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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. |
Find the value of k if kx+ 3y - 1 = 0, 2x + y + 5 = 0 are conjugate lines with respect to the circle x^(2) + y^(2) - 2x - 4y - 4 =0. |
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| 2. |
Number of bijections from Set-A containing n elements onto itself is 720 then n is |
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Answer» 5 |
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| 3. |
Find the vector equation of the line through the point whose position vector is 2hati-hatj+hatk and parallel to the line joining the points whose position vectors are hati+4hatj+hatk and hati+2hatj+2hatk. Also find the cartesian equation of the line. |
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Answer» `(x-2)/(2)=(y+1)/(-2)=(z-1)/(1)` |
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| 4. |
Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr.(hati+2hatj-5hatk)+9=0 |
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| 5. |
Examine the continuity of the function f(x)= x^(3) + 2x^(2)-1 " at " x=1 |
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| 6. |
Let ' A'. and 'B' be independent events with 'P(A)=0 .3' and 'P(B)=0.4'. Findi) 'P(A nn B)'ii) 'P(A uu B)'iii) 'P(A | B)'iv) 'P(B | A)' |
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Answer» <P> SOLUTION :P(B/A) = P(B) = 0.4 |
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| 7. |
Let ADbe theanglebisector ofangle AofDelta ABCsuchthatAD= alphaAB + betaAC ,then |
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Answer» `ALPHA =(|AB|)/(|AB|+|AC|),beta =(|AC|)/(|AB|+|AC|)` `thereforeAD =(|AB|AC||AC|AB)/(|AB|+|AC|)` `implies |AD|= alpha AB + beta AC , ` where ` alpha =(|AC|)/(|AB|+|AC|)and beta =(|AB|)/(|AB|+|AC|)` |
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| 8. |
Two person A and B have 16 and 15 fair coin respectively. If both of them tosses all the coin then probability that A gets more head than B is p then the value of 16p is |
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Answer» i.e. 15 coins `P_(A)` = probability that A OBTAINS more heads than B `P_(B)` = probability that B obtains more heads than A `P_(D)` = probability that A obtains as many heads as B Such that `P_(A) + P_(B) +P_(D) = 1` ...(i) DUE to symmetry `P_(A) = P_(B)` as both FLIP equal number of coins. Now 'A' flips extra coin (`16^(TH)` coin). If it gives tail then does not contribute but if it gives HEAD then A gets more head than B required probability = `P_(A) + 1/2.P_(D)` `=P_(A) + 1/(2)(1-P_(A)-P_(B)) = 1/2`. |
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| 9. |
Find the equation of the circle passing through (-2,3) and having centre (0,0) |
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| 10. |
Find the maximum and minimum values, if any, of the functions given by f(x) = 9x^(2) + 12x + 2 |
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| 11. |
Evaluate the definite integrals int_(0)^(1)(xe^(x)+sin(pix/4))dx |
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| 12. |
9 persons enter a lift from ground floor of a building which stops in 10 floors (excluding ground floor), if it is known that persons will leave the lift in groups of 2,3, & 4 in different floors. In how many ways this can happen? |
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| 14. |
If alpha, beta, gamma are the roots of the equation x^3 - x^2 + 4 = 0, then form an equation where roots are (betagamma + beta + gamma)/(beta + gamma - alpha), (agamma + alpha + gamma)/(alpha + gamma - beta) , (beta alpha + beta + alpha)/(beta + alpha - gamma) |
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| 15. |
The equation of the tangent to the parabola y^(2)=8x inclined at 30^(@) to the x axis is |
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Answer» `3x-sqrt(3)y+4=0` |
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| 16. |
int_(0)^(pi) (x Sin x)/(1+Cos^(2)x)dx= |
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Answer» `(PI^(2))/(4)` |
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| 17. |
A natural number x is chosen at random from the first 100 natural numbers. Find the probability that ((x-20)(x-40))/((x-30)) lt 0. |
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| 18. |
find the general solution of (e^(x) + e^(-x))dy - (e^(x) - e^(-x)) dx = 0 |
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| 19. |
Which of the following statements is contingency? |
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Answer» <P>`(pvvq)vv ~Q` `-= p vv (q vv q) -= p vv T` `-= T` which is a TAUTOLOGY. Option (2) `(p vv q) v ~` `-= (p vv ~ p) vv q -= T vv q` `-= T` which is tautology. Option (3) `(p vv q) ^^ ~q` `-= (p ^^ q) vv (q ^^ ~ q) -= ( p ^^ ~ q) vv F` `-= (p ^^ ~ q)` if `p to T, q to T`, Then, `p ^^ ~ q to F` if `p to T, q to F` Then `p ^^ ~ q to T` So, `(p ^^ ~q)` is a contingency. Therefore statement `(p vv q) ^^ ~ q` is contingency. |
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| 20. |
A person standingon thebankofa riverobservesthatthe angleof elevationof topofa treeon theoppositebank of theriveris 60^@ and whenthe retires 40metresaway fromthe treethe angleof elevationbecomes30^@the breadth of theriver is |
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Answer» 40 m |
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| 21. |
If bar(a)=(2,0,1) and bar(b)=(1,1,1) then sin(bar(a)""_(,)^(hat)bar(b))= ………….. |
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Answer» `SQRT((3)/(5))` |
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| 22. |
Differentiate the following w.r.t x. (i) cos^(-1) (sin x) (ii) tan^(-1) ((sin x)/(1 + cos x)) (iii) sin^(-1) ((2^(x+1))/(1+4^(x))) |
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| 23. |
findthe area of theregionboundedby thecurvey=x^3 ,y = x+6 andx=0 |
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| 24. |
If 4 less than the product of b and 6 is 44, what is the value of b? |
| Answer» Answer :C | |
| 25. |
Check the injective and surjective of the following functions : f : Z rarr Z given by f(x) = x^3 |
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Answer» SOLUTION :We have `F(x_1) = f(x_2)` `implies x_1^3 = x_2^3 implies x_1 = x_2` for all `x_1, x_2` in Z `therefore` f is not SURJECTIVE |
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| 26. |
Let S_(1),S_(2),S_(3) be three sets of complex numbers such thatS_(1)= {z:1m gt 1) S_(2) = {z : |z -2 -1|=3}S_(3) = {z : Re((1-i)z) = sqrt2, thenStatement -1The number of subsets of the setS_(1)cap S_(2) capS_(3) is 2.Statement -2Letz in S_(1) cap S_(2) cap S_(3) " then " |z +1-i|^(2) + |z -5-i|^(2) =36Statement -3 Let z be any point inS_(1) cap S_(2) Cap S_(3) and z_(1) " be any pointsatisfying " |z_(2)-2-i| lt 3, then(|z|-|z_(1)+3) lies between -3 and 9 ,. |
| Answer» ANSWER :A | |
| 27. |
If the normals at the four points (x_1,y_1),(x_2,y_2),(x_3,y_3) and (x_4,y_4) on the ellipsex^(2)/a^(2)+y^(2)/b^(2)=1 are concurrent, then the value of (sum_(i+1)^4x_1)(sum_(i=1)^(4)1/2) |
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| 28. |
If A is a squyare matrix then which one of the following is not a symmetric matrix |
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Answer» A +A' |
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| 29. |
If |z-(4)/(z)|=2 then the miximum value of |z| is |
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Answer» `3+sqrt(5)` |
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| 30. |
Show that the equation of the circle with centre at origin and passing through the vertices of an equilateral triangle whose median is of length 3a is x^(2)+y^(2)=4a^(2). |
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| 31. |
A purse contains 6 Silver coins and 3 Gold coins. Another purse contains 4 Silver coins and 5 Gold coins. A purse is selected at random and a coin is drawn from it. It's known that a coin is Gold then what is the probability that a Gold coin is selected from another (II^(nd)) purse? |
| Answer» Answer :C | |
| 32. |
Let f, g: R to R by f(x) = x|x| -1 AA x in R and g(x) = {{:(3/2x, if x gt 0),(2x, if x le 0):}. The number of subsets of S is |
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Answer» 2 |
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| 33. |
Find (dy)/(dx), if x= a (theta + sin theta), y= a (1- cos theta) |
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| 34. |
The smaller side of the rectangle with the largest area, that can be inscribedinside a semi- circle of radius 2 units is of length |
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Answer» `1/SQRT2` |
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| 35. |
Solvetheequation x^5-x^4+ 8x^2 - 9x+ 15=0twoof its rootsbeing- sqrt(3) ,1-2 sqrt(-1) |
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| 36. |
Let R+ be the set of all non negative real numbers. Show that the function f: R_(+) to [4, infty]given by f(x) = x^2 + 4 is invertible and write inverse of 'f'. |
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| 37. |
IfPQis a focal chord of the parbolay^(2)=4ax withfocus at s then(2SP,SQ)/(SP+SQ)is equal to |
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Answer» a |
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| 38. |
If n is an integer then the value of int_(0)^(pi) e^(cos^2x)cos^(3) ((2n+1)x)dx= |
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Answer» 1 |
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| 39. |
The straight line x-2y+1=0 intersects the circle x^(2)+y^(2)=25 in points P and Q the coordinates of the point of intersection of tangents drawn at P and Q to the circle is |
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Answer» (25,50) |
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| 40. |
Simplify the following (sqrt(x+1) + sqrt(x-1))^(6) +(sqrt(x+1) - sqrt(x-1))^(6) |
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| 41. |
Three fair dice are rolled. Find the probability that the greatest number on the dice must exceed 3. |
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| 43. |
Integrate the following intsec(x+2)tan(x+2)dx |
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Answer» SOLUTION :`intsec(x+2)cdottan(x+2)DX` put `x+2=d THETA` then `dx=d theta` `intsecthetacdot TANTHETA d theta` `sectheta+C=sec(x+2)+C` |
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| 44. |
The value of sec^(-1)((1)/(4)sum_(k=0)^(10)sec((7pi)/(12)+(kpi)/(2))sec((7pi)/(12)+((k+1)pi)/(2))) in the inerval [-(pi)/(4),(3pi)/(4)] equals.......... |
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Answer» `=Sigma_(k=0)^(10) (1)/(cos ((7pi)/(12)+(kpi)/(2))cos((7pi)/(12)+((k+1)pi)/(2)))` ` =Sigma_(k=1)^(10) (sin [((7pi)/(12)+((k+1)pi)/(2))-((7pi)/(12)+(kpi)/(2))])/(cos ((7pi)/(12)+(kpi)/(2))cos ((7pi)/(12)+((k+1)pi)/(2)))` `[because (7pi)/(12)+((k+1)pi)/(2)-((7pi)/(12)+(kpi)/(2))=(pi)/(2) and sin (pi)/(2)=1]` `sin ((7pi)/(12)+((k+1)pi)/(2))cos ((7pi)/(12)+(kpi)/(2))` `=Sigma_(k=0)^(10) (-sin ((7pi)/(12)+(kpi)/(2))cos ((7pi)/(12)+((k+1)pi)/2))/(cos ((7pi)/(12)+(kpi)/(2))cos ((7pi)/(12)+((k+1)pi)/(2)))` `= Sigma _(k=0)^(10) [TAN ((7pi)/(12)+((k+1)pi)/(2))-tan ((7pi)/(12)+(kpi)/(2))]` `=tan ((7pi)/(12)+(pi)/(2))-tan ((7pi)/(12))+tan ((7pi)/(12)+(2pi)/(2))-tan ((7pi)/(12)+(pi)/(2))+tan ((7pi)/(12)+(11pi)/(2))-tan((7pi)/(12)+(pi)/(2))` `=tan ((7pi)/(12)+(11pi)/(2))-tan (7pi)/(12)=tan(pi)/(12)+COT (pi)/(12)` `=(1)/(sin(pi)/(12)cos. (pi)/(12))=(2)/(sin.(pi)/(6))=4` So, `sec^-1 ((1)/(4)Sigma_(k=0)^(10)sec((7pi)/(12)+(kpi)/(2))sec((7pi)/(12)+((k+1)pi)/(2)))=sec^-1(1)=0` |
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| 45. |
Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle then SA + SB + SC is equal to |
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Answer» SG `IMPLIES SA+SB+SC=SA+2SD` = (1+2) SG = 3SG 
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| 46. |
Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider P (x) =x ^(6)-x ^(5) -x ^(3) -x ^(2) -x, then the value of p (a) +p(b) +p(c ) +p(d) is equal to : |
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| 47. |
The solution of (dy)/(dx) + (3)/(x) y = (1)/(x^(2)),at y=2, x=1 |
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Answer» `2X^(3)y = X^(2) - 3` |
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| 48. |
int sec^((2)/(3))x*"cosec"^((4)/(3))x dx=.... |
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Answer» `-3(tanx)^((1)/(3))+C` |
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| 49. |
Let u = int_(pi//6)^(pi//2) min. (sqrt(3)sinx, cosx) dx and V = int_(-3)^(5)x^(2)sgn (x-1) dx. If V =lambdaU, then find the value oflambda. |
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