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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 (l_1, m_1, n_1), (l_2, m_2, n_2)" and "(l_3, m_3, n_3) are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to (l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3) makes equal angles with them, |
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| 2. |
Verify Rolle's theorem for the following functions: f(x)= x(x-3)^(2), x in [0, 3] |
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| 3. |
If A={a, b, c, d}, then a relation R={(a,b),(b,a),(a,a)} on A is |
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Answer» SYMMETRIC and TRANSITIVE only |
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| 4. |
A= sin 78^(@) - sin 18^(@) + cos 132^(@) , B= cos 12^(@) + cos 84^(@) + cos 132^(@) + cos 156^@ and C= ( sin 75^(@) + sin 15^@)/( cos 75^(@)+ cos 15^(@))then by arranging in the ascendingorderis |
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Answer» C,A,B |
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| 5. |
The rectangle shown in the figure below is partitioned into 3 triangles, 2 of which are shaded. What is the total area, in square inches, of the 2 shaded regions? |
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Answer» 20 |
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| 6. |
If A=[(2,3,1),(0,1,5)],B=[(1,2,-1),(0,-1,3)] then [(1,0,5),(0,1,1)]= |
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Answer» `2A-B` |
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| 7. |
If the polar of a point on the circle x^(2) + y^(2) = p^(2) with respect to the circle x^(2) + y^(2) = q^(2) touches the circle x^(2) + y^(2) = r^(2) then p,q r are in |
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Answer» AP and `S_(3) = x^(2) + y^(2) - R^(2) = 0` Let p `(x_(1), y_(1))` be a point on `S_(1) - 0` then `S_(1) = x_(1)^(2) + y_(1)^(2) - p^(2)` EQUATION of polar of p w.r.t `s_(2) = 0` is `x x_(1) + y y_(1) - q^(2) - 0` Equation (1) touches the circle S = 0 then `r = (|0 + 0 - q^(2)|)/(sqrt(x_(1)^(2) + y_(1)^(2)))` `implies q^(2) = r sqrt(x_(1)^(2) + y_(1)^(2))` `implies q^(2) = r sqrt(P^(z))` `implies q^(2) = pr` `:.` p.q and r are in G.P |
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| 8. |
If int(dx)/(x^(3)(x-1)^(1//2))=(sqrt(x-1)(3x+2))/(4x^(2)) + K tan^(-1)sqrt(x + 1) + C then the value ofK is |
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Answer» `1//2` |
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| 9. |
If the ratio of (1)/(6), (1)/(5) is equal to the ratio of 35 to x, what is the value of x? |
| Answer» ANSWER :D | |
| 10. |
If the two equations a a_(1)x^(2)+b_(1)x +c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 have a common root, then the value of (a_(1)b_(2)-a_(2)b_(1)) (b_(1)c_(2)-b_(2)c_(1)) is |
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Answer» `-(a_(1)c_(2)-a_(2)c_(1))^(2)` |
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| 11. |
The maximum value of the modulus of e^(z) on the set { z in C //0 lt="Re" (z) lt= 1,0 lt=Im (z) lt=1} is |
| Answer» ANSWER :B | |
| 12. |
Classify the following measures as scalars and vectors. (i) 5 seconds (ii) 1000cm^(3) (iii)10 Newton (iv) 30km/hr (v) 10g//cm^(3) (vi) 20m/s towards north |
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Answer» (II) Volume-Scalar (III) Force-Vector (iv) Speed-Scalar (V) Density-Scalar (vi) Velocity-Vector |
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| 13. |
(x-1)/(-1) =(y+2)/(1)=(z-3)/(-2)" and" (x-1)/(1)=(y+1)/(2)=(z+1)/(-2) |
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| 14. |
Find the area of the region BOB'RESB is enclosed by the ellipse and the lines x = 0 and x = ae. |
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| 16. |
In 1919, H. S. Reed and R. H. Holland published a paper on the growth of sunflowers. Included in the paper were the table and graph above, which show the height h, in centimeters, of a sunflower t days after the sunflower begins to grow. The growth rate of the sunflower from day 14 to day 35 is nearly constant. On this interval, which of the following equations best models the height h, in centimeters, of the sunflower t days after it begins to grow? |
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Answer» h = 2.1t − 15 Choices A, C, and D are INCORRECT because the growth rates of the sunflower from day 14 to day 35 in these choices are significantly higher or lower than the true growth rate of the sunflower as shown in the graph or the table. These choices may result from CONSIDERING time periods different from the period indicated in the question or from calculation errors. |
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| 17. |
Choose the correct answer. Answer all the questions,The slope of the line normal to the curve f(x)= 2cos4x at x= (pi)/(2) is …. |
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Answer» `-4sqrt(3)` |
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| 18. |
In triangle ABC if y=x+1 & y=2x+3 are altitude through A and angle bisector of B respectively. If vertex C-=(3,4) then equation of median through C is |
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Answer» `x+7y=25` LET slope of `AB` is `m` so, `|(m-2)/(1+2m)|=|(2+1)/(1-2)|`  `m=-1/7` So equation of `AB` is `3x+21y-123=0` So `A-=(17/4, 21/4)` mid-point of `AB=(67/24, 131/24)` Equation of MEDIUM though `C` is `7x+y=25` |
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| 19. |
Solve (x-y)^(2)(dy)/(dx)=a^(2) |
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| 20. |
Find the equation of parabola whose focus is (4,5) and vertex is (3,6). Also find the length of the latus rectum. |
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| 21. |
Evaluate the following integrals. int(1)/(2+3sinx)dx |
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| 23. |
Let **' be the binary opertion on the set {1,2,3,4,5} defined by a &&' b = H.C.F. of a and b. Is the opertion **' same as the opertion ** defined in above ? Your answer |
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| 24. |
Evaluate intsqrt(9 - 4x^(2))dx |
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| 25. |
If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))|=(x-y)(y-z)(z-x)(1/x+1/y+1/z) then value of n is |
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Answer» -1 |
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| 26. |
Let the vectors vecaandvecb be such that |veca|=3and|vecb|=(sqrt(2))/(3), then vecaxxvecb is a unit vector , if the angle between vecaandvecb is |
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Answer» `pi//6` |
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| 27. |
Which of the following experiment in Photoelectriceffect will support particle nature of light ? |
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Answer» Photocurrent is set up almost instantaneously even with FAINT light of sufficientlysmall wavelength. |
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| 28. |
Find intervals in which the function given by f(x)=sin 3x, x in [0, (pi)/(2)] is(a) Increasing(b) Decreasing. |
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| 29. |
int(2x-1)/((x-1)(x+2)(x-3))dx=Alog|x-1|+B log|x+2|+C log|x-3|+K Then A,B,C are respectively. |
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Answer» `1/6,(-1)/3,1/3` |
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| 30. |
A line AB in three-dimensional space makes angles 45^(@) " and " 120^(@) with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle theta with the positive z-axis, then theta equals |
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Answer» `45^(@)` |
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| 31. |
Ifalpha, beta , gammaare therootsofx^3 + 4x +1 =0 then theequationwhoserootsare ( alpha^2)/( beta + gamma ) , ( beta^2)/( gamma+ alpha) , ( gamma^2)/ ( alpha+ beta) is |
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Answer» `X^(3) - 4X - 1 = 0` |
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| 32. |
Out of 800 boys in a school, 242 played cricket, 250 played hockey and 340 played basketball. Of the total, 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 34 played all the three games. The number of boys who did not play any game is |
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Answer» 118 |
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| 34. |
The value of cosx cosy sin(x-y)+cosycosz sin(y-z) +cosz cosx sin(z-x)+sin(x-y)sin(y-z)sin(z-x), is |
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Answer» 0 |
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| 35. |
If sinA+sinB+sinC=0 and cosA+cosB+cosC=0, then cos(A+B)+cos(B+C)+cos(C+A) is equal to |
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Answer» OPTION1(A+B+C) |
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| 36. |
If e^x+e^y=e^(x+y), find dy/dx. |
| Answer» SOLUTION :`E^x_e^y=e^(x+y)=e^xe^yrArre^x/(e^xe^y)+e^y/(e^xe^y)=1rArre^-y+e^-x=1rArre^-y(-1)dy/dx+e^-x(-1)=0rArrdy/dx=(-e^-x)/(e^-y)=-e^(y-x)` | |
| 37. |
Evaluate the following integrals: int_(pi/6)^(pi/4) cosecx dx |
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Answer» SOLUTION :`int_(pi/6)^(pi/4) COSECX DX` =`(LOG| cosecx - cotx|)_(pi/6)^(pi/4)` =`log|sqrt2 - 1|-log|2-sqrt3| ` `log(sqrt2 - 1|-log|2-sqrt3)` `log((sqrt2-1)/(2-sqrt3))` |
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| 38. |
If OA, OB are two equal chords of the circle x^(2)+y^(2)-2x+4y=0 perpendicular to each other and passing through the origin, then the equations of OA and OB are |
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Answer» 3x+y=0, x+3y=0 |
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| 39. |
If =Xcostheta-Ysintheta,q=Xsintheta+Ycosthetaandp^(2)+4pq+q^(2)=AX^(2)+BY^(2),0le0le(pi)/(2).What is the value of theta ? |
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Answer» `(PI)/(2)` `q=xsintheta+ycostheta` GIVEN, `p^(2)+4pq+q^(2)=Ax^(2)+By^(2)` Letus take`theta=(pi)/(4)`. `p=X"COS"(pi)/(4)-y" cos"(pi)/(4)=(x+y)/(sqrt(2))` `q=x" SIN"(pi)/(4)+y" cos"(pi)/(4)=(x+y)/(sqrt(2))` `pq=(x^(2)-y^(2))/(2)rArr2pq=x^(2)-y^(2)rArr4pq=2x^(2)-2y^(2)` . . . (1) Now, `p^(2)+q^(2)=x^(2)cos^(2)theta+y^(2)sin^(2)theta-2xycosthetasintheta+x^(2)sin^(2)theta+y^(2)cos^(2)theta+2xysinthetacostheta=x^(2)+y^(2)`. . . (2) From(1) , (2) , `p^(2)+q^(2)+4pq=x^(2)+y^(2)+2x^(2)-2y^(2)=3x^(2)-y^(2)` Comparingthis with the given from , we get `theta=(pi)/(4),A=3,B=-1` |
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| 40. |
Which of the following is variance of random variable x=x_(i) and P(x=x_(i))=p_(i) |
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Answer» <P>`SUM(x_(i).P_(i))` |
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| 41. |
The upper quartile for the following distribution is given by the size of |
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Answer» `((31+1)/(4))"th term"` |
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| 42. |
If veca and vecb are mutually perpendicular unit vectors , then (3veca+2vecb).(5veca-6vecb)= |
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Answer» 5 |
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| 43. |
The sum of two number is 6 times their geometric mean, then the numbers are in the ratio is |
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Answer» `(3 + 2 sqrt(2)): (3 - 2 sqrt(2))` |
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| 44. |
The maximum value of Z = x + 3y subject to the constraints 2x+y le 20, x+2y le 20, x ge 0, y ge 0 is ………. |
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Answer» 10 |
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| 45. |
Using the method of integration find the area of the region bounded by lines: 2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0 |
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| 46. |
A mixture of gases contain H_(2) and O_(2) gases in the ratio of 1 : 4 (w/w). What is the molar ratio of the two gases in the mixture ? |
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Answer» 16 : 1 |
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| 47. |
Examine 3y^2-8xy-3x^2-29x+3y-18 is re-solvable into two linear factors. |
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Answer» `(2X + 3y+4 )(3x +5y +2)` |
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| 48. |
int(dx)/(sinx+cosx) is equal to |
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Answer» `log tan(PI//4)+X//8)+C` |
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| 49. |
Statement 1 :Ellipse(x^(2))/( 25) + ( y^(2))/( 16) =1and 12x^(2) -4y^(2) =27 intersect each other at right angle Statement 2: Given ellipse and hyperbola have same foci Then correct statement is |
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Answer» Both the STATEMENT are TRUE and 2 is the correct EXPLANATION of 1 |
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| 50. |
If n,n+1,n+2 where n in N, represent the sides of a triangle ABC, in which the largest angle is twice the smallest, then n is equal to |
| Answer» ANSWER :C | |