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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 mod-amplitude form of (1 + 7i)/((2 - i)^(2)) is |
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Answer» `SQRT2 cis "" (3pi)/(4)` |
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| 2. |
Findproducts : [[1,3],[1,4]][[1,2],[3,4]] |
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Answer» SOLUTION :`[[1,3],[1,4]][[1,2],[3,4]]` `=[[1.1+3.3""1.2+3.4],[1.1+4.3" "1.2+4.4]]=[[10,14],[13,18]]` |
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| 3. |
Find the equation of all lines having slope 2 which are tangents to the curve y=(1)/(x-1) , x ne 1 . |
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| 4. |
Find the value of a for which the function f(x)=ax^(3)-3(a+2)x^(2)+9(a+2)x-1 is decreasing. |
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| 5. |
The point (3, 1) is a point on a circle C with centre (2, 3) and C is orthogonal to x^2+y^2=8. The conjugate point of (3,1) w.r.t x^2+y^2=8 which lies on C is |
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Answer» (5,1) |
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| 6. |
Iflim_(xto 0)( (cos 4x + acos 2x + b)/(x^(4) )is finite , then the values , of a ,b are respectively . |
| Answer» ANSWER :C | |
| 7. |
On R, the set of real numbers, define a relation R as follows: xRy if |x| ge y, Then |
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Answer» R is SYMMETRIC only |
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| 8. |
P represents the variable complex number z find the locus of z if : IM((2z+1)/(iz+1))=-2 |
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| 9. |
If [.] denotes greatest integer function and x in ((2)/(3), 1 ) and int ([ 5- 3x])/(x -2) dx =k log | x - 2 )| + c then K = |
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Answer» 1 |
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| 10. |
If a=hat(i)+hat(j)+hat(k), b=2hat(i)+lambda hat(j)+hat(k), c=hat(i)-hat(j)+4hat(k) and a.(b xx c)=10, then lambda is equal to |
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Answer» Solution :Given `a=hati+hatj+hatk, b=2hati+LAMDA hatj+hatk and c= hati-hatj+4 hatk` Aslo, given `a*(bxx c)=10` `implies|{:(1,1,1),(2 , lamda,1),(1,-1,4):}|=10` `implies1(4lamda+1)-1(8-1)+1(-2-lamda)=10` `implies 4 lamda +1-7-2-lamda=10` `implies3 lamda =18 implieslamda =6` |
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| 11. |
If two ogives intersect at (21, 52)then number of observations in the data is ______ |
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| 12. |
Let P denotes the plane consisting of all points thata are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R. The planar P is parallel to plane Q |
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Answer» for no value of c  Plane P will CONTAIN the point `M(-1,-1,2)` and dr's of its NORMAL will be proportional to `(3,-3,1)`. Thus, equation of the plane P is `3(x+1)-3(y+1)+1(z-)=0` `therefore P:3x-3y+z-2=0`………..(1) `therefore P:3x-3y+z-2=0` Also, `Q:x-y+cz-1=0` ......(2) If P is parallel to Q then `3/1=1/c rArr c=1/3`. |
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| 13. |
If A = int_(0)^(1) (e^(t))/(1+ t)dt then int_(0)^(1) e^(t) ln (1 + t) dt= |
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Answer» `E LN 2 - A` |
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| 15. |
A position-time graph for linear motion of an object in one dimension shows the object's displacement d from some origin at any given time t. If the graph is linear, its slope m is given by m="rise"/"run"="charge in d"/"charge in t"=(d_1-d_2)/(t_1-t_2)=barv, where barv is the average velocity of the object . (t_1,d_1) and (t_2,d_2) are any two points on the line. The graph above is a position time graph for a person who takes a walk from her house . Which of the following scenarios is consistent with the graph ? |
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Answer» After 20 minutes the DISPLACEMENT of the person from her house is approximately 230 + 230 +410 + 900 =1770 m |
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| 16. |
Is the function defined by f(x)= |x|, a continuous function |
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| 18. |
If vector bar(AB) = 2 hat(i) - hat(j) + hat(k) and bar(OB) = 3 hat(i) - 4hat(j) + 4 hat(k), find the position vector bar(OA) |
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| 19. |
Find gof and fog , if f(x) = 8x^(3) and g(x) =x^(1/3) |
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| 20. |
If the extremities of the base of an isosce- les triangle are the points (2a, 0) and (0,a) and the equation of one of the sides is x=2a, then the area of the triangle is |
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Answer» `5a^(2)` SQ. UNITS |
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| 21. |
Statement I A A_(1), B B_(1), C C_(1) are the medians of triangle ABC whose centroid is G. If the points A, C_(1), G and B are concylic, then c^(2), a^(2), b^(2) are in AP. Statement II BG. C C_(1)=BC_(1). BA |
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Answer» Both Statement I and Statement II are CORRECT and Statement II is the correct explanation of Statement I |
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| 22. |
Find points on the curve (x^(2))/(9) +(y^(2))/(16) =1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. |
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| 23. |
Find the distance of the plane 2x – 3y + 4z - 6 = 0 from the origin. |
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| 24. |
Evaluate the following integrals. int(5x-3)sqrt(x^(2)-6x+13)dx |
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| 25. |
A variable plane passes througha fixed point (1,2,3) Then , the foot of the perpendicularfrom the origin to the planelies on |
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Answer» a circle |
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| 26. |
Evaluate the following integrals. int(1)/((2x+1)sqrt(x^(2)-x-2))dx |
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| 27. |
Find the normals at the ends of the latus-rectum (in first quadrant) of the ellipse 9x^(2)+16y^(2)=144 |
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| 28. |
Findthe areaof theregionboundedby parabolaf(x)= 4 -x^2andg(x)=x^2 -4. |
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| 30. |
The order and degree of the differential equation (y''')^(3) + (y'')^(4) + (y')^(4) + y=7 are …..... Respectively. |
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Answer» 4 and 1 |
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| 31. |
The set of values of 'c' for which the equation x^(2)-4x-c-sqrt(8x^(2)-32x-8c)=0 has exactly two distinct real solutions, is (a,b) then find the value of (b-a). |
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| 32. |
It is possible for a computer to pick up an erroneous signal that does not show up as an error on the screen. The error is called a silent error. A particular terminal is defective and when while using the system ' word processor', it introduces a silent paging error with probability 0.1. The word processor is used 20 times during a given week. The probabillity that no silent error occur |
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Answer» `1-(0.9)^18` |
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| 33. |
Assertion (A) : Ifalpha, betaare the roots of ax^(2)+bx+c=0 then ((alpha)/(alphabeta+b))^(3)- ((beta)/(aalpha+b))^(3)=0 Reason (R) : If a,B are the roots of ax^(2)+bx+c=0 then (alpha)/(alphabeta+b)= (beta)/(aalpha+b) |
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Answer» Both A, R are true and R explain Assertion |
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| 34. |
A and B are two independent events. The probability that both A and B occur, is 1//6 and the probability that none of them occur, is 1//3. The minimum value of probability of occurance of A is |
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Answer» `1//2` |
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| 35. |
If f(x) = |x+1|(|x|+|x-1|), then at what points the function is/are not differentiable at the interval [-2, 2] ? |
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Answer» -1 |
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| 37. |
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings ? |
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| 38. |
Find the derivative of (3x^(2) - 7x + 3)^(5//2) with respect to x. |
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| 39. |
Maximum number of total nodes is present in :- |
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Answer» 5s |
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| 40. |
If 0 gt a gt b gt cand the roots alpha, beta are imaginary roots of ax^(2) + bx + c = 0 then |
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Answer» `|ALPHA|= |beta|` |
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| 41. |
Statement I : If centroid and circumcentre of a triangle are known its orthocentre can be found Statement II : Centroid, orthocentre and circumcentre of a triangle are collinear. |
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Answer» STATEMENT I is TRUE, Statement II is true, Statement II is a CORRECT EXPLANATION for Statement I. |
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| 42. |
A wholesale dealer wants to starts the business with Rs. 2,40,000. The cost price of a quintal wheat is Rs. 2000 and the cost price of a quintal rice is Rs. 3000. He has the space capacity for 200 quintals grain. The profit from the sale of one quintal wheat is Rs. 125 and that from one quintal rice is Rs. 200. If he has x quintalrice and y quintal wheat then the objective function for the maximum profit is ............ |
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Answer» 125X + 200y |
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| 43. |
Consider the lines L_(1) -=3x-4y+2=0 " and " L_(2)-=3y-4x-5=0. Now, choose the correct statement(s). |
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Answer» The line x+y=0 BISECTS the acute angle between `L_(1) "and " L_(2)` containing the origin. `L_(2)-=4x-3y+5 =0` Here, `a_(1)a_(2) + b_(1)b_(2) = (3)(4) + (-4)(-3) = 24 GT 0` So, acute angle bisector is 3x-4y+2=4x-3y+5 or x+y+3=0 This bisector goes through the regions where expressions 3x-4y+2 and 4x-3y+5 have the same sign. ALSO, this is the bisector of ANLGE which contains origin. |
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| 44. |
One die and a coiin (both unbiased) are tossed simultaneously . The probability of getting 5 on the top of the die and tail on the coin , is |
| Answer» ANSWER :B | |
| 45. |
Using the vertices of a polygon having 12 sides a triangle is constructed at random. The probability that the triangle so formed is such that no side of the polygon is side of the triangle is |
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Answer» `(18)/(55)` |
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| 46. |
If y=sqrt(x+sqrt(x+sqrt(x+............oo))), m then dy/dx= |
| Answer» Answer :D | |
| 47. |
If the sum of first n positive integers is 1/5 times the sum of their square then n equals |
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Answer» 5 |
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| 48. |
Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= "cosec " x = (1)/(sin x), x in R- {n pi}, n in I |
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| 49. |
If the equation (b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0 has equal roots, then |
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Answer» a, B, C are in G.P. |
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| 50. |
If cos alpha, cos beta, gamma are direciton cosines then cos 2 alpha + cos 2 beta + cos 2 gamma = ................ |
| Answer» ANSWER :A | |