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.
| 13501. |
Let f(x)-=(x^(2) +bx+c)/(x^(2)+b_(1)+c_(1)) where alpha,beta are the roots of the equation x^(2)+bx+c=0andalpha_(1),beta are the roots of x^(2)+b_(1)x+c_(1)=0 Now answer the following questions for f(x) A combination of graphical and analytical approach may be helpful in solving these problems If alpha_(1)andbeta_(1) are real then f(x)has vertical asymptote at x=alpha_(1),beta_(1). If alpha_(1)ltalphaltbeta _(1)ltbeta then |
|
Answer» f(x) is INCREASING in `(alpha_(1),beta_(1))` |
|
| 13502. |
continuous at x = 0 Let f(x) = {{:((1 + |sin x| )^((a)/(|sin x|)), - (pi)/(6) lt x lt 0 ),(b , x = 0 ),(e^(tan 2x //tan 3x), 0 lt x lt (pi)/(6)):} Determine a and b such that f(x) continuous at x = 0 . |
|
Answer» |
|
| 13503. |
If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have? |
|
Answer» |
|
| 13504. |
A variable triangle ABC is circumscribed about a fixed circle of unit radius. Side BC always touches the circle at D and has fixed direction. If B and C vary in such a way that (BD)(CD)=2, then locus of vertex A will be a straight line |
|
Answer» PARALLEL to SIDE BC |
|
| 13505. |
x/(costheta)=y/(cos(theta-(2pi)/3))=z/(cos(theta+(2pi)/3)) then x+y+z= |
|
Answer» 1 |
|
| 13506. |
the periodof sin ((pi)/(3) -x )sin ((pi)/(3) + x)is |
|
Answer» `(PI)/(2 ) ` |
|
| 13507. |
The value of 'c' in Lagrange's mean value theorem for f(x) = lx^(2) + mx + n ( l cancel(=)0) on [a,b] is |
|
Answer» 1 |
|
| 13508. |
The value of C in the lagrange's mean value theroem for f(x) = sqrt( x-2) in the intervale [2,6] is |
| Answer» ANSWER :B | |
| 13509. |
Two line are given (x-2y)^2+k(x-2y)=0. The value of k, so that the distance between then is 3, is |
|
Answer» k=0 |
|
| 13511. |
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find B ∪ C ∪ D |
|
Answer» |
|
| 13512. |
sinh^(-1)(2^(3//2))= |
|
Answer» `log_(e )(2+SQRT(18))` |
|
| 13513. |
n((n-1)P_((r-1)))=................ . |
|
Answer» |
|
| 13514. |
Let f:RtoR:f(x)=x^(3)" for all "x""inR. Find its domain and range. Also, draw its graph. |
|
Answer» Solution :Let `f:RtoR:f(x)=x^(3)" for all "x""inR` Then, dom (f)=R and range (f)=R. Now, we have:  On a graph paper, we draw X' OX and YOY' as the x-axis and the y-axis respectively. We take the SCALE as 5 small divisions = 1 unit. Now, we PLOT the points A(-2,-8), B(-1.5,-3.375), C(-1,1), O(0,0), D(1,1), E(1.5,3.375) and F(2,8). We join these points freehand successively to obtain the required curve. 
|
|
| 13515. |
Let f ((x + y )/( 2)) = (f (x) + f (y))/( 2) AA x,y,in R. If f (0) =1. f '(0) exists and equal -1, find f' (2) . |
|
Answer» |
|
| 13516. |
It is required to seat 5 men and 4 women in a row so that the wom even places. How many such arrangements are possible ? |
|
Answer» |
|
| 13517. |
A plane passes through (1, -2, 1) and is perpendicular to two planes 2x - 2y + z=0 and x - y + 2z =4,then the distance of the plane from the point (1,2,2) is |
| Answer» ANSWER :D | |
| 13518. |
If (tan(alpha + beta - gamma))/(tan(alpha - beta + gamma)) = (tan gamma)/(tan beta), (beta ne gamma), then sin 2alpha + sin 2beta + sin 2gamma= |
|
Answer» 0 |
|
| 13519. |
Find the centriod and hence find the area of the triangle formed by the following lines 3x^(2)-4xy+y^(2)=0, 2x-y=6 |
|
Answer» |
|
| 13520. |
For 0 lt theta lt 2pi, sin^(-1)(sintheta) gt cos^(-1)(sintheta) is true when |
|
Answer» `(pi/4,pi)` |
|
| 13521. |
Find the direction cosines of the sides of the triangle whose vertices are (3,5,-4), (-1,1,2) and (-5,-5,-2). |
|
Answer» |
|
| 13522. |
Find the domains of the following functions f(x) = ( 1)/( 2x-1) |
|
Answer» |
|
| 13523. |
The measures of the sides of a right angle triangle are in A.P. The sum ofsin e of two acute angles is……. |
| Answer» Answer :A | |
| 13524. |
If for a distribution sum(x-5) = 3, sum(x - 5)^2 = 43 and the total number of item is 18, find the mean and standard deviation. |
|
Answer» |
|
| 13525. |
Find the approximate change in the volume v of a cube of side 'x' mts caused by increasing the side by 3% |
|
Answer» |
|
| 13526. |
Let PQR be right angled isoscles triangle right angled at P (2,1). If the equation of the line QR is 2x+y=3. Then the equation representing the pair of lines PQ and PR is |
|
Answer» `3x^2-3y^2+8xy+20x+10y+25=0` |
|
| 13527. |
Find the middle terms in the expansions of(x/3 + 9Y)^10. |
|
Answer» |
|
| 13528. |
One of the diagonals of a square is the portion of the line x//2+y//3=2 intercepted between the axes. The the extremities of the other diagonal are |
|
Answer» (5,5),(-1,1) |
|
| 13529. |
Write down the negation of following compound statements. All rational numbers are real and complex. |
|
Answer» |
|
| 13530. |
Find the centre and radiusof equation of circle inx^(2) + y^(2) - 4x + 6y = 5 |
|
Answer» |
|
| 13531. |
If tan ((theta)/(2))= sqrt((1-e)/(1+e)) tan(( alpha)/(2)) then cos alpha= |
|
Answer» `(1-e COS THETA)/(cos theta+e)` |
|
| 13533. |
If the equation 2hxy+2gx+2fy+c=0 represents two straight lines and form a rectangle with coordinate axes then its area is (sq.u) |
|
Answer» `(absf)/G^2` |
|
| 13534. |
Which of the following are incorrect |
|
Answer» `underset(x in R)(["min" E^(x)])!=[e^(-PI//2)]`, ([.] = greatest INTEGER function) |
|
| 13535. |
Find the distance between parallel lines i. 15x+8y-34= 0 and 15x+8y+31=0 ii. l(x + y) + p = 0 and l(x + y) - r = 0. |
|
Answer» <P> |
|
| 13536. |
The ratio between area of a square inscribed in a circle and an equilateral triangle circumscribed about |
|
Answer» `(3sqrt(3))/(2)` |
|
| 13537. |
Find the roots of the equations. Q. (2x)/(x-4)+(2x-5)/(x-3)=8(1)/(2). |
|
Answer» |
|
| 13538. |
The period of the function | sin^(3)"" (x)/(2) |+ | cos^(5)""(x)/(5)| is |
| Answer» Answer :B | |
| 13539. |
Find the coordinates of the point (1, 2) in the new system when the origin is shifted to (-2, 3) . |
|
Answer» |
|
| 13540. |
From the prices of shares X and Y below, find out which is more stable in value: |
|
Answer» |
|
| 13541. |
If the orthocentre and the centroid of a triangle are (-3,51),(3,3,-1) then find circumcentre. |
|
Answer» |
|
| 13542. |
Ig |bar(a)| = 11 ,|bar(b)| = 23,|bar(a)-bar(b)| = 30 then find the angle between the vectors bar(a),bar(b) and also find |bar(a)+bar(b)|. |
|
Answer» |
|
| 13543. |
Find the value of (sqrt(1+sin2A)+sqrt(1-sin2A))/(sqrt(1+sin2A)-sqrt(1-sin2A)), when | tan A | lt 1 and |A| is acute . |
|
Answer» COT A |
|
| 13544. |
If vec(r )= x vec(i) + y vec(j) + z vec(k) then find (vec(r ) xx vec(i))^(2)- (vec(r )xx vec(k))^(2) |
|
Answer» |
|
| 13545. |
absbara=absbarb=absbarc=abs(bara+barb+barc)=1 and bara bot barb , (barc,bara) = alpha , (barc,barb) = beta , " then " cos alpha + cos beta = |
|
Answer» `3//2` |
|
| 13546. |
Assertion (A): n in N product of n (n+1) (n+2) is divisible by 6 Reason (R) : Product of 3 consecutive +ve integers is divisible by 3! |
|
Answer» |
|
| 13547. |
Two tress A and B are on the same side of a river . From a point C in the river the distane of the tress A and B are 250m and 300m respectively . If the angle C is 45^(@) find the distancesbetween the tress (use sqrt(2)=1.414 ) |
|
Answer» `215.5` |
|
| 13549. |
Sand is being poured on the ground from the orifice of an elevated pipe and from a pile which has always the shape of a right circular cone whose height is equal to the radius of the base. If the sand if falling at the rate of 1000 cubic cm per, sec, the rate at which the height of the pile is rising when the height is 40 cm is |
|
Answer» `5//8 PI` cm/sec |
|
| 13550. |
The solution set of cos x gt 0is |
|
Answer» `[2n pi -(pi)/(2), 2n pi+(pi)/(2)], N in Z` |
|