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.
| 4901. |
Match the following |
|
Answer» `{:(I,II,III,IV),(d, a, b, C):}` |
|
| 4902. |
lim_(n rarr oo) [(1)/(1-n^(4))+(8)/(1-n^(4))+…...+(n^(3))/(1-n^(4))] equals : |
|
Answer» `(1)/(8)` |
|
| 4903. |
Prove that 3 sin ^(-1) x = sin^(-1) (3x - 4x^3), x in [-1/2,1/2] |
|
Answer» Solution :Put `sin^(-1) x = y`. Then sin y = x `therefore 3 x - 4 x^3 = 3 sin y - 4 sin^3 y = sin 3Y` `implies 3y = sin^(-1) (3X - 4x^3)` `implies 3 sin^(-1) x = sin^(-1) (3x - 4x^3)` |
|
| 4904. |
If A(veca).B(vecb) and C(vecc) are three non-collinear point and origin does not lie in the plane of the points A, B and C, then for any point P(vecP) in the plane of the triangleABC such that vector vec(OP) is botto plane of trianglABC, show that vec(OP)=([vecavecbvecc] (vecaxxvecb+vecbxxvecc+veccxxveca))/(4Delta^(2)) |
|
Answer» Solution :P LIES in the plane of A,B and C , therefore, `vec(AP).(vec(Bp) xx vec(CP))=0` `Rightarrow (vecp.veca).(veccxxvecp+vecpxxvecb+vecbxxvecc)=0` `or 0 +0+vecp . (vecbxxvecc)-veca.(veccxxvecp)` `-veca.(vecpxxvecb)-veca.(vecbxxvecc)=0` `or vecp . (vecbxxvecc)=vecp.(veccxxveca) +vecp.(vecaxxvecb)` `-veca . (VECB xx vecc) =0` `or vecp.(vecbxxvecc+veccxxveca+vecaxxvecb) = [veca vecbvecc]` now vector perependicular to the plane ABC is `(vecb xx vecc +vecc xx veca +veca xxvecb)` Let ` vec(OP) = LAMBDA(veca xx vecb + vecb +vecb xx vecc +vecc xx veca)` since `vec(OP).(vecaxxvecb+vecbxxvecc+veccxxveca)=[veca vecbvecc]` `or ([veca vecb vecc])/(4Delta^(2))` `vec(OP) = ([veca vecb vecc] (veca xxvecb + vecb xxvecc +veccxxveca))/(4Delta^(2))` |
|
| 4905. |
Let DeltaABC be a given triangle, if |BA-tBC|ge|AC| for any t in R, then DeltaABC is |
|
Answer» Equilateral |
|
| 4906. |
The maximum area of the rectangle that can be inscribed in a circle of radius r is |
| Answer» Answer :A | |
| 4907. |
Evaluateunderset(n to oo)("lim")[(1+(1)/(n))(1+2/n)* * * (1+(n)/(n))]^(1/n) |
|
Answer» |
|
| 4909. |
Using elementary row transformations , find the inverse of [{:(3,-1),(-4,2):}] |
|
Answer» |
|
| 4910. |
If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) terms = |
|
Answer» `-1` |
|
| 4911. |
If for somesx in Rthe frequency distribution of marks obtained by 20 students in a test is: Then the mean of the marks is: |
|
Answer» ` 2.5` |
|
| 4912. |
Let P be a plane passing through the points (2,1,0),(4,1,1) and (5,0,1) and R be any point (2,1,6). Then the image of R is the plan P is : |
|
Answer» (6,5,2) |
|
| 4913. |
Let 0ltaltblt(pi)/(2).Iff(x)= |{:(tanx,tana, tanb),(sinx,sina,sinb),(cosx,cosa,cosb):}|,then find the minimum possible number of roots of f'(x) = 0 in (a,b). |
|
Answer» |
|
| 4914. |
IF P (E ) =0.6 ,P( F) =0.3 and P (EnnF )=0.2 ,find P(F|E). |
|
Answer» |
|
| 4915. |
Integrate the function is exercise. sqrt(1+3x-x^(2)) |
|
Answer» |
|
| 4916. |
Lt_(n rarr oo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/(n^(2)))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2))).....(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))] |
|
Answer» |
|
| 4917. |
Prove that[vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2). |
|
Answer» |
|
| 4919. |
If the mean and veriance of a binomial veriate X are 8 and 4 respectively , thenP(X lt3) equals to |
|
Answer» `(265)/(2^(15))` |
|
| 4920. |
The vector equation of the plane which is at distance 8 units from origin and having normal 2hat i + hat j + 2 hat k is........ |
|
Answer» `bar(r). (2 hat i + hat J + hat K) = 24` |
|
| 4921. |
Find the value of a ,b,c and d from the equation : [{:(a-b,2a+c),(2a-b,3c+d):}]=[{:(-1,5),(0,13):}]. |
|
Answer» |
|
| 4923. |
If O be the origin and the coordinates of P be (1, 2, - 3), then find the equation of the plane passing through P and perpendicular to OP. The required plane is perpendicular to OP. |
|
Answer» |
|
| 4924. |
When a 20 ml of 0.08 M weak base BOH is titrated with 0.08 M HCl, the pH of the solution at the end point is 5. What will be the pOH if 10 ml of 0.04M NaOH is added to the resulting solution? |
|
Answer» `5.40` |
|
| 4925. |
Find the number of ways of arranging 8 persons around a circle if two particular persons wish to sit together. |
|
Answer» |
|
| 4926. |
Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base. |
|
Answer» |
|
| 4929. |
A man wants to reach a centain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes aboat. His speed of traveling in mud, in water, on tar road is in the ratio3 : 4 : 5. The ratio ratio of the durations he requires to cross the patch of mud, stream and tar road is |
|
Answer» `1/2:4/3:5/2` `{:(,,"mud",:,"tar",:,"stream"),("distance",,"x",:,"3X",:,"2x"),("speed",,"3v",:,"5V",:,"4v"),("time",,(x)/(3v),:,(3x)/(5v),:,(2x)/(4v)),(,,10,:,18,:,15):}` |
|
| 4930. |
If 3x +2y- 1 =0 is a tangent to a hyperbola (x^2)/(16) - (y^2)/(9)=1, then the point of contact is |
|
Answer» `(24, 9)` |
|
| 4931. |
Find the mean deviation about the median for the data (i)Find median. (ii)Hence find mean deviation from the median. |
|
Answer» (II) `=5.1` |
|
| 4932. |
Examine the continuity of the following function at the indicated pionts. f(x)={{:(,x-[x] x ne 1),(,0 x =1):}" at x =0" |
|
Answer» |
|
| 4933. |
The vertices of DeltaABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the rectangular hyperbola is |
|
Answer» `xy=2x+y-2` It PASSES through (3,2). Hence, `lambda=-2`. So, the equation of hyperbola is `xy=x+y+1` |
|
| 4934. |
The vertices of DeltaABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the pair of asymptotes is |
|
Answer» `xy-1=x-y` |
|
| 4935. |
The vertices of DeltaABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The number of real tangents that can be drawn from the point (1, 1) to the rectangular hyperbola is |
|
Answer» 4 |
|
| 4936. |
The volume of the tetrahedron having the edges I + 2j + k, I + j + k, I - j + lambda K as coteninous is 2/3 cubic units. Then lambda = |
|
Answer» 1 |
|
| 4937. |
If a is positive integer then the number of values of 'a' satisfying int_(0)^(pi//2) {a^(2)((cos3x)/(4)+(3)/(4)cosx)+a sin x-20cosx} dx le (a^(2))/(3) are |
|
Answer» 1 |
|
| 4938. |
Find the derivative of the following functions with respect to x (sec x-1)/(sec x + 1) |
|
Answer» |
|
| 4939. |
Let xy - 2x - y + 2 = 0are the asymptotes of a hyperbola H, passing through (2, 10) . Statement -1 : The locus of the centroid of equilateral triangle inscribed in the hyperbola 'H' is a conic, whose length of latus rectum is 8. because Statement -2 : Centroidof all equilateral triangle inscribe in a hyperbola, lies on the hyperbola itself . |
|
Answer» Statement -1 is True,Statement -2 is True , Statement - 2 is a CORRECT EXPLANATION for Statement - 1 |
|
| 4940. |
Discuss the relative position of the fol- lowing pair of circles. (x-2)^(2) + (y+ 1) ^(2) = 9, (x+ 1) ^(2) + (y-3)^(2) + (y-3)^(2) = 4 |
|
Answer» (ii) Touch each other (iii) CUT each other in TWO points. |
|
| 4941. |
The projection of the point (1, 3, 4) in the plane vecr.(2hati-hatj+hatk)=-3 is |
|
Answer» (1,3,4) |
|
| 4942. |
Evalute the following integral int (sin (x + a))/(sin (x + b))dx |
|
Answer» |
|
| 4943. |
If r, n in N r > 1, n > 2 and the coefficient of (r +2)th term and (3r)th term in the expansion of (1 +x)^(7n) are equal, then n equals |
|
Answer» 3r |
|
| 4944. |
Find which of the operations given above has identity. a"*"b=a^(2)+b^(2) |
|
Answer» |
|
| 4945. |
The solution of the equation(3|x| -3)^(2) =|x| +7 which belongs to the domain of definition of the function y= sqrt(x(x-3)) are given by |
|
Answer» `PM (1)/(9), pm 2` |
|
| 4946. |
|{:(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0):}|=".........." |
|
Answer» |
|
| 4947. |
int (cos x - sin x )/(sqrt(8 - sin 2x )) dx = |
|
Answer» `sin^(-1) ((sin x + cos x)/(2) ) + c ` |
|
| 4948. |
Find the number of element of P(P(phi)) |
|
Answer» <P> SOLUTION :We have `|P(PHI)|=2^@ =1``:.|P(P(phi))|=2^1=2` |
|
| 4950. |
If the locus of the moving poin P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a. |
|
Answer» `:. SP+S'P=a` So, licus of P is ELLIPSE if `agtSS'` or `agtsqrt(4+12)` or `agt4` |
|