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.
| 11552. |
If a matrix has 8 elements , what are the possible orders it can have ? |
|
Answer» |
|
| 11553. |
Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[sinalpha,cosgamma,cos(gamma+delta)]]=0 |
|
Answer» Solution :`[[SINALPHA,cosalpha,COS(alpha+delta)],[sinbeta,COSBETA,cos(beta+delta)],[sinalpha,cosgamma,cos(gamma+delta)]]` `[C_3rarrC_3-(cosdelta)C_2+(sindelta)C_1]` =`[[sinalpha,cosalpha,cos(alpha+delta)-(cosalphacosdelta-sinalphasindelta)],[sinbeta,cosbeta,cos(beta+delta)-(cosbetacosdelta-sinbetasindelta)],[sinmu,cosgamma,cos(gamma+delta)-(cosgammacosdelta-sinalphasindelta)]]` =`[[sinalpha,cosalpha,0],[sinbeta,cosbeta,o],[sinalpha,cosalpha,0]]`=0 |
|
| 11554. |
Assertion (A) : Integrating factor of 1+(x tan y - sec)(dy)/(dx) = 0 is sec y Reason (R) : Integrating factor of (dy)/(dx) +P(x)y = Q(x) is e^(int P(x)dx) Then the statement among the following is |
|
Answer» Both (A) and (R) are true and R is correct explanation of A |
|
| 11555. |
If int _(0)^(1) e ^(-x ^(2)) dx =0, then int _(0)^(1) x ^(2)e ^(-x ^(2)) dx is equal to |
| Answer» | |
| 11556. |
Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then arg z = |
|
Answer» `(pi)/(4)` |
|
| 11557. |
int(dx)/(x^(r)(1+x^(r))^((1)/(r)))=I, r in N and I= alpha(1+x^(3))^(beta) then the euation whose does are alpha and beta is .... |
|
Answer» `6X^(2)-x-2=0` |
|
| 11558. |
Let x and y be two variables such that x gt 0 and xy =1. Then the minimum value of x+y is |
|
Answer» 2 |
|
| 11559. |
If f (x) = int _(0) ^(x) sin [2x] dx then f ( pi//2)is (where [**] denotes greatest integer function) |
|
Answer» `1/2 { SIN 1+ (pi-2) sin 2}` |
|
| 11560. |
Let Delta_(k)be the area of triangle AP_(k)B which is inscribed in a circle or radius 2units. If AB diameterof circle ,angle ABP_(k)=(lpi)/(2n) and sum_(k=1)^(n+1)=4 cot""(pi)/(32), then(n)/2 is equal to |
|
Answer» |
|
| 11561. |
M and N are the mid-points of the diagonals AC and BD respectively of quadrilateral ABCD, then AB+AD+CB+CD is equal to |
|
Answer» 2 MN a,b,c,d, m and n. Since, M and N are the mid-points of AC and BD. `therefore m=(a+c)/(2),n=(b+d)/(2)` Now, `AB+AD+CD+CD` `=(b-a)+(d-a)+(b-c)+(d-c)` `=2(b+d)-2)a+c)` `=2xx2n-2xx2m` `=4 (n-m)=4 NM` |
|
| 11562. |
An urn contains two balls each of which is either white or black. A white ball is added to the urn. What is the probability of drawing a white ball from the bag now. |
|
Answer» |
|
| 11563. |
Structure of N_(2)O is N = N = O. Calculate bond enthalphy of N = N bond in N_(2)O. Given : {:(DeltaH_(f,N_(2)O)^(@)=100 "kJmol"^(-1)""BE_(N=N)=950 kJ mol^(-1)),(BE_(N=0)=600 "kJmol"^(-1)""BE_(O=O)=500 "kJmol"^(-)):} and resonance energy of N_(2)O = - 100 kJ mol^(-1) |
|
Answer» `500 kJ mol^(-1)` |
|
| 11564. |
Areaof theregiionbounded by(x^2 )/(16) +(y^2)/(9) = 4 |
| Answer» ANSWER :C | |
| 11565. |
If the chords of contact of tangents from two points (x_(1),y_(1)) and (x_(2),y_(2)) to the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 are at right angles, then find (x_(1)x_(2))/(y_(1)y_(2)) |
|
Answer» |
|
| 11566. |
Let a=(1//3) (-hati + 2hatj + 2hatk), then |
|
Answer» a is a unit VECTOR |
|
| 11567. |
Find the vector equation of the plane passing through the intersection of the planes vecr.(2hati+2hatj-3hatk)=7,vecr.(2hati+5hatj+3hatk)=9 and through the point (2, 1, 3). |
|
Answer» |
|
| 11568. |
The pole of lx + my = 1 with respect to the ellipse lies on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=4 if: |
|
Answer» `b^2l^2 + a^2m^2 = 4` |
|
| 11569. |
If the lines barr =(i-j+k) +lambda(pi+j) and barr=(2i-j) +mu(i-j+4k) are coplanar then: p= |
|
Answer» `3/7` |
|
| 11570. |
If P(A | B) gt P(A) then which of the following is true ? |
|
Answer» <P>`P(B|A) lt P(B)` |
|
| 11571. |
If three complex number are in A.P then they lie on |
| Answer» Answer :A | |
| 11572. |
If Z= (1+ xi)^(n) be a complex number such that its real and imaginary parts are equal where x in R, n in I^(+) then positive values of x are |
|
Answer» `x= tan ((PI)/(4n))` |
|
| 11574. |
Find (dy)/(dx): x=a sin^(2) theta cos theta, y= 2b cos^(2) theta (-sin theta) |
|
Answer» |
|
| 11575. |
Volume occupied one molecule of water (density = 1g cm^(-3)) is :- |
|
Answer» `3.0 XX 10^(-23) CM^(3)` |
|
| 11576. |
Find the equation of plane passing through the line of intersection of planes vecr.(hati+3hatj) +6=0 and vecr.(3hati-hatj-4hatk)=0,whose perpendicular distance from origin is one unit. |
|
Answer» |
|
| 11577. |
The tangent to the cureve xy+ax+by=0 at (1, 1) makes an angle with X - axis is tan^(-1)2 then …………. |
|
Answer» a = 1, B = 2 |
|
| 11578. |
There are 16 coins in bag. Out of which 2 coins are defective having both sides head and remaining coins are good. One coin is selected at random from box and is tossed. Then ........ is the probability of event that head is obtained on it. |
|
Answer» `(9)/(16)` |
|
| 11579. |
(i) Find the equation of circle which touches x^(2)+y^(2)-4x+6y-12=0 at (-1,1) internally with a radius of 2. (ii) Find the equation of circle which touches x^(2)+y^(2)-2x-4y-20=0 externally at (5,5) with radius of 5. |
|
Answer» (II) `x^(2)+y^(2)-18x-16y+120=0` |
|
| 11580. |
Statement 1: The only circle having radius sqrt10and a diameter along line 2x+ y= 5is x^(2) +y^(2) -6x +2y =0 Statement 2: 2x+y = 5is a normal to the circlex^(2) + y^(2) -6x +2y=0 |
|
Answer» STATEMENT 1 is FALSE ,statement 2 is true |
|
| 11581. |
the numberof valuesofthetain theinterval[ -pi , pi] satisfyingtheequationcos theta + sin 2theta=0is |
|
Answer» 1 |
|
| 11582. |
The value of the sum sum_(j=0)^(8)1/((j+1)(j+2))(8/j) is |
|
Answer» `1003/90` |
|
| 11583. |
Given that the derivative f'(a) exists. Indicate which of the following statements(s) is/are always true? |
|
Answer» `F'(a)=lim_(htoa)(f(H)-f(a))/(h-a)` |
|
| 11584. |
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economic, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is |
|
Answer» 7 |
|
| 11585. |
int(f(x)g'(x)-f'(x)g(x))/(f(x)g(x)) [ log (g(x))-log(f(x))]dx= |
|
Answer» `(1)/(2)(" log "(G(X))/(f(x)))^(2) + C` |
|
| 11586. |
A particle moves 30m in east and 40 m in north then ratio of magnitude of displacement of the distance is :- |
|
Answer» `5/7` |
|
| 11587. |
Find the centre and radius of each of the circles whose equations are given below. 3x^(2) + 3y^(2) - 6x - 12y - 1 =0 Find the radius and centre of the circle. |
|
Answer» |
|
| 11588. |
If the regions A and B are given by A= {(x,y): y gt x}, B= {(x,y): y lt 2-x^(2)} find the area of A nn B |
|
Answer» |
|
| 11589. |
For x to 2 determine the order of smallness, relative to the infinitesimal beta(x)=x-2, of the following infinitesimals (a) 3(x-2)^(2)+2(x^(2)-4), (b) root3(sin pi x) |
|
Answer» |
|
| 11590. |
Find the co-ordinates of the points on the curve y = x^(2)-1/x^(2)+1, x gt 0 such that tangent at these point(s) have the greatest slope. |
|
Answer» |
|
| 11591. |
Consider a binary operation on Q -{1} define by a*b =a+b-ab (i) Find the identity element in Q-{1} (ii) Show that each a in Q-{1} has its invese |
|
Answer» `a*e=a rarr a+e-ae=a` `rarr e(1-a=0 rarr e=0` [before a `ne` 1] `therefore` 0 is the identity element (II) Let a in Q-{1} be an arbitray element and let b be its INVERSE Then `a*b=0 rarr a+b-ab=0 rarr ab-b=a` `rarr b(a-1)=a rarr b=(a)/(a-1)` Thus each a in Q-{1} has `(a)/(a-1)` as its inverse |
|
| 11592. |
If the vertices of a feasible region are O(0,0),A(10,0), B(0,20), C(15, 15), then minimum value of a objective function Z= 10 x - 20y + 30 is…....... |
| Answer» ANSWER :D | |
| 11593. |
The maximum number of points of intersection of 8 circles is |
|
Answer» 16 |
|
| 11594. |
Number of different permutations of the word "INTERMEDIATE' is |
|
Answer» `(12!)/(3!3!2!)` |
|
| 11595. |
If f(x)=|(x^(n),sinx,cosx),(n!,sin(npi//2),cos(npi//2)),(a,a^(2),a^(2))|, then (d^(n))/(dx^(n)){f(x)} at x=0 is |
|
Answer» -1 |
|
| 11596. |
Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi)cos^(3)x.sin^(4)xdx=.......... |
| Answer» ANSWER :B | |
| 11597. |
IF11theta= pithencostheta . cos2 theta. cos 3 theta cos4 theta . Cos5 thetais |
|
Answer» `1/5` |
|
| 11598. |
(sin(alpha+beta))/(sin(alpha-beta))=(a+b)/(a-b) then (tan alpha)/(tan beta)= |
| Answer» ANSWER :A | |
| 11599. |
Consider the following differential equations. D_(1) : y=4((dy)/(dx) )^2+ 3x, D_(2), (d ^(2)y)/(dx ^(2))= (3+ ((dy)/(dx)) ^(2) )^(4/3)D_(3):[1+ ((dy)/(dx))]^(2) = ((dy)/(dx)) ^(2) The ratio of the sum of the orders of D_(1),D_(2)and D_(3) to the sum of their degrees is |
|
Answer» `1:2` |
|
| 11600. |
Using vectors, find the area of the DeltaABC with vertices A(1,2,3),B(2,-1,4) and C(4,5,-1). |
|
Answer» |
|