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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. |
If the abscissae of points A, B are the roots of the equation x^(2) + 2ax -b^(2) =0and ordinates of A, B are roots ofy^(2)+ 2py -q^(2)=0 ,then find the equation of the circle for which AB is a diameter. |
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| 2. |
Jackson High School's basketball team scored an average of 90 points in each of the first 10 games of the season. If it scored 102 points in each of the next 2 games , which of the following is closest to its average for all 12 games ? |
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Answer» 102 |
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| 3. |
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B? |
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| 4. |
Evaluate the following:lim_(xtoinfty)(x^3+2x^2+3)/(x^4-3x^2+1) |
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Answer» SOLUTION :`lim_(xtoinfty)(x^3+2x^2+3)/(x^4-3x^2+1)` `lim_(xtoinfty)(1/x+2/x^2+3/x^4)/(1-3/x^2+1/x^4)=0/1=0` ``[thereforeAs` `xtoinfty, 1/xto0]` |
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| 5. |
Find the ratio in which the curve,y=[-0.01 x^(4)-0.02 x^(2)] [where, [.] denotes the greatest integer function) divides the ellipse (3x^(2)+4y^2)=12. |
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| 6. |
Let and g be differentiable on R and suppose f(0) =g(0) and f(x) le g'(x)for all x ge 0. Theshow that f(x) le g(x) for all x ge0. |
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| 7. |
Find the angle at which the two curves x^(3)-3xy^(2)+2=0and3x^(2)y-y^(3)+3=0 intersect each other. |
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| 8. |
The number of ways in which 7 persons can address a meeting so that out of the three persons A, B and C, A will speak before B and B before C is |
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Answer» 1680 |
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| 9. |
If f is every where continuous function then 1/c int_(ac)^(bc) f(x/c) dx= |
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Answer» `1/c int_(a)^(B) f(x)dx` |
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| 10. |
The solution of the differential equation 3xy' - 3y + (x^(2) - y^(2))^(1//2) = 0, satisfying the condition y (1) = 1 is |
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Answer» `3 cos^(-1) ((y)/(x)) = In |x|` |
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| 11. |
A gardener has a supply of fertilizers of the type I which consists of 10% nitrogen and 6% phosphoric acid, and of the type II which consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, he finds that he needs at leat 14 kg of nitrogen and 14 kg of phophoric acid for his crop. If the type-I fetilizer costs 60 paise per kg and the type-II fertilizer costs 40 paise per kg, determine how many kilograms of each type of fertilizer should be used so that the nutrient requirements are met at a minimum cost. What is the minimum cost? |
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Answer» `XGE0,yge0,(10)/(100)x+5/100yge14,(6)/(100)x+10/100y ge14.` COST function is `Z=60/100x+40/100y,i,E,. Z=3/5x+2/5y.` |
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| 13. |
Area under the curve x+y=1 in the first quadrant is_______ |
Answer» Solution :AREA of the CURVE`x+y=1` in first quadrant `=underset0overset1intydx=underset0overset1int(1-x)DX`
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| 15. |
For Delta = abs{:(2019, 2020, 2021),(2022,2023,2024),(2025, 2026, 2027):} sum of minor and cofactor of 2020 is......... |
| Answer» ANSWER :B | |
| 16. |
If P (A) = 0.4,P (B | A)= 0.3 and P (B^c | A^c)=0.2. find P(B) |
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Answer» <P> SOLUTION :`P(B)=0.6=6/10=3/5` |
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| 17. |
If tan^(-1)sqrt((1-sqrt(x))/(1+sqrt(x))) = (pi)/(4)-(alpha)/(2), then express tan^(2)alpha in terms of x. |
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| 18. |
Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A^c cup B^c) |
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Answer» <P> `P(A^CcupB^C)=P(AcapB)^C=1-(AcapB)` `1-1/4=3/4` |
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| 19. |
Identify thecorrect pair from the following statements: (i)For an odd degree reciprocal equation of Type II x=1 is a solution . (ii)For an even degree reciprocal equation ofType II,the middle term must be zero. (iii) The no. of positive roots of a polynomial p(x) cannot be less than the no. of the sign changes in coefficients of P(x). (iv)Polynomial of degree 4 is called cubic equation. |
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Answer» (i)&(II) |
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| 20. |
Lt_(n rarr oo)[(1)/(n)+(1)/(sqrt(n^(2) -1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+... "to n terms"] |
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| 21. |
If |veca|=16, |vecb|=4," then",sqrt(|vecaxxvecb|^(2)+|veca.vecb|^(2))= |
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Answer» 16 |
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| 22. |
int_(-1)^(1) (coshx)/(1+e^(2x)) dx is equal to |
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Answer» 0 |
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| 23. |
Form the differential equation by eliminating the arbitrary constant from the equation y = e^(x) (a cos 2x + b sin 2x) |
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Answer» `(d^(2)y)/(dx^(2)) -2 (DY)/(dx) + 5Y = 0` |
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| 24. |
Solve the following system of linear equations by matrix method 4x+3y+2z=60, 2x+4y+6z= 90, 6x+2y+3z=70 |
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| 25. |
The value of int(dx)/(4sqrt((x-1)^(3)(x+2^(2)))) is |
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Answer» `3(x-1)^(1//4)-(5//3)(x+2)^(5)+C` |
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| 26. |
If a body (coated black) at 600 K surrounded by atmosphere at 300 K has cooling rate r_(0), the same body at 900 K, surrounded by the same atmosphere will have to colloing rate close to : |
| Answer» Answer :A | |
| 27. |
A particlemovingon a curve has the position at time t given by x=f'(t) sin t + f''(t) cos t, y= f'(t) cos t - f''(t) sin t. where f isa thrice differentiable function. Then prove thatthe velocity of theparticle at time t is f'(t) +f'''(t). |
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| 28. |
Statement-I A point on the straight line 2x+3y-4z=5 and 3x-2y+4z=7can bedetermined by taking x=k and then solving the two for equation for y and z, where k is any real number. Statement-II If c'nekc, then the straightline ax+by+cz+d=0, Kax+Kby+c'z+d'=o does not intersect the plane z=alpha, where alpha is any real number. |
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Answer» STATEMENT I is true, Statement II is ALSO true, Statement-II is the CORRECT explanation of Statement-I. |
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| 29. |
Integrate the following functions sinx/(1+cosx)^2 |
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Answer» Solution :LET t = 1+cosx. Then DT = -SINX dx `gt sinx dx = -dt` THEREFORE `int sinx/(1+cosx)^2 dx = int 1/t^2 xx -dt = 1/t+c = 1/(1+cosx) +c` |
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| 30. |
A triangle is formed by the lines whose equations are AB: x+y-5=0, BC: x+7y-7=0 and CA: 7x+y+14=0. Then |
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Answer» angle at A is acute  The slopes of the LINE AB, BC and CA are -1, `-(1)/(7)` and -7, respectively, `"LET " m_(1) = -(1)/(7), m_(2) = -1, m_(3) =-7.` `thereforem_(1) gt m_(2) gtm_(3)` So, tangent fo internal angles of the triangle are `"tan" A = (3)/(4), "tan" B = (3)/(4) " and tan" C = -(24)/(7)` So, interior angles A and B are acute and interior angle C is abtuse. `therefore " Internal bisector of B "-= " Acute angle bisector at B"` `"" -= " Acute angle bisector of lines AB and BC "` `"" -= 3x+6y-16=0` External bisector of C `-= " Acute bisector of C" ` ` "" -= " Acute angle bisector of lines AC and BC"` ` "" -=8x+8y+7=0` |
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| 32. |
The value of int_(2)^(8)(sqrt(10-x))/(sqrt(x)+sqrt(10-x))dx is |
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Answer» 1)10 |
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| 33. |
Let F_1 and F_2 be two fixed points and P be a point such that ||PF_1|-|PF_2||=2a where a gt 1/2|F_1F_2|. Then locus of P is |
| Answer» Answer :D | |
| 34. |
If f(x) = (3x+2)^100 and f ' (x) = n(3x+2)^99 then what is the value of n ? |
| Answer» SOLUTION :`F(x)=100(3x+2)^100rArrf(x)=100(3x+2)^99 3=n(3x+2)^99(GIVEN)thereforen=300` | |
| 35. |
If -6 le a le -4 and 3 le b le 7 , what is the maximum value of |a-2b| ? |
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Answer» 10 |
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| 36. |
If values of m for which the line y= mx +2 sqrt5 touches the hyperbola 16x^(2) -9y^(2) =144 are roots of the equationx^(2) -(a+b)x-4 =0then value of (a+b)is equal to |
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Answer» 2 |
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| 37. |
Show that addition and multiplication are associative binary opertion on R. But substraction is not associative on R. Division is not associative on R _(**). |
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| 38. |
{:( " Column - I" , " Column - II") , ( "(A)A curve passingthrough(2,3)having the property that lengthof the radius vectorof any of its point Pis equalto the lengthof thetangentdrawnat thispoint , can be " , "(P) Straightline " ) , ( "(B)A curve passing through(1,1)havingthe propertythatany tangentintersects the y-axis at the point whichis equidistantfromthe pointof tangencyand theorigin , can be " , "(Q)Circle " ) , (" (C)A curve passingthrough (1,0) for whichthe lengthof normalis equalto the radiusvector,canbe " ,"(R)Parabola " ) , ( "(D)A curvepassesthrough the point (2,1)and havingthe property that the segmentof any of itstangentbetweenthe point of tangency and thex-axis, is bisected by the y-axis, can be " ,"(S)Hyperbola " ) :} |
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Answer» <P> |
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| 39. |
If f(x) = {((tan3x)/(x),,, x!=0,),(4k,,,x,=0):} is continuous at x=0' then K= |
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Answer» 3 |
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| 40. |
Let G be subset of real numbers. For a,b, hat(I) G, define a**b=a+b-ab. Then ** is not a binary operation on the set of |
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Answer» natural NUMBERS |
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| 41. |
If I= int_(0)^(pi) sin^(3) theta (1+ 2 cos theta) (1+ cos theta)^(2) d theta then the value of I is |
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| 42. |
The number of ways can 11 persons sit around a table so that all shall not have the same neighbours in any two arrangements is |
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Answer» `10!` |
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| 43. |
If 2alpha is a root of ax^(2)+bx+c=0". "beta is a roots of ax^(2)-2bx-c=0 and the real numbers a,b,c (agt0) are such that betaltalpha, than a root gamma of ax^(2)+4bx+2c=0 always satisfies : |
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Answer» `gammaltbetaltalpha` |
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| 44. |
Differentiate the following w.r.t. x : log (log x), x gt 1. |
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| 45. |
The tangent and normal to the ellipse x^2+4y=4 at a point P(theta) on it meets the major axis is Q and R respectively. IF theta lt theta lt pi/2 and QR=2 then show that theta=cos^-1(2/3) |
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| 46. |
Which of the following options is the only Correct combination ? |
| Answer» Answer :D | |
| 47. |
If a, b, c are the intercepts of the plane 2x + 3y + 5z - 30 = 0 on the coordinate axes respectively then the increasing order of a, b, c is |
| Answer» ANSWER :A | |
| 48. |
Which of the following options is the only Correct combination ? |
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Answer» III, I, P |
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| 49. |
The projection of vector veca=2hati+3hatj+2hatk along vecb=hati+2hatj+1hatk is |
| Answer» Answer :A | |