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.
| 11301. |
f: R rarr R , f(x) =x^(2)+1. Find the preimage of 17 and -3. |
|
Answer» |
|
| 11302. |
Write down the first three terms is the following expansions(3 + 4x)^(-2//3) |
|
Answer» |
|
| 11303. |
If vec a and vec b are collinear vectors, then which of the following are incorrect? |
|
Answer» `vecb=lambdaveca`,for some SCALAR `lambda` |
|
| 11305. |
Let E_(1)={x in R :x ne 1 and (x)/(x-1) gt 0} and E_(2)={x in E_(1):sin^(-1)(log_(e)((x)/(x-1))) " is real number"} (Here, the inverse trigonometric function sin^(-1)x assumes values in [-(pi)/(2),(pi)/(2)].) Let f:E_(1) to R be the function defined by f(x)=log_(e)((x)/(x-1)) and g:E_(2) to Rbe the function defined byg(x)=sin^(-1)(log_(e)((x)/(x-1))) . The correct option is |
|
Answer» `a to s, b to Q, C to p, d to p` `implies x in (-OO ,0) cup (1,oo)` Also `E_(2) : -1 lt log_(e)((x)/(x-1)) le 1` `implies (1)/(e) le (x)/(x-1) le e` `implies (1)/(e) le 1 +(1)/(x-1) lee` `implies (1)/(e)-1 le (1)/(x-1) le e-1` `implies (x-1) in (-oo, (e)/(1-e)] cup [(1)/(e-1),oo)` `implies x in (-oo, (e)/(1-e)] cup [(1)/(e-1),oo)` Now, `(x)/(x-1) in (0, oo)-{1} AA x in E_(1)` `implies log_(e) ((x)/(x-1)) in (-oo,oo)-{0}` `implies sin^(-1)(log_(e)((x)/(x-1))) in [-(pi)/(2),(pi)/(2)]-{0}` `("considering "log_(e) ((x)/(x-1)) in [-1,1]-{0})` |
|
| 11306. |
Find limit of the ratio of the area of the triangle formed by the orgin and intersection points of the parabola y-4x^2 and the line y=a^2,to the area between the parabola and the line as a approaches to zero. |
|
Answer» |
|
| 11307. |
z_(1) = 1 +i , z_(2) = -sqrt3 + i , z_(3) = 1 + sqrt3i , z_(4) = 1 - i Arrange z_(1) , z_(2) , z_(3) , z_(4) is descending order of their principal values |
|
Answer» `z_(3) , z_(2) , z_(1) , z_(4)` |
|
| 11308. |
Determine order and degree (if defined) of the following differential equations y''' + 2y'' + y' = 0 |
| Answer» SOLUTION :The highest ORDER derivative in the DIFFERENTIAL equation is y... and its degree is 1. `therefore` The order and the degree of the differential equation are 3 and 1 RESPECTIVELY. | |
| 11309. |
If the equation of conic 2x^(2) + xy+3y^(2) - 3x+ 5y + lambda =0 represents a single point, then find the value of lambda. |
|
Answer» |
|
| 11310. |
Solve the following equations 2x^5+x^4-12x^3-12x^2+x2=0 |
|
Answer» |
|
| 11311. |
If equation of the plane passing through i+2j-k and perpendicular to the line of intersection of the planes r.(3i-j+k)=4 and r.(i+4j+2k)=12, is (x)/(a)+(y)/(b)+(z)/(c )=1, then 91(a+b+c)=________ |
|
Answer» |
|
| 11312. |
Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6 and vecr.(2hati+3hatj+4hatk)=-5 and the points (1,1,1). |
|
Answer» |
|
| 11313. |
If ((10),(x-1)) gt 2((10),(x)) ,then |
|
Answer» X`EPSI` [2,9] |
|
| 11314. |
Find the values of k so that the function f is continuous at the indicated point f(x)= {(kx+1",","if" x le pi),(cos x,"if" x gt pi):} " at " x= pi |
|
Answer» |
|
| 11316. |
If A,B,C are angles of a triangle such thatx = cis A , y = cis B , z = cis C, then find the value of xyz . |
|
Answer» |
|
| 11317. |
The solution of the differential equation (dy)/(dx)+xyln y=x^(3)y is equal to (where, C is the constant of integration) |
|
Answer» `lny=X^(2)+Ce^(-x^(2))` |
|
| 11318. |
alpha , beta, gamma are the roots of the equation x^(3)-10x^(2)+7x+8=0, Match the following columns and choose the correct answer. {:("Column I","Column II"),("A)"alpha+beta+gamma,"1)"(-43)/(4)),("B)"alpha^(2)+beta^(2)+gamma^(2),"2)"(-7)/(8)),("C)"1/alpha+1/beta+1/gamma,"3)"86),("D)"(alpha)/(beta gamma)+(beta)/(gammaalpha)+(gamma)/(alpha+beta),"4)"0),(,"5)"10):} |
|
Answer» `{:("(A)","(B)","(C)","(D)"),(5,3,1,2):}` |
|
| 11319. |
If water sample are taken from sea, rivers or lake, they will be found to contain hydrogen and oxygen in the approximate ratio 1 : 8. This indicates the law of :- |
|
Answer» MULTIPLE PROPORTION |
|
| 11320. |
A variable line L intersects the parabola y=x^(2) at points P and Q whose x- coordinate are alpha and beta respectively with alpha lt beta the area of the figure enclosed by the segment PQ and the parabola is always equal to 4/3. The variable segment PQ has its middle point as M Which of the following is/are correct? |
|
Answer» <P>equations of the pair of TANGENTS, drawn to the curve, represented by locus of `M` from origin are `y=2x` and `y=-2x` Equation of `PQ, y-alpha^(2)=(alpha+beta)(x-alpha)` `y=(alpha+beta)x-alpha beta` Required area `int_(alpha)^(beta)((alpha+beta)x-alpha beta-x^(2))dx` `IMPLIES beta-alpha=2` Pair of tangents from origin are `y=2x` and `y=-2x` Area `int_(0)^(1)((x^(2)+)-2x)dx=2/3` 
|
|
| 11321. |
B(OH)_(3)(aq)+" glycol "toproduct X. How many chelate rings are present in product X. |
Answer» 
|
|
| 11323. |
Integrate the functions xsin3x |
|
Answer» |
|
| 11324. |
int(x^(2)+cos^(2)x)/((1+x^(2))sin^(2)x)dx= |
|
Answer» `cotx+tan^(-1)x+c` |
|
| 11325. |
Integrate the following functions xsinx |
|
Answer» Solution :`INT x SINX dx` =`x(-COSX)- int 1XX -cosx dx` =`-xcosx + int cosx dx` =`-x cosx +sinx+c` |
|
| 11326. |
Identify statements S_(1),S_(2),S_(3) in order for true(T)false(F) S_(1)="If A"=[{:(,cos theta,-sin theta,0),(,sin theta,cos theta,0),(,0,0,1)]:} then adj=A=A' S_(2)="If A"=[{:(,a,0,0),(,0,b,0),(,0,0,c):}]"then "A^(-1)=[{:(,a,0,0),(,0,b,0),(,0,0,c):}] S_(3): If B is non-singular matrix A is a squre matrix, then det (B^(-1),AB) =det(A) |
|
Answer» TTF |
|
| 11327. |
For 0 lt theta lt (pi)/(2), four tangents are drawn at the four points ( pm 3 cos theta, pm 2 sin theta ) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 . If A(theta) denote the area of the quadrilateral formed by these four tangents, the minimum value of A(theta) is |
|
Answer» 21 `(-x cos theta)/(3)+(y sin theta)/(2)=1` `(-x cos theta)/(3)-(y sin theta)/(2)=1` `x=0,y=2 cos theta` AREA `=4.(1)/(2) 3 sin theta. 2 cos theta` `=(12)/( sin theta cos theta)=(24)/( sin 2 theta)` `:. ` MIN. area =24 |
|
| 11328. |
If onerootof10 x^3-x^2 - 278x + 165=0is5 thenproductof theremainingtworootsis |
|
Answer» 33 |
|
| 11329. |
Which of the following points maximise the objective function P=x/2+y/3? |
|
Answer» (4,0) |
|
| 11330. |
20.0 kg of N_(2(g)) and 3.0 kg of H_(2(g)) are mixed to produce NH_(3(g)). The amount of NH_(3(g)) formed is :- |
|
Answer» 17 kg |
|
| 11331. |
check the validity of the following statement (a) r : if x is a real number such that x^3+9x then x is 0. (b) r : If x is an integer and x^3 is even , then x is also even (c) r : If a polygon regular thon it is equiangular and equilateral. |
|
Answer» Solution :(a) Component STATEMENTS are p : X is a real number such that `x^3+9x=0` Q : x is 0 Now to check validity of r (i) Direct Method : Let p is true, then q is true. `therefore` x is real number such that `x^3+9x=0` `therefore` x is a real number such that `x(x^2+9)=0` `therefore x=0` `therefore` q is true Thus , p is true `rArr` q is true So, given statement r is true (ii) Contrapositive Method : Let q is false , i.e.,`x ne 0` Now , according to p x is real number such that `x^3+9x=0` So, `x(x^2+9)=0` It shows that x is real number and x=0 , but according to q , `x ne 0` , so this is a contradiction So, r is true Component statement are p : x is an integer and `x^3` is even q : x is an even integer Suppose q is false (i.e.,~q is true) i.e.,x is an odd integer So, `x^3= " odd"xx "odd"xx"odd "` `=" (odd"xx "odd)"xx"odd "` `" odd"xx "odd"` `x^3` is also odd , so p is false It shows that `~q rArr ~p` (C) Component statements of r be p : A polygon is REGULAR. q : A polygon is equiangular and equilateral. |
|
| 11332. |
If x = {1,2,3 …., 10 } and a represents any elements of X then write the follwing sets containing all the elements satisfing the given conditionsa in X but a^2 in X a in X but a//2in X a is factor of 24 |
|
Answer» (a) Since `1^2,2^2,3^2 in X` `{a|a in X and a^2 notin X}` ={4,5,6,7,8,9,10} (b) ` a in X but a//2 of 24` `rArra=1,3,5,7,9` `THEREFORE of 24` `RARR{a|a in X buta//2in X} `= {1,3,5,7,9} ( c) a is FACTOR of 24 `rArra= 1,2,3,4,5,6,8 ` `therefore{ a|a is" factor of "24 }={ 1,2,3,4,6,5,6,8}` |
|
| 11334. |
If int(sinx)/(cosx(1+cosx))dx = f(x)+c, then f(x) is equal to |
|
Answer» `|(1-COSX)/(cosx)|` |
|
| 11335. |
If n coins are tossed simultaneously, the probability of getting head an odd number of times is |
|
Answer» `(1)/(2^(N))` |
|
| 11336. |
A={:[( 1,1,1),(1,2,-3),(2,-1,3)]:}Show that A^(3) - 6A^(2) +5A +11 I =O. Hence , findA^(-1) |
|
Answer» |
|
| 11337. |
If alpha, beta, gamma are roots of a cubic equation satisfyingthe relationsalpha + beta + gamma = 2,alpha^(2) + beta^(2) + gamma^(2) = 6 and alpha^(3) + beta^(3) + gamma^(3) = 8then the cubic equation is |
|
Answer» `X^(3) + 2X^(2) - x + 2 = 0 ` |
|
| 11338. |
Compute the integral int_(0)^(pi//4) (dx)/( a^(2) cos^(2) x + b^(2) sin^(2) x) (a gt 0, b gt 0) |
|
Answer» |
|
| 11339. |
Evaluate int(1)/(2sin^(2)x+3cos^(2)x)dx |
|
Answer» |
|
| 11340. |
The value of intdx/(16x^2-25) is |
|
Answer» `1/20 LOG|(4x-5)/(4x+5)|+C` |
|
| 11341. |
Determine whether a**b=sqrt(a^2+b^2) on Q_+operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation. |
|
Answer» SOLUTION :for all `a,B in Q^+` `a**b =sqrt(a^2+b^2) !in Q^+` `:. **` is not a binary operation on `Q^+`. |
|
| 11342. |
If the two lines (x-1)/(3)=(y-k)/(6)=(z+1)/(-2)and(x-2)/(-1)=(y-2)/(4)=(z+1)/(-1) intersect at a point, then k is |
|
Answer» `(13)/(5)` |
|
| 11343. |
Let f be a real valued function with (n +1) derivatives at each point of R. For each pair of real numbers a,b, a lt b, such that ln [(f(b)+f (b)+.....+ f ^((n))(b))/(f (a) + f'(a) +.....+ f ^((n))(a))] Statement-1 : There is a number c inh (a,b) for which f ^((n+1))(c) =f (c)because Statement-2: If h (x) be a derivable function such that h (p) =h (q) then by Rolle's theorem h'(d) =9,d in (p,q) |
|
Answer» Statement-1 is TRUE, statemet-2 is true and statement-2 is CORRECT EXPLANATION for statement-1 |
|
| 11344. |
A dealer wants to purchase 5 litres oil tin and 1 kg ghee tin. He has only Rs. 5760 to invest and has a space for atmost 20 tins. 5 l oil tin costs him Rs. 360 and 1 kg ghee tin costs him Rs. 240. He can sell oil tin at a profit of Rs. 22 and ghee tin at a profit of Rs. 18. Assuming that he can sell all the items that he buys, how should he invest his money for maximum profit ? |
|
Answer» |
|
| 11345. |
Given two independent events A and B such that P(A) = 0 . 3, P (B) = 0 . 6 . FindP(A and B) |
|
Answer» |
|
| 11346. |
If x+1/x=2costheta then x^(10)+(1)/(x^(10))= |
|
Answer» `2^(10)cos10 THETA` |
|
| 11347. |
Evaluate the following : [[2,3,4],[1,-1,3],[4,1,10]] |
|
Answer» SOLUTION :`[[2,3,4],[1,-1,3],[4,1,10]]`=`[[5,3,4],[0,-1,3],[5,1,10]]` (REPLACING `C_1` by `C_1+C_2`) `5[[1,3,4],[0,-1,3],[1,1,10]]=[[1,3,4],[0,-1,3],[0,-2,6]]` (`R_3`~`R_3-R_1`) = `5xx1[[-1,3],[-2,6]]=5(-6+6)=0` |
|
| 11348. |
If A=[(1,3),(4,2)],B=[(2,-1),(1,2)]," then "|ABB'|= |
|
Answer» 100 |
|
| 11349. |
Integrate the following rational functions : int(x^(3))/(x^(2)-4)dx |
|
Answer» |
|
| 11350. |
Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}] |
|
Answer» Solution :we have, `[{:(2,-1),(1,0),(-3,4):}]_(3xx2)A=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}]_(3xx3)` From the given equation , it is clear that ORDER of A should be `2xx3` LET `A=[{:(a,b,c),(d,E,f):}]` `[{:(2,-1),(1,0),(-3,4):}][{:(a,b,c),(d,e,f):}]=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}]` `rArr[{:(2a-d,2b-e,2c-f),(a+0d,b+0.e,c+0.f),(-3a+4d,3b+4e,-3c+4l):}]=[{:(-1,-8,-10),(1,-2,-5),( 9,22,15):}]` `rArr [{:(2a-d,2b-e,2c-f),(a,b,c),(-3a+4d,-3b+4e,-3c+4f):}]=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}]` By equality of matrices, we get `a=1,b=-2,c=-5` and `2a-d=-1rArrd=2a+1=3` `rArr 2b-e=-8rArre=2(-2)+8=4` 2c-f=-10`rArr`f=2c+10=0 `therefore A=[{:(1,-2,-5),(3,4,0):}]` |
|