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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.
| 11601. |
Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(3) haslocal maxima, |
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| 11602. |
Find the approximate value of(5.001), where f(x) = x^(3) – 7x 2 + 15. |
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| 11603. |
Find the second order derivatives of the function e^(6x) cos 3x. |
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| 11604. |
Write the distance of the point (1,1,2) from x-axis. |
| Answer» SOLUTION :DISTANCE of (2,3,6) from zx-plane = 3 | |
| 11605. |
Which of the following equaion (s) is/are linear? |
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Answer» `(dy)/(DX)+(y)/(x)=INX` |
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| 11606. |
If x, 2y, 3z are in A.P. where the distinct numbers x, y, z are in G.P. Then find the common ratio of G.P. |
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| 11607. |
The value of underset(x to 0)(lim) e^(-4) ((1-x)/(1-x))^(1//x) is equal to |
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Answer» `E^(2)` |
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| 11608. |
Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}| |
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| 11609. |
Let f (x) be a polynonial of degree 4 with f (2) =-1, f '(2) =0-, f ''(2) =2, f ''(2) =-12,f''(2) =24 then f ''(1) = |
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Answer» 26 |
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| 11610. |
At point (0, 0) the curve y=x^((1)/(5)) has ………… |
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Answer» a vertical TANGENT (PARALLEL to Y = AXIS) |
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| 11611. |
The sum of all the coefficients in the binomial expansion of (1+2x)^n is 6561. Let R=(1+2x)^n=1+F, where 1 in N and 0 lt F lt 1. IF x=1/sqrt2 then 1-F/(1+(sqrt2-1)^4)= |
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Answer» `(3sqrt2-4)` |
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| 11612. |
|bara+barb|=|barc|=|bara+barb|=1.bara.barc=0 IF bara=hati/sqrt2+hatj/sqrt3 and hata.hatk and barb are linearly dependent IF maximum and minimum value of barb.barc is M and m then 4(M^2+m^2) is 1. 1 2. 5 3. 3 4.6 If for some barc.|barb times barc|=|bara times barc|and barc=phati+qhatj+rhatk then 16(p^4+q^4+r^4) is 1. 8 2. 21 3. 21//3 4. 4 IF barb=shati+thatj+uhatk then 8(s^4+t^4+u^4) is 1. 4 2. 5 3. 25//21 4. 19//4 |
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| 11613. |
A line is at a distance c from origin and meets axes in A an dB. The locus of the centre of the circle passing through O,A,B ais |
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Answer» `X^(-2)+y^(-2)=c^(-2)` |
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| 11614. |
Abscissa of two points P and Q on parabolay^(2)=8x are roots of equation x^(2)-17x+11=0. Let Tangents at P and Q meet at point T, then distance of T from the focus of parabola is : |
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Answer» 7 |
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| 11615. |
For all real number x such that x != 0, 4/5 + 7/x = ? |
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Answer» `11/(5X)` |
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| 11616. |
Three mangoes and three apples are in a box. IF two fruits are chosen at random the probability that one is a mango and the other is an apple is………. |
| Answer» Answer :C | |
| 11617. |
Evalute the following integrals int (dx)/(x^(2) + 81) |
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| 11618. |
A(2,3,7),B(-1,3,2),C(p,5,r) are vertices of DeltaABC. If the median through A is equally inclined to the co-ordinate axes, then the values of p and r are |
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Answer» `7,14` |
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| 11619. |
If vec(a) is a unit vector and vec(b)=(2,1,-1) and vec( c )=(1,0,3). Then the maximum value of [vec(a)vec(b)vec( c )] is………….. |
| Answer» Answer :B | |
| 11620. |
Let A be the event that a family has children of both sexes. If each family has n children and the probability that each child being a boy is 0.5, then |
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Answer» `(2)^(1-n)` |
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| 11621. |
Evalute the following integrals int (e^(x))/(e^(x//2) + 1) dx |
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| 11623. |
The rangeof thefunctionsf(x)= (x^2 +8)/(x^2 +4) x inRis |
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Answer» `[-1,3/2]` |
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| 11625. |
Evaluate int tan ^(2) x sec^(4) x dx |
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| 11626. |
If lim_(x to oo) (1+a/x+b/x^2)^(2x)=e^2 , then the values of a and b are |
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Answer» `a in R , B=2` |
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| 11627. |
Evaluate the following:""^(10)C_(9)= |
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| 11628. |
Statement I : If a and b are any two vectors, then |a xx b|^(2) + |a.b| = |a|^(2) |b|^(2) Statement II : If a and b any two vectors then |a xx b|^(2) = {:(a.a, a.b),(b.a, b.b):}. Then |
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Answer» Both statement are true and II is a CORRECT explanation of I |
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| 11629. |
Findthepolynomialwithrationalcoefficientsand whoserootsare 0,1,-3//2,5//2 |
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| 11630. |
For all real p, the line 2px+ysqrt(1-p^(2))=1 touches afixed ellipse whose axex are the coordinate axes The locus of the point of intersection of perpendicular tangent is |
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Answer» `x^(2)+y^(2)=5//4` `(x^(2))/(y^(2))+(y^(2))/(b^(2))=1` The line `y==mx+-sqrt(a^(2)m^(2)+b^(2))`touches, the ellipse for all m. Hence, it is identical with `y=-(2X)/(sqrt(1-p^(2)))+(1)/(sqrt(1-p^(2)))` Hence, `m=-(2p)/(sqrt(1-p^(2)))` and `a^(2)m^(2)+b^(2)=(1)/(1-p^(2))` or `a^(2)(4p^(2))/(a-p^(2))+b^(2)(1)/(1-p^(2))` or `p^(2)(4A^(2)-b^(2))+b^(2)-1=0` This equation is true for all real p if `b^(2)=1 and 4a^(2)=b^(2)` `b^(2)=1 and a^(2)=(1)/(4)` Therefore, the equation of the ellipse is `(x^(2))/(1//4)+(y^(2))/(1)=1` If e is its ECCENTRICITY, then `(1)/(4)=1-e^(2) or e^(2)=(3)/(4) or e=(sqrt(3))/(2)` be `=(sqrt(3))/(2)` Hence, the FOCI are `(0,+-sqrt(3)//2)` The equation of director circle is `x^(2)+y^(2)=(5)/(4)` |
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| 11631. |
Show that the function f(x) = 1/(1+x^(2)) is increasing function in the interval (- infty, 0]. |
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| 11632. |
Evaluate int(1)/(sqrt(3x^(2)-5))dx |
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| 11633. |
If (c-d)/(c)=(5)/(8), which of the following must also be true? |
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Answer» `(c-d)/(d)=(8)/(5)` |
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| 11635. |
If in the expansion of (x^(3)-1/(x^(2)))^(n)the sum of the coefficients of x^(5) and x^(10) is 0, then the coefficient of x^(20) is: |
| Answer» Answer :D | |
| 11636. |
An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K.The men time between two successive collosions is 6xx10^(-8) s. If the pressure to 500K, the mean time between two successive collisions will be close to : |
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Answer» `2xx10^(-7)s` |
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| 11637. |
If 2 + sqrt(5)is root of x^(2) - px + q = 0where p and q are real, then the ordered pair (p,q) is equal to |
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Answer» (4,9) |
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| 11638. |
Use integral calculus to find the sum of the series (1)/(4!)+(4l)/(8l)+(8l)/(12l)+……oo. |
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| 11639. |
What is the number of possible square matrices of order 3 with each entry 0 or 1? |
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| 11640. |
For each of the differential equation find the general solution(dy)/(dx) + 3y = e^(-2x) |
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| 11641. |
Which of the following statement/s is/are true: |
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Answer» In ortho hydrogen, both electrons spin in same direction whereas in para hydrogen, both electrons spin in opposite direction. |
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| 11642. |
If the line y=2x+c is a tangent to the circle x^(2)+y^(2)=5 then a value of c is |
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Answer» 3 |
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| 11643. |
Let P, Q, R, S be the feet of the perpendicularsdrawn from a point (1, 1) upon the lines x+4y=12, x-4y+4=0and their angle bisectorsrespectively, then equation of the circle which passes through Q, R, S is : |
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Answer» `X^(2)+y^(2)-5x+3y-6=0` |
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| 11644. |
int_(0)^(pi//2) sin^(6) x.cos^(5) x dx= |
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Answer» `(8)/(693)` |
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| 11645. |
Using elementary operations, find the inverse of the matrix [(1,2),(2,-1)] |
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| 11647. |
Evaluate the following integrals int x sin^(2) x dx |
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| 11648. |
Integrate the following functions : int(sin(2+tan^(-1)x))/(1+x^(2))dx |
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