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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 3601. |
Two cards are drawn from a pack of 52 cards, find the probability that they are of different suits. |
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Answer» SOLUTION :Two CARDS are drawn from a pack of 52 cards. The cards are drawn one after another. Each suit has 13 cards. `absS=^52C_2` As the two cards are of different SUITS, their probability `=52/52xx39/51` |
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| 3602. |
If 7 white, 6 black and 1 red ball is arranged in a row, the probabilitythe no two balls of the same colour are adjacent is : |
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Answer» `(2xx7!6!)/(14!)` |
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| 3603. |
Determine the truth of falsity of the For any object x, there is a set a such that,x cancelin A propositions with reasons. |
| Answer» Solution :For EVERY OBJECT X, there is a SET A such that, `x canclinA`.It is TRUE. | |
| 3605. |
If F_1 and F_2 are foci of the hyperbola x^2/a^2-y^2/b^2=1 and Pis any point on the hyperbola, then : ||PF_1|-|PF_2|| is equal to : |
| Answer» ANSWER :A | |
| 3606. |
If (sin(x //2) + cos (x//2) + itan x )/(1 + 2isin (x //2))is real then x = |
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Answer» `n pi or n pi + (pi)/(4)` |
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| 3607. |
The plane2x+3y+kz-7=0 is parallel to the line whose direction ratios are2, -3,1, then k = |
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Answer» 5 |
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| 3608. |
IFA+ B= (pi)/(4) then( tan A +1)( tan B+1)equals |
| Answer» Answer :C | |
| 3609. |
Let : f: N rarr N be defined by f(n)={{:((n+1)/2," if n is odd"),(n/2," if n is even"):} for all n inN . State whether the function f is bijective . Justify your answer. |
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| 3611. |
Let f(x)= minimum {e^(x),3//2,1+e^(-x)},0lexle1. Find the area bounded by y=f(x), X-axis and the line x=1. |
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| 3612. |
Examine the consistency of the system of equations 2x-y =5 x+ y =4 |
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| 3613. |
In a factory which manufactures bolts, machines A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B? |
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| 3614. |
Find the antiderivative (or integral) of the following functions by the method of inspection. cos3x |
| Answer» SOLUTION :`INT COS3X DX = (sin3x)/3 +c` | |
| 3615. |
Differentiate the functions with respect to x 2sqrt(cot(x^2)) |
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Answer» |
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| 3616. |
alpha and beta are the angles made by two tangents to the parabola y^(2) = 4ax, with its axis. Find the locus of their point of intersection, if cot alpha + cot beta=p |
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Answer» <P> |
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| 3617. |
The system of equations ((3,-2,1),(5,-8,9),(2,1,a)) ((x),(y),(z))=((b),(3),(-1)) has no solution if a and b are |
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Answer» a= -3 , B `NE` 1/3 |
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| 3618. |
The unit vector bar(a) and bar(b) are perpendicualr to each other. The unit vector bar( c ) makes an angle theta with bar(a) and bar(b). If bar( c )=alpha bar(a)+beta bar(b)+gamma(bar(a)xx bar(b)) then ………… |
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Answer» `alpha=2beta` |
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| 3619. |
If (1)/((1+2x)(1-x^(2)))=(A)/(1+2x)+(B)/(1+x)+(C)/(1-x) then assending order of A, B, C. |
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Answer» A, B, C |
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| 3620. |
Write the equation of the plane perpendicular to z-axis and passing through (1,-2,4). |
| Answer» SOLUTION :GIVEN PLANS `2x+4y+z+2=0` and `x-2y+ky+5=0` are PERPENDICULAR to each other `therefore2xx1+4xx(-2)+1xxk=0rArrk=6` | |
| 3621. |
Solve as directed : 2x + 3 gt x-7 in R |
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Answer» Solution :2X + 3 `gt` X-7 `rArr 2x - x gt -7 - 3` `rArr x gt -10` x `in` R the solution set is S = {x:x `in` R and x `gt` -10 } = (-10, `INFTY`) |
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| 3622. |
One ticket is selected from pack of 100 tickets numbered with 00, 01, 02, 03 … 99. If X and Y denotes the sum and product of numbers obtain on it then P((X = 7) /(Y = 0)) =……… |
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Answer» `(2)/(3)` |
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| 3623. |
intdx/(sqrtx+x) |
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Answer» SOLUTION :`I=INTDX/(SQRTX+x)=intdx/(sqrtx(1+sqrtx))` LET `1+sqrtx=t` `rArr1/(2sqrtx)dx=dt` =`2intdt/t=2Inabst+C` =`2Inabs(1+sqrtx)+c` |
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| 3624. |
State which of the following is not true ? |
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Answer» 5 |
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| 3625. |
Find the values of the following(1+isqrt3)1/3^ |
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| 3626. |
If P, Q, R and S are the points with position vectors hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatkandhati-6hatj-hatk respectively, then the angle between PQ and RS is |
| Answer» ANSWER :A | |
| 3627. |
Find the mean and variance of the random variable X whose distribution is |
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| 3628. |
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is : |
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Answer» 2.57 |
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| 3629. |
If the middle term in the expansion of (1+x)^(2n) is the greatest term, then x lies in the interval |
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Answer» `N-1 lt X lt n` |
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| 3630. |
Evaluate the following define integrals as limit of sums : int_(0)^(4) (x +e^(2x))dx |
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| 3631. |
Solve the following differential equations (i) x(dy)/(dx) + 2y = log x (ii) xlog x(dy)/(dx) + y = 2 log x |
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Answer» (ii) `y log x = (log x)^(2) + c` |
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| 3632. |
Minimise and minise Z=3x-4y subject to x-2y le 0, -3x+y le 4, x-y le 6 and x,y le 0 |
Answer»  From the shown graph, for the feasible region, we see that it is unbounded and coordinates of corner points are (0,0),(12,6) and (0,4)  For given, unbounded reigon the MINIMUM value of Z may or may be -16 So, for deciding this, we graph the inequality 3x-4y larr16 and check whether the resulting open half plane has common points with feasible region or not. Thus, from the figure it shows it has common points with feasible region, so it does not have any minimum value. Also, SIMILARLY for maximum value, we graph the in equality `3x-4y gt 12` nad see that resulting open half plane has no common points with the feasibleregion and HENCE maximum value for Z=3x-4y. |
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| 3633. |
Let hata and hatb be two unit vectors. If the vectors c=hata+2hatb and d=hata-4hatb are perpendicular to each other, then the angle between hata and hatb is |
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Answer» `(pi)/(6)` `thereforec*d = 0` `RARR (hata + 2hatb)*(5 hata - 4 HATB) = 0 ` `rArr 5 hata * hata - 4 HAT a *hat b + 10 hat b * hata - 8 hatb * hatb = 0 ` ` rArr6 hata * hatb= 3 ` `rArr hata *hatb= (1)/(2)` So, the angle between `hata and hatb` is `(pi)/(3)`. |
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| 3634. |
Find the number of ways of arranging 7 guests and a host around a circle if 2 particular guests wish to sit on either side of the host. |
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| 3635. |
(cosalpha+isinalpha)^(5)/((sinbeta+icosbeta)^(3))= |
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Answer» `SIN(5alpha+3alpha)+i COS (5alpha+3beta)` |
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| 3636. |
For 0ler < 2n, (""^(2n + r)C_(n)) (""^(2n-r)C_(n)) cannot exceed |
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Answer» `""^(4n)C_(n-)` |
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| 3637. |
If f(x) be any function, which assumes only positive value and f'(x) exists, then f'(x) is |
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Answer» `F(X)=(d)/(dx)(e^(LOGF(x)))` |
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| 3638. |
If a + b = k,when a, b gt o and S(k, n) = sum _(r=0)^(n) r^(2) (""^(n) C_(r) ) a^(r) cdot b^(n-r), then |
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Answer» `S(1,3) =3 (3A^(2)+ab) ` `=b^(n) sum_(r=0)^(n) r^(2) cdot (""^(n/r) cdot^(n-1)C_(r-1))cdot (a/b)^(r)` `nb^(n)sum_(r=0)^(n) ((r-1) + 1) ^(n-1) C_(r-1)cdot (a/b)^(r)` `nb^(n)sum_(r=0)^(n) ((n-1) cdot ^(n-1)C_(r-2)+^(n-1)C_(r-1)) (a/b)^(r)` `=nb^(n) cdot (n-1) cdot (a/b)^(2) sum _(r=0)^(n) ""^(n-2)C_(r-2)(a/b)^(r-2)` `+nb^(n)cdot (a/b)sum_(r=o)^(n) ""^(n-1) C_(r-) (a/b)^(r-1)` `=nb^(n) cdot (n-1)(a/b)^2(1+a/b) ^(n-2) + nb^(n) cdot (a/b) .(1+a/b)^(n-1)` `= n(n-1) a^(2)k^(n-2)+nak^(n-1)` `=n^2a^(2)k^(n-2) + nak^(n-2) (k-a) = n^(2)a^(2) k^(n-2) + nabk^(n-2)``THEREFORE S(1,3) = 9a^(2) + 3ab = 3 (3a^(2) + ab)[because a + b = k]` `S(2,4) = 16 (4a^(2) + ab)` `S(3,4) = 135 (5a^(2) + ab)` ` S(4,6) = 1536 (6a^(2)+ab)` |
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| 3639. |
When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is: |
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Answer» forward for all tires |
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| 3640. |
There are two bags I and IL Bag I contains 3 white and 4 black balls, and bag II contains 5 white and 6 black balls. One ball is drawn at random from one of the bags and is found to be white. Find the probability that it was drawn from bag I. |
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| 3641. |
(3x^(2)+x+1)/(x-1)^(4)=a/(x-1)+b/(x-1)^(2)+c/(x-1)^(3)+d/(x-1)^(4) rArr [{:(a,b), (c, d):}]= |
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Answer» `[(3,7),(5,0)]` |
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| 3642. |
Construct Collection of all kings having more than one queens in the form of set and describe it with the help of proposition. |
| Answer» SOLUTION :B ={X:x is a KING having more than ONE queen.} | |
| 3643. |
f(x) = (1- tan x)/(4x-pi), x ne (pi)/(4). If the function f(x), x in [0, (pi)/(2)) is continuous then find f((pi)/(4)). |
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| 3644. |
Let R = {(a,a^3) | ais a prime number less than 10}.Find rng R. |
| Answer» Solution :R = {(a,a^3)| a is a PRIME NUMBER LESS than 10. rng R = {8,27,125,343} | |
| 3645. |
If a+b+c=0 and |a|=sqrt(37),|b|=3, |c|=4 then the angle between b and c is |
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Answer» `30^(@)` Now, `a+b+c=0` `implies a=-(b+c)` `implies |a|^(2)=|-(b+c)|^(2)` `implies |a|^(2)=|b|^(2)+|c|^(2)+2|b||c| cos theta` `=9+16+24 cos theta` `implies 37=25+24 cos theta` `implies 24 cos theta =12 implies theta = 60^(@)` |
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| 3646. |
If int (6x + 7)/((x+ 2)^(2))dx = A in |x+2| + (B)/(x + 2)+ c then (A,B) = |
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Answer» `(6, (1)/(5)) ` |
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| 3647. |
A,B,C, are three non-collinear points with position vector veca, vecb,vecc respectively. Given, P,Q, R are points on BC, CA and AB respectively such that: BP : PC =CQ :QA =AR: RB=1:2 Find the position vectors of the vertices of the triangle XYZ formed by the lines AP, BQ, CR. Hence show that the centroid of triangleABC is same as that of triangleXYZ |
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| 3648. |
Find the equation of locus of P ifA=(4,0),B(-4,0) and |PA-PB|=4 |
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| 3649. |
Let I=int_(pi//4)^(pi//3)(sinx)/(x)dx. Then |
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Answer» `(1)/(2)leI le 1` |
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| 3650. |
Integrate the following functions : intsin^(3)xcos^(2)xdx |
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