InterviewSolution
Saved Bookmarks
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.
| 10451. |
The solutio set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x="cot"^(-1)(sqrt(1-x^(2)))/x-sin^(-1)x is |
|
Answer» `[-1,1]-{0}` |
|
| 10452. |
Find the n^(th) term of the A.P 84, 80,76,..... |
| Answer» SOLUTION :`-4n+88` | |
| 10453. |
Find the point to which the origin has to be shifted to eliminate x and y terms in the equation 4x^(2) + 9y^(2) - 8x + 36y + 4 = 0 |
|
Answer» |
|
| 10454. |
Let y = ln (1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y//2) equals |
|
Answer» 0 |
|
| 10456. |
Find real theta such that (3 + 2i sin theta)/(1-2i sin theta) is purely real. |
|
Answer» |
|
| 10457. |
Two adjacent sides of a parallelogram are given by 4x+5y=0, 7x+2y=0 and one diagonal is 11x+7y=9. Find the equations of the remaining sides and the other diagonal. |
|
Answer» |
|
| 10458. |
A(x)=|{:(1,2,3),(x+1,2x+1,3x+1),(x^(2)+1,2x^(2)+1,3x^(2)+1):}|rArrint_(0)^(1)A(x)dx= |
|
Answer» 0 |
|
| 10459. |
Origin is shifted at (1,6) and new co - ordinate of point A is (1,3) then old co - ordinates are (2,9) . |
|
Answer» |
|
| 10460. |
On the curve x^(3)=12y, find the interval of value of x for which the abscissa changes at a faster rate than the ordinate? |
|
Answer» |
|
| 10462. |
cos^(-1) sqrt((a-x)/(a-b))= sin^(-1) sqrt((x-b)/(a-b)) is possible if |
|
Answer» `a GT x gt B or a LT x lt b` |
|
| 10463. |
If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is |
|
Answer» |
|
| 10464. |
Equation of the locus of the centroid of the triangle whose vertices are (acos k, a sin k),(b sin k, -b cos k) and (1,0) where k is a p arameter is |
|
Answer» `(1-3x)^(2)+9y^(2)=a^(2)+B^(2)` |
|
| 10465. |
Let f(x) be defined on [-2, 2] and be given by f(x)= {:{(-1,-2 le x le0),(x-1,0 lt 2 le 2):} and g(x)=f(|x|)+|f(x)|, Then find g(x) |
|
Answer» `g(X)={:{(-x,-2 le x le 0),(0,0 lt x le 1),(2(1-x),1 lt x le 2):}` |
|
| 10466. |
If the function f(x)=3x+a and g(x) =4x+9 are such that (g@g)(x)=(g@f)(x), then: a= |
|
Answer» 1 |
|
| 10467. |
The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-pi/2)cot^(-1)x-3tan^(-1)x-3(2-pi/2)gt 0 is (a, b) then the value of cot^(-1)a+cot^(-1)b is |
|
Answer» |
|
| 10468. |
Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1,cosxsin2y=a+1 The number of values of a for which the system has a solution is |
|
Answer» - 1 |
|
| 10469. |
Vertex of the parabola (y - 2)^(2) = 16 (x - 1) is …….. |
| Answer» ANSWER :A | |
| 10470. |
The position vectors of A and B are bar(a) and bar(b) respectively. If C is a point on the line bar(AB) such that bar(AC)=5bar(AB) then find the position vector of C. |
|
Answer» `5bar(B)-4bar(a)` |
|
| 10471. |
If y=x^4 then find the average rate of change of y between x= 2 and x= 4. |
|
Answer» |
|
| 10474. |
Which of the following planes is equally inclined to the planes 4x + 3y - 5z = 0 and 5x-12y+13z=0 is: |
|
Answer» `11x-3y=0` |
|
| 10475. |
The triangle ABC is defined by the vertices A =(0,7,10), B = (-1,6,6) and C = (-4,9,6) Let D be the foot of the altitude from B to the side AC. Then bar(BD) is |
|
Answer» `bari+2barj+2bark` |
|
| 10476. |
If theta is acute angle between the pair of lines x^(2)-3xy+2y^(2)+3x-5y+2=0 then sintheta= |
|
Answer» `(1)/(10)` |
|
| 10478. |
Height of the tower and multy storied building is same of 30 mets . The angle at elevation at some point joining base at both is alpha and beta then .......... |
|
Answer» |
|
| 10479. |
E and F are two events associated with a random rxperimentfor which P(F)=0.35,P(E or F) =0.85,P(E and F)=0.15 Find P€. |
|
Answer» |
|
| 10480. |
Find the coordinates of the points which trisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6). |
|
Answer» |
|
| 10481. |
A family is using petroleum gas (LPG) of weight 14.2 kg for consumption . (Full weight 29.5 kg ) Includes the empty cylinder tare weight of 15.3 kg ). If it is are with constant rate then It lasts for 24 days. Then the new cylinder is replaced (i)Find the equation relating the quantity of gas in the cylinder to the days . (ii) Draw the graph for first 96 days. |
|
Answer» |
|
| 10482. |
18 mice were placed in two experimental groups and one control groups with all groups equally large. In how many ways can the mice be placed into three groups ? |
|
Answer» Solution :It is given that 18 mice were placed equally in two experimental groups and ONE control group i.e., three groups. `THEREFORE` REQUIRED arrangements `= ("TOTAL arrangement")/("Equally likely arrangement") = (18"!")/(6"!"6"!"6"!")` |
|
| 10483. |
The pressure p and the volume of a gas are connected by the relalson pv=300. If the volume is increasing at the rate of 0.6 cubic cm per minute then find the rate of change in pressure of the gas when the volume is 30 cubic cm. |
|
Answer» |
|
| 10484. |
Prove that, costhetacos((theta)/(2))-cos3thetacos((9theta)/(2))=sin7thetasin8theta. |
|
Answer» |
|
| 10485. |
Find the values of k for which the line (k - 3) x - (4 - k^(2)) y +k^(2) - 7k + 6 = 0is (a) Parallel to the x-axis,(b) Parallel to the y-axis, (c) Passing through the origin. |
|
Answer» |
|
| 10486. |
If the surface area of a sphere of radius r is increasing uniformly at the rate cm^(2)//s, then the rate of change of its volume is : |
|
Answer» costant |
|
| 10487. |
Let f be a function defined by f(x)=(x-5)/(x-3), x != 3, 2 f'(x) denote the composition of f with itself takenk time i.e. f^(3)(x)=f(f(f(x))) then |
|
Answer» `f^(-2012)(2009) = 2009` |
|
| 10489. |
(bara.bari)^(2) + (bara.barj)^(2) + (bara.bark)^(2) = |
|
Answer» `BARA^(2)` |
|
| 10490. |
If two angles of a Delta ABC are 45^@ and 60^@, then the ratio of the smallest and the greatest sides are |
|
Answer» ` sqrt3- 1: 1` |
|
| 10491. |
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed? |
|
Answer» |
|
| 10492. |
If A, B, C are in A.P and B = pi/4 then tan A tanB tan C= |
|
Answer» 1 |
|
| 10493. |
A point moves in the xy - plane such that th sum of its, distances from two mutually perpendicular lines is always equal to 5 units. The area (in square units) enclosed by the locus of the point is |
| Answer» Answer :3 | |
| 10494. |
Write the first five terms of each of the sequencesand obtain the corresponding series: a_(1)=3,a_(n)=3a_(n-1)+2 for all n gt 1 |
|
Answer» |
|
| 10495. |
Number of common points for the curves y=sin^(-1)(2x)+tan^(-1)(1/([2x]))=2 and y=cos^(-1)(2x+5)+1 is (where [.] denotes greatest integer function) |
|
Answer» 0 |
|
| 10496. |
In the interval (0,pi), f(x)=sinx-x is |
|
Answer» DECREASING |
|
| 10497. |
Calculate the index number for the year 1979 with 1970 as base from the following data using weighted average of price relatives. |
|
Answer» |
|
| 10498. |
Eccentricity e of ellipse is .............if length of minor axis is distance between its focii. |
|
Answer» |
|
| 10499. |
If cos x cos 2x cos 3x=1//4, then x= |
|
Answer» `(2n+1)(PI)/8, n pi +-(pi)/3, n in Z` |
|
| 10500. |
Match the following {:("Column - I " ,"Column - II "),("A) The set of allreal values of parameter ''p'' for which the equation " sqrt(p) cos x - 2 sin x = sqrt(2) + sqrt(2 - p) " possesses at least one real root is ","p) [- 3, - 2] "),("B) The set of all real values of parameter 'a' for which the equation cos 2 x + a sin x = 2 a - 7 possesses at least one real rootis ","q) " [(-3)/(2),(1)/(2)]),("C) The set of all real values of parameter 'a' for which the equation " sin^(4) x + cos ^(4) x + sin 2 x + a = 0 " possesses at least one real root is " ,"r) [2, 6] " ),("D) The set of all real values of parameter 'a' for whichthe equation " cos^(4) x - (a+ 2) cos ^(2) x - (a + 3) " possesses at least one real root is ","s) " [ sqrt(5) - 1, 2] ),(,"t) " [2 "," sqrt(5 ) + 1 ] ) :} |
|
Answer» |
|