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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. |
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him? |
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| 4. |
A(3, 2, 0), B(5, 3, 2), C(-9, 6, -3) are three points forming a triangle and AD, the external bisector of BAC, meeting BC at D then find D. |
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| 5. |
Let A denote the plane consisting of all poins that are equdistant from the points P (-4,2,1) and Q(2, -4, 3) and B be the plane x - y + cz = 1where c in RIf the angle between the planes A and B is 45^(@) then the product of all possible values of c is |
| Answer» ANSWER :B | |
| 6. |
Let A denote the plane consisting of all poins that are equdistant from the points P (-4,2,1) and Q(2, -4, 3) and B be the plane x - y + cz = 1where c in R If the line L with equation (x-2)/(1) = (y-1)/(3) = (z-5)/(-1) intersects the plane A at the point M (lamda, mu , v) then coordinate of M is |
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Answer» `((8)/(7), (11)/(7), (41)/(7))` |
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| 7. |
If the line ax+by=1 passes through point of intersetion ofy=x tanalpha+psec alpha, ysin(30^@-alpha)-xcos(30^@-alpha)=p " and in inclined at " 30^@ " with " y=tanalpha," then " a^2+b^2= |
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Answer» `1/p^2` |
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| 8. |
From the employees of a company, 5 person are selected to repreent them in the managing committee of the company. Particular of five persons are as follows: {:("S.No.","Name ","sex","age in years"),(1.,"harish ",M,30),(2. , "Rohon",M,33),(3.,"sheetal",F,46),(4.,"Alis",F,28),(5. ,"Salim",M,41):} A person is selected at random from this group to act as a spokespersons. What is the probability that the spokespersons will be either male or over 35 years? |
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| 9. |
...........is the measure of an angle in radian through which the pendulum swings if its length is 75 cm and makes an arc of length 21 cm |
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| 10. |
Transform the following equations intothe form L_(1)+lamdaL_(2)=0 and find the point of concurrency of the family of straight lines represented by the equation (2+5k)x-3(1+2k)y+(2-k)=0 |
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| 11. |
On the interval [(5pi)/(4),(4pi)/(3)]the least value of the function f(x)=int_(5x//4)^(x)(3sint+4cost)dt is |
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Answer» `(3)/(2)+(1)/(SQRT(2))-2sqrt(3)` |
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| 12. |
If A=[(0,-1),(1,0)]B=[(0,i),(i,0)]C=[(i,0),(0,-i)] then |
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Answer» `A^(2)=B^(2)=C^(2)=0` |
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| 13. |
Solve each of the following equations for real x and y : x+2yi= i - (-3 + 5) |
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| 14. |
Write the component statements of the following compound statements and check whether the compound statement is true or false: (i) the perimeter of a right-angled triangle and an equilateral triangle is equal to the sum of three sides. (ii) 72 is a multiple of 18 and 24. (iii) 0 is smaller than every positive integer and every negative integer. (iv) a line is straight and extends indefinitely in both directions. |
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Answer» Solution :(i) component statements L: p: the perimeter of a right -angled triangle is equal to the sum of three sides. q : the perimeter of an equilateral triangle is equal to the sum of three sides . compound statements is true. (ii) component statements : p: 72 is a multiple of 18. q: 72 is a multiple of 24. compound statement is true. (iii)compound statements : p: 0 is smaller than EVERY positive integer. q: 0 is smaller than every negative integer. compound statement is false. (iv) component statements : p: a LINE is straight. q: a line EXTENDS indefinitely in both dirction . |
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| 15. |
Write down the converse of following statements: If S is a cyclic quadrilateral, then the opposite angles fo S are supplementary. |
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| 16. |
For all values of theta, the values of 3-cos theta+cos (theta+(pi)/(3)) lies in the interval |
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Answer» `[-2,3]` |
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| 17. |
Which of the following sets are finite or infinite The set of months of a year |
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| 18. |
Show that the line 3x+4y +20=0 touches the circle x^(2) + y^(2) =16 and find the pointof contact |
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| 20. |
If x takes negative permissible value, then sin^(-1)x= |
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Answer» `Cos^(-1)SQRT(1-X^(2))` |
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| 21. |
The sum of …….terms of on A.P. 3, 7, 11, 15,….. Will becomes 406 |
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Answer» 5 |
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| 23. |
Find the sum of n terms of the following series : (i) 5+55+555+… (ii) 4+44+444+… (iii) 0.3+0.33+0.333+… (iv) 0.7+0.77+0.777+… |
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| 24. |
If z_(1), z_(2), z_(3), z_(4) are complex numbers, show that they are vertices of a parallelogram In the Argand diagram if and only if z_(1) + z_(3)= z_(2) + z_(4) |
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| 25. |
Let the function f (x) be defined as follows : f(x)={{:(x^(3)+x^(2)-10x",",-1lexlt0),(cosx",",0lexlt(pi)/(2).),(1+sinx",",(pi)/(2)lexlepi):}Then f(x) has |
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Answer» a local minimum at `x=(pi)/(2)` |
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| 26. |
If no solution of 3siny+12sinx^(3)=a lies on the line y=3x, then |
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Answer» `a in (-OO, -9)UU(9,oo)` |
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| 27. |
Find a if the coefficients of x^2 and x^3 in the expansion of 3 + ax)^9 are equal. |
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| 28. |
ABC is a right angled triangle right angled at A. If B(2,0,2) and C(0,-1,-1) are the two vertice and the equation to the locus of A isx^(2)+y^(2)+z^(2)+px+qy+rz+s =0 , " then " p+q+r+s is equal to |
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Answer» -1 |
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| 29. |
Find the stationary points and stationary values for the following functions. x^(2) + (16)/(x) |
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| 30. |
A function f: R rarr R satisfies sin x cosy (f(2x2y))-f(2x-2y))= cosxsiny(f(2x+2y))+f(2x-2y))If f'(0)=1/2 , then |
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Answer» `F''(x) = f(x) =0` |
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| 31. |
If the foot of the line perpendicular from (-4,5) to the straight line 3x-4y-18=0 is (alpha, beta) then the value of alpha+beta= |
| Answer» ANSWER :B | |
| 32. |
The value of k, if the angle between the straight lines 4x-y+8=0,kx-5y-9=0 is 45^(@) is |
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Answer» `(-25)/3,3` |
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| 33. |
Differentiatesqrt( ax+b) with respect to x from definition. |
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| 34. |
Sum of n^( th) bracket of (1) + (2+ 3+4) + ( 5+ 6+ 7+ 8+9) + ….. is |
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Answer» 65225 |
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| 35. |
Find the gradient of the straight line joining between two points (7,3) and (8,12) |
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| 36. |
Identify the Quantifiers in the following statements: For every natural number x,x+1 is also a natural number. |
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| 37. |
A man starts repaying a loan as first instalment of Rs 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30^(th) instalment? |
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| 38. |
If a:b:c: =3:5:5 then "cot"(A)/(2)":cot"(B)/(2):"cot"(C)/(2)= |
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Answer» `5:6:7` |
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| 39. |
State whether the given statement is true or false : (i) if A sub B andx linthen x lin A. (ii) If A sube phi then A = phi (iii) If A,B and C are three sets such thatin B and B sub C then A sub C . (iv) If A, B and C are three sets such that A sub B and B in C " then "A in C. (v) If A, Band C are three sets such tahtA cancel(sub) B and B cancel(sub)C " then " A cancel(sub)C. (vi) If A, B are sets such thatx in A and A in B then x in B. |
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Answer» Then , `{a} in B` and `B SUB C`. But., `{a} CANCEL(sub) C`. (iv) Let A = {a}, B = {a, b} and C = {{a, b}, c}. Then, `A cancel(sub) B` and `B in C`.But, `A cancel(in)C`. Let A= {a}, B = {b,c} and C = {a, c}. Then, `A cancel(sub)B` and `B cancel(sub)C`. But `A sub C`. Let A= {x}, B = {{x}, y}. Then, `x in A` and `A in B`. But, `x in b`. |
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| 40. |
A ladder rests against wall at an angle alpha to the harizontal. Its foot is pulled away from the wall through a distance 'a' so that it slides a distance 'b' down the wall making an angle beta with the horzontal, then tan((alpha+beta)/2)= |
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Answer» `b//a` |
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| 41. |
Write out the expansions of the following: (3+2x^(2) )^(4) |
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| 42. |
Find the derivative of the following from the first principle. (i) sin x^(2) , (ii) cos (x^(2)+ 1) (iii) tan x^(2) |
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Answer» Solution :(i)Let `y = sin^(2)X` . Let `deltay` be an increment in y, corresponding to an increment `deltax`in `x`. Then, `y + deltay = sin(x+deltax)^(2)` `rArr deltay = sin(x+deltax)^(2)` `rArr (deltay)/(deltax) =(sin(x+deltax)^(2) - sinx^(2))/(deltax)` `rArr (dy)/(dx) = underset(deltaxrarr0)("lim") (deltay)/(deltax)` `= underset(deltaxrarr0)("lim") (sin(x+deltax)^(2) - sinx^(2))/(deltax)` `= underset(deltaxrarr0)("lim") (2cos[((x+deltax)^(2) + x^(2))/(2)] sin [((x+deltax)^(2) -x^(2))/(2)])/(deltax)` [Using `[using(sin C - sinD) = 2 COS((C+D)/(2)) sin((C-D)/(2))]` `= underset(deltaxrarr0)("lim") 2cos[((x+deltax)^(2) + x^(2))/(2)] (sin[(x+(deltax)/(2)).deltax])/((x+(deltax)/(2)).deltax).(x+(deltax)/(2))` `2.underset(deltararr0)("lim")cos[((x+deltax)^(2)+x^(2))/(2)].underset(deltararr0)("lim") (sin[(x+(deltax)/(2)).deltax])/((x+(deltax)/(2)).deltax).underset(deltaxrarr0)("lim") (x+(deltax)/(2))` `= [2xx COSX^(2) xx 1 xx x] = 2x cos x^(2)`. Hence, `d/(dx) (sinx^(2)) = 2x cos x^(2)`. (ii) Let `y = cos(x^(2) + 1)` . Let `deltay` be an increment in y, corresponding to an increment`deltax` in x. Then, `y + deltay = cos[(x+deltax)^(2) + 1]` `rArr deltay = cos[(x+deltax)^(2) + 1] - cos(x^(2) + 1)` `rArr (deltay)/(deltax) = (cos[(x+deltax)^(2) + 1] - cos(x^(2) + 1))/(deltax)` `rArr (dy)/(dx) = underset(deltaxrarr0)("lim") (deltay)/(deltax)` `=underset(deltaxrarr0)("lim")({cos[(x+deltax)^(2)+1]-cos(x^(2)+1)})/(deltax)` `=underset(deltaxrarr0)("lim") (-2sin'[({(x+deltax)^(2) + 1+ (x^(2)+1)})/(2)].sin[({(x+deltax)^(2)+1-(x^(2)+1)})/(2)])/(deltax)` `=-2.underset(deltaxrarr0)("lim")sin[x^(2)+x.deltax+1+((deltax)^(2))/(2)].(sin[(x+(deltax)/(2)).deltax])/([(x+(deltax)/(2)).deltax]).(x+(deltax)/(2))` `=-2.underset(deltaxrarr0)("lim")sin[x^(2)+x.deltax+1+((deltax)^(2))/(2)].underset(thetararr0)("lim") (sintheta)/(theta).underset(deltaxrarr0)("lim") (x+(deltax)/(2))`. where `theta = (x+(deltax)/(2)).deltax` clearly, `[deltaxrarr0] rArr[theta rarr 0]` `=- 2sin(x^(2)+ 1) xx 1 xx x` `= -2x sin (x^(2) + 1)`. Hence, `d/(dx) [cos(x^(2) + 1)] = - 2xsin (x^(2) + 1)`. (iii) Let `y = TAN^(2) x^(2)` Let `deltay` be an increment in y, correponding to an increment `deltax`in x. Then, `y + deltay = tan(x+deltax)^(2)` `rArr deltaxy = tan(x+deltax)^(2) - tanx^(2)` `rArr (deltay)/(deltax) = (tan(x+deltax)^(2) - tanx^(2))/(deltax)` ` rArr (dy)/(dx) = underset(deltax rarr0)("lim") (deltay)/(deltax) = underset(deltaxrarr0)("lim") (tan(x+deltax)^(2) - tanx^(2))/(deltax)` `= underset(deltaxrarr0)("lim") ({(sin(x+deltax)^(2))/(cos(x+deltax)^(2))- (sinx^(2))/(cosx^(2))})/(deltax)` `= underset(deltaxrarr0)("lim")([sin(x+deltax)^(2)cos x^(2)-cos(x+deltax)^(2)sinx^(2)])/(deltax.cos(x+deltax)^(2).cosx^(2))` `= underset(deltaxrarr0)("lim")(sin[(x+deltax)^(2)-x^(2)])/(deltax.cos(x+deltax)^(2).cosx^(2))` `= underset(deltaxrarr0)("lim")(sin[(2x+deltax).deltax])/([(2x+deltax).deltax]) .((2x+deltax))/(cos(x+deltax)^(2).cosx^(2))` `= (underset(thetararr0)("lim") (sintheta)/(theta)). underset(deltaxrarr0)("lim") (2x+deltax). underset(deltaxrarr0)("lim") (1)/(cos(x+deltax)^(2).cosx^(2))` where `(2x+deltax). deltax = theta` [clearly, `(deltaxrarr0) rArr (theta rarr0)`] `= 1 xx 2xxx (1)/(cosx^(2).cosx^(2)) = 2x SEC^(2)x^(2)`. Hence `d/(dx) (tan x^(2)) = 2 x sec^(2) x^(2)`. |
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| 43. |
Sum of roots of the equation x ^(4) - 2 x ^(2) sin ^(2)""(pi x)/(2) + 1 = 0is |
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Answer» 0 |
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| 44. |
If 4sin^(2)x+cos^(4)x=1, then one general value is: |
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Answer» `(NPI)/(12)` |
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| 45. |
The points (-2, 3, 5 ) (1,2,3 ) (7,0,-1 ) are |
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Answer» collinearpoints |
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| 46. |
Give negation of the followings: Every natural number is an integer. |
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| 47. |
If the period of oscillation of a simple pendulum is increased by a% then the percentage increase in its length is |
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Answer» `a//2` |
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| 48. |
In a binomial expansion, ( x+ a)^(n), the first three terms are 1, 56 and 1372 respectively. Find values of x and a. |
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| 49. |
The value of 'a' for which x^(3)-3x +a=0 has two distinct roots in [0,1] is given by |
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Answer» `-1` |
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