(X))+C` |
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| 45. |
fair coin is tossed 5 times. Find the probability that number of heads on the coins is more than the number of tails. |
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| 46. |
If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that h^2=ab. |
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| 47. |
If a number is a selected at random from first 100 natural numbers then the probabilitiy that the number is a two digited number with atleast one even digit either at the beginning or ending is |
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Answer» `(13)/(20)` |
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| 48. |
Find intxsec^(2)xdx. |
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| 49. |
Integration of some particular functions : int (dx)/(5-4 cosx)=....+c |
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Answer» `(1)/(3)TAN^(-1)(3"tan"(x)/(2))` |
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