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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 absA = 2, absB = 5 then abs(AB) = 10 |
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| 2. |
Evaluate the definite integrals int_(0)^(pi)(xtanx)/(secx+tanx)dx |
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| 3. |
A biologist was interested in the number of times a field cricket chirps each minute on a sunny day. He randomly selected 100 field crickets from a garden, and found that the mean number of chirps per minute was 112, and the margin of error for this estimate was 6 chirps. The bilogist would like to repeat the procedure and attempt to reduce the margin of error. Which of the following samples would most likely result in a smaller margin of error for the estimated mean number of times a field cricket chirps each minute on a sunny day? |
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Answer» 50 RANDOMLY SELECTED CRICKETS from the same garden. |
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| 4. |
Evalute the following integrals int (1)/((x + 3)sqrt(x + 2)) dx |
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| 5. |
IfA=[(1,2,3),(3,-2,1),(4,2,1)]thenshow that A^3-23A -40 I=0. |
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| 6. |
If the area of the triangle on the complex plane formed by the points z ,iz and z+iz is 50 sq. units then |z| is |
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Answer» 15 |
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| 7. |
If the letters of the word "SIPRON' are arranged in all possible ways and the words thus formed are arranged in dictionary order. Find the rank of the word 'PRISON'. |
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| 8. |
If the tangents at t_(1)andt_(2) on y^(2) = 4ax are at right angles if |
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Answer» `t_(1)t_(2)=-1` |
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| 9. |
Evaluate the following :[[x,1,2],[y,3,1],[z,2,2]] |
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Answer» SOLUTION :`[[X,1,2],[y,3,1],[Z,2,2]]` `x[[3,1],[2,2]]-y[[1,2],[2,2]]+z[[1,2],[3,1]]` =x(6-2)-y(2-4)+z(1-6) 4x+2y-5z |
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| 10. |
Evaluate the following definite integrals int_0^1 x/(x^2+1) dx |
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Answer» Solution :`x^2+1 = t` Then dt = 2x dx `gt x dx = dt/2` ALSO x = 0 `gt t = 1` and x = 1 `gt t = 2` THEREFORE `int_0^1 x/(x^2+1) dx = int_1^2 1/t dt/2` =`1/2[LOG |t|]_1^2` =`1/2[log|2| -log|1|]` `=1/2(log 2-0) = 1/2 log2` |
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| 11. |
Let A_(1), A_(2),.., A_(75) be 75 arithmetic means inserted between two distinct numbers a and b, then (b+A_(75))/(b-A_(75))+(a+A_(1))/(a-A_(1))= |
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| 12. |
Two straight lines from origin forms an equiliatral triangle ABC with y = 4 . On the sides AB, BC and CA, other three equilateral traingles DeltaPAB , DeltaQBC and Delta RAC are drwan. Find the equations of the containing the sides of Delta PQR and also the area of DeltaPQR. |
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| 14. |
Two tangents T _(1) , T _(2) as a pair of tangents from (-2, 0)and radius greater than the radius of C is |
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Answer» `X ^(2) + y ^(2) - 6x + 5=0` |
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| 16. |
If a and b are two unit vectors such that c=(a xx c)+b then the maximum value of [a bc] is |
| Answer» ANSWER :B | |
| 17. |
Along a road lies an odd number of stones placed at intervals of 10 m. These stones have to be assmbled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. find the number of stones |
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| 18. |
a, b are positive real numbers such that 1/a+9/b=1 The smallest value of a + b is |
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| 19. |
If ""^(n)P_(4)=1680, find n. |
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| 20. |
I. If a gt 0" then " underset(x to oo)"Lt" ([ax+b])/(x)=a II. underset(x to pi//2)"Lt" [sin x]= |
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Answer» only I is true |
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| 21. |
Kellogg is a new cereal formed of a mixture of bran and rice that contains at least 88 grams of protein and at least 36 milligrams of iron. Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogram and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs. 5 per kg and rice costs Rs. 4 per kg. |
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| 22. |
Consider a parabola y = (x^(2))/(4) and the point F (0,1). Let A _(1)(x_(1), y_(1)),A _(1)(x _(2), y_(2)), A_(3)(x_(3), y_(3)),....., A_(n ) (x _(n), y _(n))are 'n' points on the parabola such x _(k) gt - and angle OFA_(k)= (k pi)/(2pi) (k =1,2,3,......, n ). Then the value of lim _( n to oo) 1/n sum _(k =1) ^(n) FA_(k), is equal to : |
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Answer» `2/pi` |
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| 23. |
A beam of fast moving electrons having cross-sectional area A falls normally on a flat surface. The electrons are absorbed by the surface and the average pressure exerted by the electronson this surface is found to be P. If the electrons are moving with a speed v, then the effective current through any cross-section of the electron beam is |
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Answer» Ape/(mv) (NAV)(mv)=F,`P=F/A ` `rArr n=P//(mv^(2))` `:. i=nAve=(Ape)/(mv)` |
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| 24. |
Differentiate the functionsx^(sin x) + (sin x)^(cos x) |
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| 25. |
If ABCD is a rombus whose diagonals cut at the origin O, then OA + OB + OC + OD equals to |
| Answer» Solution : since, the diagonals of a rhombus bisect each other OA = - OC and OB =- OD OA + OB +OC + OD = - OC - OD + OC + OD = 0 | |
| 26. |
If, in Delta ABC, a^(4) + b^(4) + c^(4) = 2a^(2)(b^(2) + c^(2)) then : m/_A = ... |
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Answer» `30^(@)` |
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| 27. |
If int (x^(2) + 4)/(x^(4) + 16) dx = (1)/(k) tan^(-1) ((x^(2) - 4)/(kx) ) + Cthen k = |
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Answer» `SQRT(2)` |
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| 28. |
underset(k=1)overset(oo)sum underset(r=0)overset(k)sum (1)/(3^(k))(""^(k)C_(r)) is equal to |
| Answer» Answer :D | |
| 29. |
Fill in the gaps with correct answer .sin35^@ + cos5^@ = _____. |
| Answer» SOLUTION :`sqrt3cos25^@` | |
| 30. |
Integrate the following int(dx)/(3x^2+7) |
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Answer» Solution :`int(dx)/(3x^2+7)` [PUT `x= sqrt(7/3) TAN THETA` then `dx=sqrt(7/3)sec^2theta d theta` `(1/3)int(dx)/(x^2+(7/3))=1/3 sqrt(7/3)/(7/3)int(sec^2theta d theta)/(sec^2theta)` (1/sqrt21)tan^(-1)((sqrt3x)/SQRT7) +C` |
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| 31. |
Obtain a mxxn matrix A=[a_(ij)] . Such that a_(ij)=2i-j,m=2,n=4. |
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| 35. |
Let a=sin^(-)(sin3)+sin^(-1)(sin4)+sin^(-1)(sin5),f(x)=e^(x^(2)+|x|), domain of f(x) be [a,oo) & range of f(x) be [b,oo) and g(x)=(4cos^(4)x-2cos2x-1/4"cos"4x-x^(7))^(1//7), domain & range of g(x) is set of real numbers. Which of the following are correct |
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Answer» `a=-2` `f(-2)=f(2)impliesf(x)` is many one `IMPLIES` non invertible Let `t=x^(2)+|x|,t epsilon [0,OO)` `f(x) epsilon [1,oo)` `impliesb=1` & `a+b=-1` `g(x)=[(1+cos2x)^(2)-2cosx-1/2(2COS^(2)2x-1)-x^(7)]^(1//7)` `g(x)=(3/2-x^(7)]^(1/7)` `f(g(g(b)))=f(b)=e^(2)` |
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| 36. |
int e^(3x).sin 5x dx = |
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Answer» `(E^(3x))/(34) ` [ 3 sin 5 x + 5 cos 5 x ] + c |
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| 37. |
Statement 1: In an ellipse the sum of the distances between foci is always less than the sum of focal distances of any point on it. Statement 2: The eccentricity of any ellipse is less than I. |
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Answer» Both the STATEMENT are True and statement 2 is the CORRECT explanation of statement 1 |
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| 38. |
Consider two point A(1,-1) and B(3,2) in the XY plane . P is a point divides the line segment AB externally in the ratio 1:2 .Find the co ordinate of P. |
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| 39. |
The orthocentre of the triangle formed by (0, 0), (3, 1), (1, 3) is |
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Answer» `(3//2, 3//2)` |
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| 40. |
Let S be the set of all 2xx2 real matrices A = [(a,b),(c,d)] such that a+d=3 and A=A^(2) -3A . Then |
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Answer» S CONTAINS infinite number of ELEMENTS |
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| 41. |
int tan^(2) (2x - 3) dx. |
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| 42. |
Statement 1: If the system of equations a_(1)x+b_(1)y+c_(1)z=0,a_(2)x+b_(2)y+c_(2)z=0 and a_(3)x+b_(3)y+c_(3)z=0 have a solution (alpha, beta, gamma) such that alpha beta gamma ne 0 then for any other non trivial solution (alpha_(1),beta_(1),gamma_(1)),alpha_(1).beta_(1).gamma_(1) ne 0. because Statement 2 : If alpha, beta, gamma is any non trivial solution of the equations a_(1)x+b_(1)y+c_(1)z=0,a_(2)x+b_(2)y+c_(2)z=0 and a_(3)x+b_(3)y+c_(3)z=0, then alpha beta gamma ne 0. |
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Answer» STATEMENT - 1 is TRUE, Statement - 2 is True, Statement - 2 is a correct EXPLANATION for Statement - 1 |
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| 43. |
The probability that a student passes a physics test is 2//3 and the probability that he passes both a physics test and an English test is 14//45. The probability that passes atleast one test is 4//5. The probability that he passes the English test is |
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Answer» `4//9` |
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| 44. |
Determine whether a ** b = 2a +3b "on" Zoperations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation. |
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Answer» Solution :For all `a,b in Z` `2A +3B in Z` ` implies a**b in Z` `:. ` * is a binary operation on Z. |
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| 45. |
The projection vector of bar(a) on bar(b) is …………. |
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Answer» `((BAR(a).bar(B))/(|bar(b)|^2)).bar(b)` |
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| 46. |
From first 20 natural numbers 1, 2, …., 20. Three are selected at random and found that they are in A.P., find the probability that the selected 3 numbers are in A.P. |
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| 47. |
If x^(2)/(12-k) -(y^(2))/(k-8)=1 represents a hyperbola then |
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Answer» `K LT 8` |
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| 48. |
Check , whether , (1)/(11)[{:(-1,8,alpha),(1,-19,14),(2,6,-5):}]is an inverse of A=[{:(1,2,5),(3,1,1),(4,2,1):}], if so , that alpha=…… |
| Answer» Answer :A | |
| 49. |
STATEMENT-1 :If the angle of a convex polygon are in A.P.120^(@) , 125^(@) , 130^(@) …, then it has 16 sidesand STATEMENT-2 :The sum of the angles of a polygon of x sides is(n -2) 180^(@) |
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Answer» Statemant-1 is True , Statement-2 is True, Statement -2 is a correct explanation for Statement-1 |
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| 50. |
Find the value of (i) (log_(10)5)(log_(10)20)+(log_(10)2)^(2) (ii) root3(5^((1)/(log_(7)5))+(1)/((-log_(10)0.1))) (iii) log_(0.75)log_(2)sqrtsqrt((1)/(0.125)) (iv)5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5) (v)((1)/(49))^(1+log_(7)2)+5^(-log_(1//5)7) (vi) 7^(log_(3)5)+3^(log_(5)7)-5^(log_(3)7)-7^(log_(5)3) |
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Answer» `(IV) -72` `(v) 7+(1)/(196)` `(vi) 0` |
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