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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.
| 2. |
let P be a point the first quadrant lying on the ellipse 9x^(2) +16y^(2)=144,such that the tangent at P to the ellipse is inclined at an angle135^(@)to the positive direction of x-axis Then the coordinates of P are |
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Answer» ` ((sqrt(143))/( 3), (1)/(4) ) ` |
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| 3. |
If2a+b +3c =0 , thenthe linea x+by+ c =0passesthroughthe fixedpointthat is |
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Answer» ` (( 2 )/( 3),( 1 ) /( 3)) ` and LINE, ` ax+ by+c= 0 ` ` rArr3ax+ 3by+3c =0 ""`… (II) On subtractingEq.(i)from Eq.(ii),weget ` ( 3x-2 ) a+(3y- 1 )b = 0 * a +0* b ` On comparingbothsides , we get `3x- 2= 0rArrx=(2 )/( 3 ) ` `and3y- 1= 0rArry=( 1 ) / (3 ) ` `therefore`Line`ax+by+ c =0 `passesthroughthefixedpoint` (( 2 ) /( 3 ) , ( 1 ) /( 3 ) ) ` |
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| 4. |
int (1)/(16 sin^(2) x + 25 cos^(2) x)dx = |
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Answer» `(1)/(40) TAN^(-1) ((5)/(4) tanx) + C ` |
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| 6. |
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y - axis. |
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| 7. |
When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. which of the following values CANNOT be the sum of x and y? |
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Answer» 12 |
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| 8. |
If the radius of a sphere is measured as 9cm with an error of 0.03m, find the approximate error in calculating its surface area. |
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| 9. |
Find the magnitude of two vector veca and vecbhaving same magnitude such that the angle between them is 60 and their scalar product is 1/2 |
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| 10. |
Which of the following pair (s) is//are orthogonal ? |
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Answer» `16x^(2)+y^(2)=C and y^(16)=KX` |
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| 11. |
The point of intersection of the lines represented by equation 2(x+2)^(2)+3(x+2)(y-2)-2(y-2)^(2)=0 is |
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Answer» (2,2) |
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| 12. |
Show that the area enclosed between the curvesy y = x and y=x^(3) is (1)/(2) sq unit. |
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| 13. |
If bar(a) is any non-zero vector, then (bar(a).bar(i)).bar(i)+(bar(a).bar(j)).bar(j)+(bar(a).bar(k)).bar(k) is equal to ……………… |
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| 14. |
Find the values of the following integrals (iii) int_(0)^(pi/2) sin^(2) x cos^(7) x dx |
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| 15. |
Examine the continuity of the function f(x)= {((1-cos(2x))/(x^(2)),"if "x ne 0),(5",","if" x = 0):} at x=0 |
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| 17. |
If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb|. |
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Answer» SOLUTION :`(|veca|+|vecb|)^2` = `|veca|^2 + |vecb|^2 + vec2|veca|.|vecb|` = 9+4+12 = 25 THEREFORE `|veca+vecb|` = 5 `|veca-vecb|^2` = `(|veca|+|vecb|)^2-2|veca|.|vecb|` = 9+4-12= 1 `IMPLIES |veca-vecb|` = 1 |
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| 18. |
A student while solving a quadratic equation in x, he copied its constant term incorrectly and got its roots as 5 and 9. Another student copied the constant term and coefficient of x^2 of the same equation correctly as 12 and 4 respectively. Ifs,p and Deltadenote respectively the sum of the roots, the product of the roots and the discriminate of the correct equation, then (Delta)/(3p + s) = |
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Answer» 48 |
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| 19. |
If |z_(1)| = 1, |z_(2)| = 2, |z_(3)| = 3 and |9z_(1)z_(2) + 4z_(1)z_(3) + z_(2)z_(3)| = 12, then the value of |z_(1) + z_(2) + z_(3)| is |
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Answer» 3 |
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| 20. |
If the straight line 8x+3sqrt(2)y= 36 touches the ellipse (x^(2))/(9)+(y^(2))/(4)= 2 " at (a, b),then " a+ sqrt(2b)= |
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Answer» `(36)/(5sqrt(2))` |
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| 21. |
The ratio of the ordinates of a point and its .corresponding point is(2sqrt(2))/(3)then eccentricity is |
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Answer» `1/3` |
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| 22. |
A die is thrown 6 times. If ‘getting an odd number' is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes? |
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| 23. |
A real valued function f(x) = C log |x| + Dx^(3) + x, x ne 0 where C and D are constant, has critical points at x= -1 and x=2. Then the ordered pair (C,D) is |
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Answer» `((2)/(3), - (1)/(9))` |
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| 24. |
f(x) = {(2+ sqrt(1-x^(2))",",|x| le 1),(2e^((1-x)^(2)),|x| gt 1):} Discuss the continuity of f(x) at x=1 |
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| 26. |
A person plays a game of tossing a coin thrice. For each head, he is given Rs 2 by the organiserof thegame and for each tail, he has to give Rs.1.50 to the organise. Let X denote the amount gained or lost by theperson . Thus write the Range of Distribution. |
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Answer» {-1, 2 . 50, - 4.50, 6} |
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| 27. |
The vector equation of a plane whose distance from the origin is p and perpendicular to a unit vector hatn is ......... |
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Answer» `vecr.vecn=p` |
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| 28. |
Find thearea of theregionenclosed by thecurvex^2 = 4y and linex=4y-2 |
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| 29. |
Given, p=3hati+2hatj+4hatk,a=hati+hatj,b=hatj+hatk,c=hati+hatk and P = xa + yb + zc, then x, y, z are respectively |
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Answer» `(3)/(2), (1)/(2), (5)/(2)` `implies3hati+2hatj+4hatk=x(hati+hatj)+y(hatj+HATK)+z(hati+hatk)` `implies 3hati+2hatj+4hatk=(x+z)hati+(x+y)hatj+(y+z)hatk` On comparing both SIDES, the coefficients of `hati, hatj, hatk`, we get `x+z=3"... (i)"` `x+y=2"... (ii)"` and `y+z=4"... (iii)"` On solving EQS. (i), (ii) and (iii), we get `x=(1)/(2), y=(3)/(2), z=(5)/(2)` |
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| 30. |
If n(A) =5, then number of relations on A that are not symmetric is |
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Answer» `2^(25)` |
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| 31. |
Few distance into the rough sea, they decide to call it a day. Tintin and five of his comrades decide to take turns in controlling their ship. In each ‘sitting’, some of them sleep while the others control the ship. How many such ‘sittings’ are needed so that every person has a chance to control the ship to every other person sleeping? |
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Answer» Solution :Four sittings are needed to fulfill the requirements. A sitting must include all possibleordered pairs (a, p), where a are the ones sleeping while p are the ones controlling the ship.There are 6×5 = 30 such ordered pairs. In any sitting, if EXACTLY m people to control the ship, thenumber of ordered pairs covered is m(6 − m). This is maximised if m = 3 and m(6 − m) = 9.Hence three sittings can cover at most 3 × 9 = 27 ordered pairs. This is insufficient since werequire 30 ordered pairs. To show that four concerts are sufficient, number the people 1 to 6and use the following construction.Controlling the Ship: 456 235 136 124 Sleeping: 123 146 245 356 It is easy to check that every ordered pair is covered by this construction. Hence, the Answer is 4 |
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| 32. |
Vertex A of a variable triangle ABC, inscribed in a circle of radius R, is a fixed point. If the angles subtended by the side BC at orthocentre (H), circumcentre (O) and incentre (I) areequal than identify the locus of orthocentre of triangle ABC. |
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| 33. |
Let vec(a) and vec(b) be two unit vectors and theta is the angle between them. Then vec(a)+vec(b) is a unit vector if ………. |
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Answer» `theta=(PI)/(4)` |
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| 35. |
The radical axis of two circles S=0, S'=0 does not exist if |
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Answer» the CENTRES of the circles are INVERSE points of S = 0 |
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| 36. |
5/(3^2 7^2)+9/(7^2 11^2)+13/(11^2 15^2)+....oo |
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Answer» `1/8` |
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| 37. |
a.b and c are three vectors such that |a| =1, |b| = 2, |c| = 3 and b,c are perpendicular. If projection of both is the same as the projection of c on a, then |a - b + c| is equal to |
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Answer» `SQRT(2)` |
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| 38. |
I: The differential equation for the family of curves x^(2) + y^(2) - 2ay = 0, where a is an arbitraryconstantis (x^(2) -y^(2)) y' = 2xy II : The differential equation of the family of parabolas having vertices at the origin and foction y-axis is (dy)/(dx) = (2y)/(x) |
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Answer» only I is TRUE |
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| 39. |
Using properties evaluate the following definite integrals, evaluate the following: int_0^(pi/2) (sinx-cosx)/(1+sinx cosx) dx |
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Answer» Solution :`int_0^(pi/2) (sinx-cosx)/(1+sinx cosx) dx`____ (a) Then `I = int_0^(pi/2) (SIN(pi/2-x) -cos(pi/2-x))/(1+sin(pi/2-x) cos(pi/2-x)) dx` int_0^(pi/2) (cosx-sin)/(1+cosx sinx) dx` ____(b) (a)+(b) `GT 2I = int_0^(pi/2) 0/(1+sinx cosx) dx` = 0 `gt I` = 0. |
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| 40. |
If ""^(4)C_(r)=""^(4)C_(r+1), then the value of r is |
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| 41. |
The vector a= lambda hat (i) + hat(j) + 2 hat (k) , vec(b) = hat(i) + lambda hat(j) - hat(k) and vec(c ) = 2 hat (i) - hat(i)- hat(j) + lambda hat(k) are coplanar if - |
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Answer» ` lambda = -2` |
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| 42. |
If theta is the angle between the lines in which the planes 3x-7y-5z=1 and 5x-13y+3z+2=0 cuts the plane 8x-11y+2z=0, then sintheta is |
| Answer» Answer :D | |
| 43. |
The solution for the differential equation (dy)/(y)+(dx)/(x)=0 is |
| Answer» Solution :N/A | |
| 44. |
If A and B are two events such that A subset B and P(B) ne 0, then which of the following is correct? a)P(A | B)=(P(B))/(P(A)) b)P(A | B)ltP(A) c)P(A | B) ge P(A) d)None of these |
| Answer» Answer :C | |
| 45. |
Let E and F be events with P(E)=(3)/(5), P(F)=(3)/(10) and P (E cap F) =(1)/(5) Are E and F independent? |
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| 46. |
By using the properties of definite integrals, evaluate the integrals int_(0)^(pi)(1+cos x) dx |
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| 47. |
Three electric lamps are fitted in a room. 3 bulbs are chosen at random from 20 bulbs having 16 good bulbs. The probability that the room is lighted is |
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Answer» `(282)/(285)` |
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| 48. |
If I_(n)= int cot^(n)x dx" then " I_(0)+I_(1)+2(I_(2)+I_(3))+I_(4)+I_(5)= |
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Answer» `-[Cot X+(Cot^(2)x)/(2)+(Cot^(3)x)/(3)+(Cot^(4)x)/(4)]+c` |
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| 49. |
A committee of 5 persons is to be formed from 7 men and 3 women. i. Find the number of ways to form the committee so that it contains 5 men. ii. Find the number of ways to form the committee so that it contains 4 men and 1 women. iii. Find the number of ways to form the committee so that it contains atleast 1 women. |
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Answer» II. 105 iii. 231 |
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| 50. |
If z and w are complex numbers such that bar(z)-bar(iw)=0 and Arg (zw) = (3pi)/(4), "then Arg "z= |
| Answer» Answer :B | |