Saved Bookmarks
This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If [(x+2,y-3),(0,4)] is a scalar matrix. Find x and y. |
|
Answer» |
|
| 2. |
if f(x) ={{:((1-|x|)/(1+x),xne-1),(1, x=-1):}thenf([2x]) , where [.] represents thegreatest integer function , is |
|
Answer» DISCONTINUOUS at x=-1 |
|
| 3. |
If P(A cap B)= (7)/(10) and P(B)= (17)/(20) then P(A//B) equals = ……… |
|
Answer» `(14)/(17)` |
|
| 4. |
Which of the following numbers are solutions to the inequality x lt 10? Indicate ul("all") that apply. |
|
Answer»
All of these numbersare to the LEFT of 10 on the NUMBER LINE . `(##GRE_MAT_MAN_PRP_C03_E01_006_A01##)` |
|
| 5. |
Let alpha=(pi)/(5) and A=[(cosalpha,sinalpha),(-sinalpha,-cosalpha)], then B=A+A^(2)+A^(3)+A^(4) is |
|
Answer» singular |
|
| 6. |
Find dy/dx If y=sin^(-1)(frac(1-x^2)(1+x^2)) , 0 < x < 1 |
| Answer» SOLUTION :`y=sin^-1((1-x^2)/(1+x^2))=pi/2-cos^-1((1-x^2)/(1+x^2))=pi/2-2tan^-1xtherefore(DY)/(DX)=0-2xx1/(1+x^2)=2/(1+x^2)sin^-1x=pi/2cos^-1x` | |
| 7. |
Examine the consistency of the system of equations x+ y +z=1 2x+ 3y +2z =2 ax+ay +2az =4 |
|
Answer» |
|
| 9. |
Two women and some men participated in a chess tournament in whichevery participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in theinterval |
|
Answer» [8,9] |
|
| 10. |
The number of values of k for which the equation x^(2) -3x +k=0has two distinct roots lying in the interval (0, 1) are interval (0, 1) are |
|
Answer» THREE |
|
| 11. |
If g(x)=x^(2)+x-2and1/2(gof)(x)=2x^(2)-5x+2, then one such function f(x) = |
|
Answer» 2X - 3 |
|
| 12. |
If a, b,c , d are the roots of the equation : x^(4) + 2x^(3) + 3x^(2) + 4x + 5 = 0 , then 1 + a^(2) + b^(2) + c^(2) + d^(2) is equal to : |
| Answer» Answer :B | |
| 13. |
Using properties evaluate the following definite integrals, evaluate the following: int_2^8 |x-5|dx |
|
Answer» SOLUTION :`|X-5|` = `{ x-5, x ge 5 -(x-5), x LT 5}` therefore `int_2^8 |x-5| dx` =`int_2^5 (5-x)dx + int_5^8 (x-5) dx` =`(5X-x^2/2)_2^5 + (x^2/2 -5x)_5^8` `(25-(25)/2)-(10-4/2)+((64)/2 - 40)-((25)/2 -25)` `(25)/2-8-8+(25)/2 = 25-16 = 9` |
|
| 14. |
How many structures are supported by cartilaginous rings ? Larynx, Trachea, Bronchi, Initial bronchioles, Terminals bronchioles, Alveolar duct, Alveoli |
|
Answer» 7 |
|
| 15. |
Statement 1: The function f(x) = |x-a_(1)| + |x - a_(2)|+ ...+|x-a_(2n-1)| where a_(1),a_(2),...a_(2n-1) are distinct numbers has no local minima.. because Statement 2: There does not exists an interval in domain f for which f'(x)= 0throughout in that interval. |
|
Answer» (A) Statement -1 is True, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement - 1. |
|
| 16. |
If Integration using trigonometric identities : int sin 2x*cos 3 x dx= A cos x+B cos 5x+c then A+B=... |
|
Answer» `(1)/(5)` |
|
| 17. |
A right angled isoceles triangle is inscribed in the circle x^(2)+y^(2)-6x+10y-38=0 then its area is (square units) |
|
Answer» 18 |
|
| 18. |
Draw the graph of f(x) = log_(e)(sqrt(1-x^(2))-x) |
|
Answer» Solution :We have `y=f(X)=log_(e)(sqrt(1-x^(2)-x))` `f(x)` is defined if `sqrt(1-x^(2)) - x gt 0` and `1-x^(2) ge0` For `1-x^(2) ge0 , -1 le x le1` `sqrt(1-x^(2))-x gt 0` For (0,1), `1-x^(2)gt x^(2)` or `0 lt x lt 1/sqrt(2)` THUS, the domain of the function is `[-1, 1/sqrt(2)]` `f^(')(x) = ((-x/sqrt(1-x^(2)))-1)/(sqrt(1-x^(2))-x)` `=(-x-sqrt(1-x^(2)))/((sqrt(1-x^(2))sqrt(1-x^(2))-x)` `f^(')(x)=0 therefore -x=sqrt(1-x^(2)` `therefore x=-1/sqrt(2)` `f^(')(x) gt 0` for `x in (-1,-1/sqrt(2))` `f^(')(x) lt 0` for `x in (-1/sqrt(2), 1/sqrt(2))` So `x=-1/sqrt(2)` is the point of maxima. `f(-1) = f(0)=0` `underset(x to 1/sqrt(2))"lim"log_(e)(sqrt(1-x^(2))-x) =- infty (therefore underset(x to 1/sqrt(2))"lim"(sqrt(1-x^(2))-x)=0)` Thus, `x=1/sqrt(2)` is an asymptote. From the above discussion, the GRAPH of the function is as shows in the following FIGURE. 
|
|
| 19. |
If y=(1)/(2x^(2)-1)" then "y+(y^(3))/(3)+(y^(5))/(5)+....= |
|
Answer» `X+(x^(3))/(3)+(x^(5))/(5)+...` |
|
| 20. |
If in a DeltaABC, the incricle passing through the point of intersection of perpendicular bisector of sides BC, AB, then 4 sin ""A/2sin ""B/2sin""C/2 equal to |
|
Answer» `SQRT2` |
|
| 21. |
Evaluate int(x)/(x^(2) + x + 1) dx |
| Answer» | |
| 22. |
The solution of x(dy)/(dx) + y= y^(2) log x is |
|
Answer» `(1)/(XY) = (-(log x)^(2))/(4) + c` |
|
| 23. |
If A and B are two events such that P(Acup B) = P(A cap B), then the incorrect statement amongstthe following is |
|
Answer» <P>A and B are EQUALLY LIKELY |
|
| 24. |
For the curve x^(2)y^(3) = c (where c is a constant), the portion of the tangent between the axes is divided in the ratio. |
|
Answer» `3:5` |
|
| 25. |
Show that the equation of the chord joining two points (x_(1),y_(1)) and (x_(2),y_(2)) on the rectangular hyperbola xy=c^(2) is (x)/(x_(1)+x_(2)) +(y)/(y_(1)+y_(2))=1 |
|
Answer» |
|
| 26. |
If the chord of contact of a point P with respect to the circle x^(2)+_y^(2) = a^(2)cut the circle at A and B such that Aoverset(wedge)("O")B= 9 0^(@) then show that P lies on the circle x^(2) +Y^(2) 2a^(2) |
|
Answer» |
|
| 29. |
If tangent at Z_1, Z_2 on the circle |Z- Z_0|=r intersect at Z_3. Then((Z_3-Z_1) (Z_0 - Z_2))/((Z_0 - Z_1)(Z_3 - Z_2)) equals. |
| Answer» Answer :B | |
| 30. |
If G is the centroid of a triangle ABC, then GA + GB + GC equals to |
Answer» Solution : We have, GB + GC = ( 1 + 1) GDGB + GC = 2GD, where , D is the mid-point of BC. Now, GA + GC = GA + 2GD G divides AD in the AD in the ratio 2 : 1 2 GD = - GA GA + GB + GC = GA - GA = 0
|
|
| 31. |
Choose the correct answer int dx/(sin^2x cos^2x) =....a) tanx+cotx+c b) tanx-cotx+c c) tanx cotx+c d) tanx-cot2x+c |
|
Answer» tanx+cotx+c |
|
| 32. |
Angle between the asymptotes of a hyperbola is 30^(@) then e= |
|
Answer» `SQRT6` |
|
| 33. |
In thequestionof maximumvalueof z = 800 x+ 12000 ysubjectto constraints9x +12y le180, 3x+ 4yle60, x + 3yle 30 , x ge30 ,x ge0,y ge0 …….. isnota point offeasibleregion . |
|
Answer» `(20,0)` |
|
| 34. |
Match the ................. |
|
Answer» (B) `Ph-overset(O)overset("||")(C)-CH_(3) overset(NaBH_(4), ETOH)(rarr) Ph-underset(OH)underset("|")(C)H-CH_(3)` (c) `Ph-NO_(2) overset(LiAlH_(4))(rarr) Ph-N=N-Ph` |
|
| 35. |
If |z-4//z|=2 then the greatest value of |z| is |
|
Answer» `SQRT(5)` |
|
| 36. |
Find the distance of the point (2, 1, 0) from the plane 2x + y + 2z + 5 = 0. |
|
Answer» |
|
| 37. |
Ifx ne 1 andf (x)= (x +1 )/( x-1) is arealfunctionthenfff (2) is |
|
Answer» 1 |
|
| 38. |
"Given "f(x)=int_(0)^(x)e^(t)(log_(e)sec t- sec^(2)t)dt, g(x)=-2e^(x) tan x, then the area bounded by the curves y=f(x) and y=g(x) between the ordinates x=0 and x=(pi)/(3), is (in sq. units) |
|
Answer» `(1)/(2)e^((pi)/(3))log_(e)2` `=overset(x)underset(0)inte^(t)[(LOG _(e) sec t - tan t )+(tan t-sec^(2)t)]dt` `=[e^(t)(log_(e)sec t-tan t)]_(0)^(x)` `=e^(x)(log_(e)sec x- tan x)` `therefore"Required area,"` `A=overset(pi//3)underset(0)INT[e^(x)(log_(e) sec x - tan x)-(-2e^(x)tan x)]dx` `=overset(pi//3)underset(0)inte^(x)(log_(e)sec x +tan x)]dx` `=[e^(x)log_(e)sec x]_(0)^(pi//3)` `=e^(pi//3)log_(e)sec""(pi)/(3)` `=e^(pi//3)log_(e)2` |
|
| 39. |
If the equation 2x^(2)+8xy+py^(2)+qx+2y-15=0 represents a pair of parallel lines, then |
|
Answer» `p=-8, q=-1` |
|
| 40. |
Evaluation of definite integrals by substitution and properties of its : int_(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx=..........(agt0) |
|
Answer» `API` |
|
| 41. |
Show that the direction cosines of a vector equally inclined to the axes OX,OY and OZ are +-((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3))). |
|
Answer» |
|
| 42. |
Number of four letter words consisting equal number of vowels and consonants,(repetition,being,allowed) is |
|
Answer» 11025 |
|
| 43. |
x and y are real numbers . If xRy hArr x - y +sqrt5 ison irrational number then R is ......... Relation . |
|
Answer» REFLEXIVE |
|
| 44. |
Solve the equationx^4+2x^3 -5x^2 +6x +2=0giventhat1+iis aroot |
|
Answer» |
|
| 45. |
Cofficient of x^4 in 1+(1+x+x^2)/(1!) +((1+x+x^2)^2)/(2!) +((1+x+x^2)^3)/(3!) + ....oo = |
|
Answer» `25/24 E` |
|
| 46. |
Solve as directed: -3x - 8 gt 19 , in integers ,in real numbers. |
|
Answer» Solution : -3x-8`gt` 19 `RARR -3x- 8 + 8 gt 19 + 8` `rArr -3x gt 27` ` rArr (-3x)/(-3) LT (27)/(-3)` `rArr X lt -9 if x `in` Z ,then the solution SET isS = { x:x `in` Z and x`lt` -9} = (-`infty` , -9) |
|
| 48. |
Expand the following using binomial theorem. (4x+5y)^(7) |
|
Answer» |
|
| 49. |
If overline (x_(2)) " and" overline (x_(2)) are the means of two distributions such that overline (x_(1)) lt overline (x_(2)) "and" overline (x) is the mean of the combined distriubtion, then |
|
Answer» `overline (x) LT overline (x_(1))` `overline (x)=(n_(1)overline(x_(1))+n_(2)overline(x_(2)))/(n_(1)+n_(2))` Now, `overline (x)-overline(x_(1))=(n_(1)overline(x_(1))+n_(2)overline(x_(2)))/(n_(1)-n_(2))-overline(x_(1))` ` =(n_(2)(overline(x_(2))-overline(x_(1))))/(n_(1)+n_(2)) gt 0 "" [because overline(x_(2))gt overline(x_(1))]` `implies overline(x) gt overline(x_(1))`, and`overline(x)-overline(x_(2))=(N(overline(x_(1))-overline(x_(2))))/(n_(1)+n_(2)) lt 0 "" [ because overline(x_(2)) gt overline(x_(1))]` `implies overline (x) lt overline (x_(2))` From (1) and (2), `overline(x_(1)) lt overline(x) lt overline(x_(2))`. |
|
| 50. |
Which of the following sentences are propositions and which are not ? Write with reason :Cuttack is a big city . |
| Answer» Solution :"Cuttack is a BIG city " is not a STATEMENT , as ITCONTAINS the word .big. (not defined ). | |