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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 statementp rarr (q vee r ) is not equivalent to |
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Answer» <P>`(p rarr Q ) vee ( p rarr R ) ` |
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| 2. |
The values of x for which (x-1)/(3x+4) lt (x-3)/(3x-2) |
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Answer» `(-oo, (5)/(4))` |
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| 3. |
For non-zero vectors vec(a)andvec(b)if|vec(a)+vec(b)|lt|vec(a)-vec(b)|,"then "vec(a)andvec(b) are |
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Answer» collinear |
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| 4. |
Assertion (A) : If (1)/(x^(3)(x+2))=A/x + B/x^(2) +C/x^(3) + D/(x+2) then A = 1/8, B= -1/4, C = 1/2, D= -1/8 Reason (R) : (1)/(x^(3)(x+a))=(1)/(a^(3)x)-(1)/(a^(2)x^(2))+(1)/(ax^(3))-(1)/(a^(3)(x+a)) |
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Answer» Both A & R are true and R is correct explanation of A |
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| 5. |
Find the radius of thesmallest circle which touches the straight line 3x-y=6 at (1-,3) and also touches the line y=x. compute upto one place of decimal only. |
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| 6. |
Evaluate int sec^(-1) sqrt(x) dx |
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| 7. |
If f'(x) = (1)/(1+x^(2))for all x and f(0) = 0, then: |
| Answer» Answer :C | |
| 8. |
Let A and B be two fixed points. If a perpendicular p is drawn fros A to the polar of with respect to the circle x^(2)+y^(2)=a^(2) and perpendicular q is drawn from B to the polar of A then |
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Answer» <P>p=Q |
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| 9. |
If x + (1)/(x) = 2 sin alpha and y + (1)/(y) = 2 cos beta, then x^(3)y^(3) + (1)/(x^(3)y^(3)) = |
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Answer» `2 COS 3 (BETA - alpha)` |
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| 10. |
Find the locus of the mid point of the chord of contact ofx ^(2)+ y ^(2)= a^(2)from the points lying on the linelx + my + n=0 |
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| 11. |
Find the scalar triple product vecb.(veccxxveca) where veca, vecb and vecc are respectively 5hati-hatj+4hatk, 2hati+3hatj+5hatk, 5hati-2hatj+6hatk |
Answer» SOLUTION : 5(18+10)+1(12-25)+4(-4-15) 140-13-76 = 140-89 = 51. |
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| 12. |
underset(x to -2)"Lt" ((1+x)^(2)(1-x)^(2))/((1+x)^(3)-(1-x)^(3))= |
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Answer» `1` |
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| 13. |
Let the equation of the circle is x^(2) + y^(2) = 25 and the equation of the line x + y = 8. If the radius of the circleof maxium area and also touches x + y = 8 and x^(2)+ y^(2) = 25 is (4sqrt(2) + 5)/(lambda). Then the value of lambda is. |
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| 14. |
If f(x)={{:([x]","if-3lt x le-1),(|x|","if-1 lt x lt 1),(|[x]|","if 1 le x lt 3):} then the set {x : f(x) ge 0} is equal to |
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Answer» `(-1,3)` |
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| 15. |
Given that E and F are events such that P(E )=0.6, P(F)=0.3 and (E cap F)=0.2, find P(E|F) and P(F|E) |
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| 16. |
If f(x)=|(secx, cosx, sec^(2)x+cot x cosecx),(cos^(2)x,cos^(2)x,cosec^(2)x),(1,cos^(2)x,cos^(2)x)| then int_(0)^(pi//2)f(x)dx= |
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Answer» `8/15+(PI)/4` |
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| 17. |
Locus of the point of intersection of two perpendicular tangents to an ellipse is x^(2)+y^(2)=25. Then the equation of tangentss to such ellipse at itspoints of intersection with the line y=x can be (length of semi major and semi-minor axis of the ellipse are integers) |
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Answer» `16x+9y=60` |
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| 19. |
If f is defined by f(x)={{:(x,"for",0lex |
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Answer» CONTINUOUS and differentiable |
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| 20. |
vec(a),vec(b) and vec( c ) are unit vectors vec(a)xx(vec(b)xx vec( c ))=(vec(b))/(2). The vector vec(a) makes the angle ………, …… with vec(b) and vec( c ) respectively. |
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Answer» `40^(@),80^(@)` |
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| 22. |
What is the maximum number of electrons in an atom that can have the quantum number n = 3 and l = 2 ? |
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Answer» 2 |
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| 23. |
Four persons A, B, C, D cut a pack of 52 cards successively in that order given. If the person who cuts a spade first wins, find their probability of winning. |
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| 24. |
Evaluate the following integral int (1 + x^(2))/(sqrt(1 - x^(2)))dx |
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| 25. |
Let the tangents at point P and R on the parabola y=x^(2) intersects at T. Tangent at point Q (lies in between the points P and R) on the parabola intersect PT and RT at A and B respectively. The value of (TA)/(TP)+(TB)/(TR) is |
| Answer» Answer :B | |
| 26. |
The vector 2hati+2hatj-hatk makes ………………measure of angles with the axes. |
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Answer» `COS^(-1)""(2)/(3),cos^(-1)""(2)/(3),pi-cos^(-1)""(1)/(3)` |
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| 27. |
Find the equation of circle passing through each of the following three points. (2,1),(5,5),(-6,7) |
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| 29. |
The sum and sum of squares corresponding to length x ( in cm) and weight y ( in gm ) of 50 plant products are given below : sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261, sum_(i=1)^(50)y_(i)^(2)=1457.6 If C.V._(x) and C.V._(y) are the coefficient of variation of length and weight respectively, then variability in weight is |
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Answer» GREATER than VARIABILITY of length |
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| 30. |
Fill int the blanks choosing correct answer from the bracket. If a cot A = b cot B then triangle ABC is _____ |
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Answer» isosceles |
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| 31. |
int_0^picos^2xdx |
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Answer» SOLUTION :`int_0^picos^2xdx=int_0^pi(1+cos2x)/2dx` =`1/2[x+sin(2X)/2]_0^pi=1/2.pi=pi/2` |
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| 32. |
Evaluate the following integrals intcos^(-1)((1-x^(2))/(1+x^(2)))dx |
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| 33. |
If overline(a), overline(b), overline(c) are three non-zero, non-coplanar, mutually perpendicular vectors, then [[overline(a), overline(b), overline(c)]]= |
| Answer» ANSWER :C | |
| 35. |
Common tagent (s) to y=x^(3)and x=y^(3) is/are |
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Answer» `x-y=1/sqrt3` |
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| 36. |
Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= cosx, x in R |
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| 38. |
If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), then y^2(dy)/(dx)= |
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Answer» `SQRT((1-y^6)/(1-x^6))` |
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| 39. |
If the angle theline 2(x+1)=y=z+4 and the plane 2x-y+sqrt(lambda)z+4=0 is (pi)/(6), then the value of lambda is |
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Answer» ` (135)/(7)` |
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| 40. |
Life span of RBC is :- |
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Answer» 90 days |
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| 41. |
Statement-1:For any n in N, we have int_(0)^(npi) |(sinx)/(x)|dx ge (2)/(pi)(1+(1)/(2)+(1)/(3)+....+(1)/(n)) Statement-2:(sin x)/(x)ge(2)/(pi)"on"(0,(pi)/(2)) |
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Answer» Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1. `underset(0)overset(NPI)int |(sinx)/(x)|DX` `rArrI=underset(r=1)overset(n)sum underset((r-1)pi)overset(rpi)int|(sinx)/(x)|dx` `rArr I=underset(r=1)overset(n)sum underset(0)overset(pi)int|(sin{(r=1)pi+u)/((r-1)pi+u)|du`, where `x=(r-1)pi+u` `rArr I=underset(r=1)overset(n)sum underset0)overset(pi)int(SINU)/((r=1)pi+u)du` `rArr I ge underset(r=1)overset(n)sum underset(0)overset(pi)int(sin u)/((r=2)pi+pi)du[:'(sin u)/((r-1)pi+u)gt(sinu)/((r-1)pi+pi)]` `rArr I ge underset(r=2)overset(n)sum(2)/(r pi)rArr (2)/(pi)(1+(1)/(2)+...+(1)/(n))` So, statement-1 is true. Let f(x)`=(sinx)/(x)`. Then, `f'(x)=(xcosx-sinx)/(x^(2))=(g(x))/(x^(2))` where g(x)=x cosx-sinx Now, `g'(x)=-xsinx lt 0` for all`x in (0,pi//2)` `rArr g(x)` is decreasing on `xin (0,pi//2)` `rArr g(x) lt g(0)" for all "x in (0,pi//2)` `rArr f'(x) lt o" for all "x in(0,pi//2)` `:.f'(x) lt 0" for all "x in(0,pi//2)` `rArr f(x)` is decreasing on `(0,pi//2)` `rArr f(x) gt f(pi//2) " for all "x in(0,pi//2)` `rArr (sinx)/(x)gt(2)/(pi)" for all "x in(0,pi//2)` So, statement-2 is true. But, it is not a correct explanation for statement-1. |
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| 42. |
The Math Team and Debate Club at Jackson City High School buy their T-shirts from different stores. The tables below show the numbers of T-shirts ordered by the Math Team and Debate Club , and the costs of medium , large , and extra-large T-shirts. Which statement about the costs of T-shirts , as shown in the tables , is true ? I.The Math Team spent more on extra-large T-shirts than the Debate Club spent . II.On average , the Math Team paid more per T-shirt than the Debate Club paid . III. Of the three sizes , extra-large T-shirts had the highest median cost. |
| Answer» Answer :A | |
| 43. |
A line makes an angle of 60^(@) with each of x and y axis, the angle which it makes with z axis is |
| Answer» Answer :B | |
| 44. |
Ifveca,vecb, veccare three non-coplanar vectors such thatvecaxx(vecbxx vecc)=(vecb+vecc)/(sqrt(2))then the angle betweenvecaandvecbis ________. |
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Answer» ` (pi)/(6) ` |
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| 45. |
Let f be a continuous function on R satisfying f(x+y) =f(x)f(y) for all x, y in R and f(1)=4 then f(3) is equal to |
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| 46. |
Integrate the following functions : intsqrt(3+8x-3x^(2))dx |
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| 47. |
Find the magnitude of the vector vec(PQ), its scalar components and the component vectors along the co-ordinate axes, if P and Q have the co-ordinates P(1,4,-), Q(2,-2,-1) |
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Answer» Solution :`vec(PQ) = (2-1)hati+(-2-4)HATJ+(-1+3)hatk` = `hati-6hatj+2hatk` `|vec(PQ)| = sqrt(1+36+4) = sqrt(41)` Scalar COMPONENTS are 1, -6, 2. VECTORS components are `hati, -6hatj, 2hatk` |
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| 48. |
Using elementary transformations, find the inverseof the matrices [(2,5),(1,3)] |
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| 49. |
If 3/5 w = 4/3, what is the value of w? |
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Answer» `9/20` |
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| 50. |
Two squares are chosen at random on a chessboard. If p denotes the probability that they have exactly one vertex in common, then 36p is _____ |
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