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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. |
In the following cases, find the distance of each of the given point from the corresponding given plane(0,0,0):3x-4y+12z = 3 |
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| 2. |
In the following cases, find the distance of each of the given point from the corresponding given plane(2,3,-5) : x+2y-2z = 9 |
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| 3. |
In the following cases, find the distance of each of the given point from the corresponding given plane (3,-2,1) : 2x-y+2z+3 = 0 |
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| 4. |
If overline(b) and overline(c) are any two perpendicular unit vectors and overline(a) is any vector, then (overline(a)*overline(b))overline(b)+(overline(a)*overline(c))overline(c)+(overline(a)*(overline(b)timesoverline(c))/(|overline(b)timesoverline(c)|))(overline(b)timesoverline(c))= |
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Answer» `OVERLINE(B)` |
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| 5. |
In the following cases, find the distance of each of the given point from the corresponding given plane (-6,0,0) : 2x-3y+6z-2 = 0 |
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| 6. |
If one b_(yx) and b_(xy)numerically greater than one, the other numerically is |
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Answer» grater than 1 |
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| 7. |
Given two independent events A and B such that P(A) = 0.3, Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B) |
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| 8. |
Let alpha = (cos 85^(@) sin 55^(@)sin65^(@))/(cos5^(@)sin 35^(@)sin25^(@)) is a root of the quadratic equation 2x^(2) - px + q = 0, where p, q in Q then the value of (p + q) is |
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Answer» 2 `(1/4 sin 15^(@))/(1/4 cos 15^(@)) = tan 15^(@)` `= 2 - sqrt(3)` other root will be `2 + sqrt(3)` [ p, q `in` Q] So, REQUIRED equation is `x^(2) - (4X) + 1 = 0` 2X^(2) - 8x + 2 = 0` `:. p + q = 10`. |
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| 9. |
The solution of the differential equation (y^(2)dx-2xydy)=x^(3)y^(3)dy+x^(2)y^(4)dx is |
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Answer» `log((X)/(y^(2)))=((xy)^(2))/(2)+C` |
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| 10. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=sin t, y= cos 2t |
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| 11. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=4 t, y= (4)/(t) |
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| 12. |
If int(((1)/(x)+(1)/(x^(2)))(x-1)dx)/(((1)/(x^(4))+(1)/(x^(2)))sqrt((x^(4)-x^(3)+x^(2))(x^(4)+x^(3)+x^(2))))=sec^(-1){f(x)}+c, then |
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Answer» Maximum value of `F(X)=-2` |
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| 14. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x= 2 "at"^(2), y= "at"^(4) |
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| 15. |
If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=a cos theta, y=b cos theta |
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| 16. |
A boy is walking along the pathy=ax^(2)+bx+c through the points (-6,8),(-2,-12), and (3,8). He wants to meet his friend at P(7,60). Will he meet his friend? (Use Gaussian elimination method.) |
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| 17. |
Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x)g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt,then The area borunded by g (x) with co-ordinate axes is (in square units): |
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Answer» `9/4` |
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| 18. |
The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is |
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Answer» `""^(30)C_(4)-20` |
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| 19. |
There are 200 tickets numbered 1 to 200. A ticket is drawn at random. Find the probability that the number on the drawn ticket is either multiple of 4 or 6. |
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| 20. |
A bag contains 5 black balls 4 white balls and3 red balls . If a ball is selected at random , the probability that it is a black or a red ball, is |
| Answer» ANSWER :D | |
| 21. |
int_(0)^(pi) (x dx)/(4 cos^(2) x + 9 sin^(2) x)= |
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Answer» `(pi^(2))/(12)` |
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| 22. |
If T, denotes the r^(th) term in the expansion of [x + 1/x]^(23), then |
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Answer» `T_(12) = T_(13)` |
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| 23. |
Integrate the following functions. intlog(2+x^(2))dx |
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| 24. |
Find the smallest integral x satisfying the inequality (x-5)/(x^(2) + 5x -14) gt 0. |
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| 25. |
A(1, -2, 4), B(5, -1, 7), C(3, 6, -2) and D(4, 5, -1) are given vectors. Then the projection of vec(AB) on vec(CD) is …………… |
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Answer» (1, -1, 1) |
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| 26. |
Theproduct of the roots of the equaiton sqrt(x^(2) - 4x + 3 ) + sqrt(x^(2) - 7x + 12) = 3 sqrt(x - 3) is |
| Answer» ANSWER :A | |
| 27. |
A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ? |
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| 28. |
If the line x/1=y/2=z/3 intersects the the line 3beta^(2)+3(1-2alpha)y+z=3-1/2{6alpha^(2)x+3(1-2beta)y+2z} then point (alpha,beta,1) lies on the plane |
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Answer» `2x-y+z=4` |
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| 29. |
In this triangle, what is the degree measure of angle c ? |
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Answer» 17 |
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| 30. |
if A=[{:(3,-2),(4,-2):}],I=[{:(1,0),(0,1):}]and A^(2)=k.A-2l,"then"k=? |
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Answer» 1 |
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| 31. |
Find the particular solution of the differential equation (1+e^(2x))dy+(1+y^(2))e^(x)dx=0. Given that y=1 when x=0. |
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| 32. |
An arbitrary cube has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws is |
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Answer» `(5)/(1296)` |
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| 33. |
Determine the sum of all possible positive integers n, the product of whose digits equals n^(2)-15n - 27. |
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| 34. |
pH of a saturated solution of silver salt of monobasic acid HA is found to be 9. Find the K_(sp) of sparingly soluble salt Ag A(s). Given : K_(a)(HA)=10^(-10) Express your answer as a, b, c, d where K_(sp)=a.bxx10^(cd) [Written in scientific notation] |
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Answer» `{:(AgA(s)+H_(2)O(l)hArrHA(aq)+OH^(-)(aq)),(x-y""y""y):}` `K_(sp)=x(x-y)` `K_(H)=(K_(w))/(K_(a))=(y^(2))/((x-y))` `(10^(-10))/(10^(-10))=((10^(-5))^(2))/((x-y))` `x-y=10^(-6)` `x=10^(-5)+10^(-6)` `x=1.1xx10^(-5)` `K_(sp)=1.1xx10^(-5)xx10^(-6)` `K_(sp)=1.1xx10^(11)`Ans. |
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| 35. |
Three poles of height a, b, c stand on the same side of a road and subtend an angle of 45^(@) at a point on the line joining their feet. The pole of height a subtends an angle alpha at the foot of the pole of height b which subtends an angle beta at the foot of the pole with height c, if a gt b gt c, then cot alpha - cot beta = |
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Answer» `(ac-b^(2))/(AB)` |
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| 37. |
Differentiate the following w.r.t x (3x^2-9x+5)^9 |
| Answer» SOLUTION :Let = `(3x^2-9x+5)^9` Then `(DY)/dx=9(3x^2-9x+5)^8(6x-9)=27(3x^2-9x+5)68(2x-3)` | |
| 38. |
The equation of the normal at the end of latusrectum in the fourth quadrant of the parabola y^(2)=4ax is |
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Answer» x+y+3a=0 |
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| 39. |
Triangle formed by variable lines (a+b)x+(a-b)y-2ab=0 and (a-b)x+(a+b)y-2ab=0 and x+y=0 is (where a, b in R) |
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Answer» equilateral `(a+b)X+(a-b)y-2ab=0 "" (1)` `(a-b)x+(a+b)y-2ab=0 "" (2)` `"and " x+y=0 "" (3)` Lines (1) and (2) are symmetrical about the line y=x (as on interchanging x and y in `1^(ST)` line gives `2^(ND)` line). So, y=x is one of the angle BISECTORS. This is perpendicular to the third side x+y=0. Therefore, triangle is isosceles. |
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| 40. |
If four points with position vectors A(-i+2j+3k),B(-i-12j-3k),C(2i-j-4k)andD(2i+lambdaj-k) are coplanar, then lambda = _________ |
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| 41. |
A circle touches the y axis at (0,2) and its x intercept equal to3 units, then the equation of the circle is |
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Answer» `x^2 + y^2 +- 4x - 5y + 4= 0` |
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| 42. |
Which of the following statements are correct E_(1)) If a + b + c = 0 then 1 is a root of ax^(2) + bx + c = 0. E_(2)) If sin alpha, cos alpha are the roots of the equation ax^(2) + bx + c = 0 then b^(2)-a^(2) =2ac |
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Answer» only `E_(1)` |
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| 43. |
Find the numerically greatest term of(5x-6y)^(14), x=(2)/(5), y=(1)/(2) |
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| 44. |
If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is |
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Answer» 256 |
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| 46. |
Findthe area oftheparabolay^2 = 4ax boundedby itslatusreactum , |
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| 47. |
At 9:00A.M. Allan began jogging and Bill began walking at constant rates around the same circular (1)/(4) mile track. The figure above compares their times in minutes and corresponding distances in miles. Which statement or statements must be true? I. Bill's average rate of walking was 2 miles per hour. II. At 9:00A.M. Allan had jogged (3)/(5) mile more than Bill had walked. III. At 9:30 A.M. Allan had completed 8 more laps around the track than Bill. |
| Answer» Answer :D | |
| 48. |
During embryonic period blood is form in :- |
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Answer» THYMUS gland |
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| 49. |
If cos A = 7/25 and (3pi)/2 lt A lt 2pi, then find the value of cot A//2. |
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| 50. |
If veca, vecb, vecc non-zero vectors such that veca is perpendicular to vecb and vecc and |veca|=1, |vecb|=2, |vecc|=1, vecb.vecc=1. There is a non-zero vector coplanar with veca+vecb and 2vecb-vecc and vecd.veca=1, then the minimum value of |vecd| is |
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Answer» `2/SQRT(13)` but `vecd.veca=1 rArr 1=x(1+0)+0 rArr x=1` `rArr vecd=veca +vecb+y(2vecb-vecc)` `rArr |vecd|^(2)=|veca|^(2)+|b|^(2)=2veca.vecb+y^(2)(2vecb-vecc)^(2)+2y(veca+vecb).(2vecb-vecc)` `rArr =1+4+y^(2)(16+1-4)+2y(8-1)` `=13y^(2)+14y+5` `therefore |vecd|_("MIN" ) = sqrt((4.13.5-14.14)/(4.13))=4/sqrt(13)` |
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