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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.
| 6351. |
Given that E and F are events such that P(E)=0.6, P(F)=0.3 and P(E cap F)=0.2, find P(E//F) and P(F//E). |
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Answer» <P> |
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| 6352. |
If the Argand plane, the points represented by the complex numbers 7-4i,-3+8i,-2-6i and 18i form |
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Answer» PARALLELOGRAM |
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| 6353. |
f:AtoA,A={a_(1),a_(2),a_(3),a_(4),a_(5)}, the numberof one one functions so that f(x_(i))nex_(1),x_(i)inA is |
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Answer» 44 |
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| 6355. |
Find the approximate value of each of the following :log_(e )(10.02) |
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| 6356. |
Evaluate the following integrals intx^(2) tan^(-1)x dx |
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| 6357. |
Find Order and Degree of given differential equation. y' + 5y = 0 |
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| 6358. |
Evalute the following integrals int (dx)/(sqrt(x^(2) - 36)) |
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| 6359. |
Which one is the contrapositive of the statement (p wedge q) to r? |
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Answer» <P>`~ r to (~p WEDGE ~q)` |
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| 6360. |
Show that the locus of a point such that the product of the perpendiculars let fall from it on three lines represented by ay^3+by^2+cyx^2+dx^3=0 is constant =k^3 ,is ay^3+by^2+cyx^2+dx^3=k^2sqrt((a-c)^2+(b-d)^2). |
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| 6361. |
A contractor submitted tenders for 2 works. If 0.4, 0.6, 0.1 are the respective probabilities that his first tender, atleast one tender, both the tenders are accepted, what is the probability that his second tender is accepted. |
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| 6362. |
Write down the equation of the normal at theta = (pi)/(3) to the hyperbola 3x^(2) - 4y^(2) = 12 |
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| 6363. |
{{:(4x-5y=10),(2x+3y=-6):} If the solution to the system of equations above is (x,y), what is the value of y? |
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Answer» `-2` `2 (2x+3y=-6)` `4x + 6y=-12` Now that the coefficients for one variable are the same, SUBTRACT the second equation from the first to eliminate the x variable. (Note that if the x-coeffcients were 4 and -4, you would add the equations instead of SUBTRACTING.) `4x-5y=10` `(-(4x+ 6y=-12))/(0x-11 y =22)` Solve this equation for y: `-11=22` `y = -2` (A) is the correct answer. If the question asked for x instead of y, you would now substitute -2 into either of the original equations and solve for x. (For the record, `x =0.)` |
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| 6364. |
If M_(g,x) is the geometric mean of N x's and M_(g,y) is the geometric mean of N y's, then the grometric mean M_(g)of the 2N values is |
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Answer» `Nsqrt(M_(g,X)M_(g,y))` |
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| 6365. |
f : R rarrR , f(x) = 2 x + |cosx|then f is ......... function . |
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Answer» ONE one and ONTO |
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| 6366. |
Choose the correct answer: Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is |
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Answer» 37/221 |
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| 6367. |
The solution of x^(2) (dy)/(dx) = sqrt(4 - y^(2)) is |
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Answer» `Cos^(-1)((y)/(2)) + (1)/(X) = c` |
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| 6368. |
Which of the following options is the only CORRECT combination? |
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Answer» <P>(I)(II)(Q) |
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| 6369. |
All the 7-digit numbers containing each of the digits 1,2,3,4,5,6,7 exactly once, and not divisible by 5, are arranged in increasing order. Find the 3200^(th) number in the list |
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| 6370. |
Which of the following options is the only CORRECT combination? |
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Answer» <P>(II)(i)(P) |
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| 6371. |
If vec(a)=2hat(i)+2hat(j)+3hat(k),vec(b)=-hat(i)+2hat(j)+hat(k)andvec(c)=3hat(i)+hat(j), then vec(a)+tvec(b) is perpendicular to vec(c), if t is equal to |
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Answer» 2 |
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| 6372. |
Which of the following options is the only CORRECT combination? |
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Answer» <P>(III)(ii)(Q) |
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| 6373. |
If S-= x^(2) + y^(2) + 2gx + 2fy + c= 0repre- sents a circle then show that the straight line lx + my + n = 0 (iii) will not meet the circle if g^(2)+f^(2)-c lt ((gl+mf-n)^(2))/((l^(2)+m^(2))) |
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| 6374. |
Let L_1be the length of the common chord of the curvesx^(2)+y^(2) = 9 and y^(2) =8xand L_ 2be the length of the latus rectum of y^(2) =8x,then |
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Answer» ` L_ 1 GT L_2` |
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| 6375. |
A positive integer n is of the form n = 2 alpha 3 beta , where alpha, beta ge 1. If n has 12 positive divisors and 2n has 15 positive divisors then number of positive divisors of 6n is |
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Answer» 21 `(alpha+2)(beta+1)=15` `implies beta = 2, alpha = 3` Now `(alpha+2)(beta+2) = 5xx4 = 20`. |
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| 6376. |
if f(x) ={: (x-5, " for "x le 1), ( 4x^(2) -9 , " for " 1 lt x lt 2 " then" f 2^(+) " isequal " ), ( 3x +4 , " for" x gt 2):}to |
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Answer» 0 |
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| 6378. |
Given the functionf(x) = {{:(1-x " at " 0 le x le 1),(0 " at " 1 lt x le 2),((2-x)^(2) "at " 2 lt x le 3):} Checkdirectly that thefunctionF(x) = int_(0)^(x) f(t) dt iscontinuous on the interval [0,3] and that itsderivative at each interior point of thisinterval exists andis equalto f(x) |
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| 6379. |
Evaluate: int("ln"(1+sin^(2)x))/(cosalpha+cosx)dx |
| Answer» Solution :`TANX"LN"(1+sin^(2)X)-2x+SQRT(2)tan^(-1)(sqrt(2).tanx)+C` | |
| 6380. |
A plane meets the coordinate axes A,B,C so that the centroid of the triangle ABC is (1,2,4) . Then ,the equation of the plane is |
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Answer» `x+2y+4z=12` |
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| 6381. |
If (2x^(2)+3x+4)/((x-1)(x^(2)+2))=A/(x-1)+(Bx+C)/(x^(2)+2), " then "B= |
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Answer» -2 |
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| 6382. |
Three forces having magnitude 5,4 and 3 units act on a particle in the directions 2i - 2j + k, i + 2j + 2k and -2i + j - 2k respectively and the particle gets displaced from the point A whose vector is 6i - 2j + 3k to the point whose position vector is 9i + 7j + 5k. Then the work done by these forces is |
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Answer» 9 unit |
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| 6383. |
A straight line is equally inclined to all the three coordinate axes. Then , an angle madebythe line with the y - axis is , |
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Answer» `cos^(-1)(1/3)` |
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| 6386. |
A (3,4,5 ),B (2,3,1 ),C(-1,6,1 ) are the vertices of a triangle then I: The circumcenter of triangle ABC is (1,5,3 ) II: the orthocenter of triangle ABC is (2,3,1 ) |
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| 6387. |
If A, B, C and D are four points in the plane such that |AB|^(2)+|CD|^(2)=|BC|^(2)+|DA|^(2)=100, then AC*BD = |
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Answer» 10 |
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| 6388. |
If n persons are sitting in a row, find the number of ways of selecting two persons, who are sitting adjacent to each other. |
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| 6389. |
Evalute the following integrals int (1)/(x^(2) sqrt(1 + x^(2)))dx |
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| 6390. |
If theta is the acute angle between any two vectors " "veca" and "vecb, then|veca.vecb|=|vecaxxvecb| when thetais equal to : |
| Answer» ANSWER :B | |
| 6391. |
Glucoma is caused by increase in : |
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Answer» Intraarterial pressure |
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| 6392. |
Evaluate the following integrals. int(x-1)/((x-2)(x-3))dx |
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| 6393. |
If the position vectors of A, B are i + 2j - 3k, 3i - 2j + 5k respectively then the position vector of C in AB produced such that 2 AC = 3 AB is |
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Answer» (1/3) (-4I + 5J + 17K) |
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| 6394. |
When two balls are drawn from a bag containing 2 white, 4 red and 6 black balls, the chance for both of them to be red is…………… |
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Answer» `(1)/(11)` |
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| 6395. |
The value of the integral int_(1)^(3^(1//n)) (dx)/(x^(n)+1)is |
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Answer» `(1)/(n)log ((2)/(3))` |
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| 6396. |
If y=(2x)^(sec x) +(tan x)^(x) ,then(dy)/(dx)= |
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Answer» ` (2x)^(SECX) secx ((1)/(x) +tan XLOG (2x)) +2(secx )^(2x) (xtan x+log(SEC x)) ` |
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| 6397. |
Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 1%. |
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| 6398. |
If alpha and betaare roots of ax^(2)+bx+c=0then theequation whose roots are alpha^(2) and beta^(2) is |
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Answer» `a^(2)x^(2)-(B^(2)-2AC)x+c^(2)=0` |
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| 6399. |
Integrate the functions (5x)/((x+1)(x+9)) |
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| 6400. |
Find the Coefficient of x^(n) in ((1+x)/(1-x))^(2) |
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