InterviewSolution
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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.
| 2502. |
What is the value of x that satisfies the equation:sqrt(x-3)=sqrt(2x+2)-2? |
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Answer» 4 |
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| 2503. |
Thevolume of arightcircularconewiththe bottomremovedto createa flatbasecan becalculatedwith thefollowingequation: V= (1)/(3)pi h ( R^(2) +r ^(2) +Rr),whereh representsthe heightof theshapeand Rand rrepresent itsradii , as shownin the figurebelow: THisformulacan bedeterminethe capacityof alargecoffeemug.Approximatelyhowmanycubicinchesof liquidcanthe cupshownbelowholdif itis filledto thebriumand itshandleholdsno liquid ? |
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Answer» 19 |
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| 2504. |
Evaluate int "x sin"^(2) x dx |
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Answer» |
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| 2505. |
x^(2)+y^(2)+2x+4y-20=0andx^(2)+y^(2)+6x-8y+10=0 are the given circles. Which one of the following is correct? |
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Answer» They INTERSECT ORTHOGONALLY and will have two common tangents. The LENGTH of their common chord is `(5sqrt3)/sqrt2` |
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| 2506. |
Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,findgog. |
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| 2507. |
On a certain exam, the medium grade for agroup of 25 students is 67. If the highest grade on the exam is 90, which of the following could be the number of students that scored 67 on the exam? I. 5 II. 20 III. 24 |
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Answer» I only |
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| 2508. |
If 4i + 7j + 8k, 2i + 3j + 4k, 2i + 5j + 7k are position vectors of A, B, C of Delta ABC then position vector of the point where the bisector of angle A meets BC is |
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Answer» `2i + (11)/(3) J + (17)/(3)k` |
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| 2509. |
The volume of the tetrahedron whose vertices hati-6hatj+10hatk,-hati-3hatj+7hatk,5hati-hatj+lambda hatk and 7hati-4hatj+7hatk is 11 ("unit")^(3) then lambda = ………….. |
| Answer» ANSWER :C | |
| 2510. |
Find x and y :[[x,-2y],[0,-2]]=[[1,-8],[0,-2]] |
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Answer» Solution :`[[X,-2y],[0,-2]]=[[1,-8],[0,-2]]` `:.x=1,-2y=-8` `x=1,y=4` |
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| 2511. |
The polygon in which no. of diagonals is twice the no. of sides is |
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Answer» HEXAGON |
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| 2512. |
If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then |
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Answer» `log_(E )((1+X)/(1-x))` |
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| 2514. |
Let X denote the number of hours you study during a randomly selected school day. The probability that X take the values of x has the following form, where k is some unknown constant. P(X=x)={(0.1 "if" x=0),(kx, "if" x=1 "or"2),(k(5-x),"if"x=3"or"4),(0,"otherwise"):} Find: (i) k (ii) the probability that you study exactly two hours, (iii) the probability that you study at most two hours. |
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| 2515. |
Construct truth tables for the following and indicate which of these are tautologies (~~p vv p) rarr ( ~~q vv q) |
Answer» SOLUTION :
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| 2516. |
C_1 + 2. C_2 + 3. C_3 + …... + n. C_n= |
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Answer» `2^n` |
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| 2517. |
For each of the differential equations , find the particular solution satisfying the given condition : 11.( x + y) dy + ( x - y) dx = 0, y = 1 when x = 1 |
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| 2518. |
int (cos x + x sin x)/(x (x - cos x))dx= |
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Answer» `log | 1 - (cos x)/(x) | +C` |
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| 2520. |
Let P and Q be 2 circles externally touhing each other at point X. Line segment AB is a direct common tangent to circle P and Q at points A and B respectively. Another common tangent to P andQ at X intersects line AB at a point Y. If BY = 10 units and the radius of P is 9 units, then the value of the reciprocal of the radius of the radius of the circle Q is equal to |
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| 2521. |
If A is a square matrix of order 3 and |A|=2, then the value of |-A A'| is |
| Answer» ANSWER :D | |
| 2522. |
Statement -1 Consider the determinant Delta=|{:(a_(1)+b_(1)x^(2),a_(1)x^(2)+b_(1),c_(1)),(a_(2)+b_(2)x^(2),a_(2)x^(2)+b_(2),c_(2)),(a_(3)+b_(3)x^(2),a_(3)x^(2)+b_(3),c_(3)):}|=0, where a_(i),b_(i),c_(i) inR (i=1,2,3) and xin R Stement -2 If |{:(a_(1),b_(2),c_(3)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| =0, then Delta =0 |
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| 2523. |
Statement-I : If a Iatusrectum of an ellipse subtends angle 60^(@) at the farthest vertex then eccentricity is 1-(1)/sqrt(3)Statement-II : If a Iatusrectum subtends 60^(@) at the centre of the ellipse then ecentricity is (sqrt(13)-1)/(2sqrt(3)) |
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Answer» only I |
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| 2524. |
A rectangle HOMF has sides HO=11 and OM=5. A triangle ABC has H as the intersection of the altitude, O the centre of the circumscribed circle M the mid point of BC, and F the foot of the altitude from A, then |
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Answer» perimeter of `DeltaABC`is greater than 70 Since `/_HFB=/_AFC, /_HBF=/_ACF` So `,DeltaBFH` and `DeltaAFC` are similar `(BF)/(HF)=(AF)/(FC)impliesBF.FC=FA.HF=75` Now `BC^(2)=(BF+CF)^(2)=(BF-CF)^(2)+4BF.FC` But `FC-BF=(FM+MC)-(BM-FM)=2FM=22` `BC=sqrt(22^(2)+4xx75)=28` 
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| 2525. |
Select reagent (s) which is /are used in laboratory to differentiate 1^(@), 2^(@) and 3^(@) amines from each other: |
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Answer» `NaNO_(2), HCl` `2^(@)underset(HCl)overset(NaNO_(2))rarrR-N-N=O` (Oily liquid) `3^(@) underset(HCl)overset(NaNO_(2))rarr`Salt (B) Hinsberg's test can distinguish `1^(@),2^(@)` and `3^(@)` amines (C) Carbylamine test is given by only `1^(@)` amines. (D) Musturd OIL reaction is also given by `1^(@)` ANIMES only. |
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| 2526. |
Evaluate the integral as limit of sum: int_(0)^(1) (e^(2x)-e^(x) +x) dx |
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| 2527. |
If the distance from 'P' to the points (2,3) and (2,-3) are in the ratio 2:3, then find the equation of the locus of P. |
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| 2528. |
int_(-1)^(0) (dx)/( x^(2) + 2x+ 2) is equal to |
| Answer» Answer :C | |
| 2529. |
The number of ways in which the letters of the word ARRANGE can be permuted such that the R,s occur together is |
| Answer» Answer :C | |
| 2530. |
If I=int(sinx-cosx)/((sinx=cosx)sqrt(sinxcosx+sin^(2)cos^(2))x)dx=cosec^(-1)(g(x))+cAAx""inR, then |
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Answer» `g(X)=1+sin2x` |
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| 2531. |
Let vec(OA)=vec(a),vec(OB)=10vec(a)+2vec(b) " & " vec(OC)=vec(b) , where O,A,C are non-collinear. Let 'p' denote area of quadrilateralOABC & 'q' denote area of parallelogram with OA & OC as adjacent sides, then (p)/(q)= |
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Answer» 2 `GE OB+AC` `ge2sqrt(2)` 
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| 2532. |
underset(n rarr infty)("lim") [(1)/(n)+ (n^(2))/((n + 1)^(3)) + (n^(2))/((n + 2)^(3)) + (n^(2))/((n + 3)^(3)) + .....+(1)/(125n)]= |
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Answer» `(3)/(8)` |
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| 2533. |
The feasible solution for a LPP is shown in Figure Let z = -3x - 4y objective function. Maximum of Z occurs at |
| Answer» ANSWER :A | |
| 2534. |
A letter is taken out at random from the word RANGE and another is taken out from the word PAGE. The probability that they are the same letters is : |
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Answer» `3//5` |
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| 2535. |
is the probability distribution of random varibale X. Find k and variance of X. |
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Answer» |
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| 2536. |
In X-Y plane, the path defined by the equation (1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0, is |
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Answer» a PARABOLA if `m = (1)/(2), k =- 1, n =0` `rArr+ y+2 sqrt(xy) =1` `rArr 4xy = (1-x-y)^(2)` (b) `(1)/(x) +(1)/(y) =1 rArr xy - x - y=0` is a hyperbola (c ) `(1)/(x) +(1)/(y) + (1)/(x+y) =0` `rArr x^(2) + 3XY + y^(2) =0`, which is a pair of lines. (d) `x + y -(1)/(x+y) =0` `rArr (x+y)^(2) =1` `rArr x+y = +-1` which is a pair of lines. |
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| 2537. |
If barz= iz^(2) then the number of values of z is |
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Answer» 1 |
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| 2538. |
Choose the CORRECT statements |
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Answer» Friction between GROUND & B is 60 N |
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| 2539. |
Let a, b, c be such that b(a+c) ne0. If |(a,a+1,a-1),(-b,b+1,b-1),(c,c-1,c+1)|+|(a+1,b+1,c-1),(a-1,b-1,c+1),((-1)^(n+2)a,(-1)^(n+1)b,(-1)^(n)c)|=0 then the value of n is : |
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Answer» any EVEN INTEGER |
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| 2540. |
If f(x)= 3x^2+15x+5, then find the approximate value of f(3.02) |
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Answer» 47.66 |
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| 2541. |
A container has 'm' gram of a gas. After a white, a little amount of the gas escapes from the container. The presure of the gas left in the container becomes half, and the absolute temperature is reduced to two-third of the original value. The amount of gas, which escaped from the container is |
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Answer» SOLUTION :`PV=nRT-m/MRT` (Since the gas escapes, SUPPOSE m' is the mass left) Now, `1/2PxxV=(m')/(M)Rxx2/3Torm/M=(4m')/(3M)` `therefore` Mass of the gas left `m'=3/4` or mass of the gas escaped `=1/4` m |
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| 2542. |
A particle moves along x-axis in such a way that its x-coordinate varies with time t according to the equation x = (8 - 4t + 6t^(2)) metre. The velocity of the particle will vary with time according to the graph :- |
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Answer»
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| 2543. |
If |r| gt 1, x = a + a/r + a/r^(2) + .......... infty, y = b - b/r + b/r^(2) - ......... infty and z = c + c/r^(2) + c/r^(4) + ...... infty, then the value of (xy)/z = |
| Answer» ANSWER :C | |
| 2544. |
The same 15 participants, on each of 3 days, threw 5 darts in order to win a bullseye contest. The number of players throwing a given number of bullseyes on each day is shown in the table above. NoParticipant threw the same number of bullseyes on two different days. IF a participant is selected at random, what is the probability that the selected participant threw 3 bullseyes on Day 1 or DAY2, given that the contestant threw 3 bullseyes on one of the three days? |
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| 2545. |
LetP(n):a^n+b^nsuch thata, bare even, thenP(n)willbe divisiblebya +bif |
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Answer» `n GT 1` |
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| 2546. |
The same 15 participants, on each of 3 days, threw 5 darts in order to win a bullseye contest. The number of players throwing a given number of bullseyes on each day is shown in the table above. What is the mean number of bullseyes each participant threw on DAY 2? |
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| 2547. |
Integrate the follwing functions: cosx/((1-sinx)(2-sinx)) |
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Answer» Solution :Put SINX = t. Then dt = COSX dx THEREFORE `INT cosx/((1-sinx)(2-sinx)) dx` `int dt/((1-t)(2-t))` (by partial fraction) =`int[1/(1-t)-1/(2-t)]dt` `LOG|1-t|/-1 -log|2-t|/-1 +c` =`log|2-t|-log|1-t|+c` =`log|(2-t)/(1-t)|+c` =`log|(2-sinx)/(1-sinx)|+c` |
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| 2548. |
Find the middle term(s) in the expansionof n in N (p^(2)-2q)^(2n-1) |
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| 2550. |
Definite integration as the limit of a sum : lim_(ntooo)[(n)/(1+n^(2))+(n)/(4+n^(2))+(n)/(9+n^(2))+.........+(n)/(2n^(2))]=...... |
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Answer» `(PI)/(2)` |
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