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.
| 27051. |
(Manufacturing problem) A manufacturing company makes two models A and B of product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model A and Rs. 12000 on each piece of Model B. How many pieces of model A and model B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ? |
|
Answer» |
|
| 27052. |
If the direction cosines of two lines are given by l + 3m +5n=0 and 5lm - 2mn + 6lm = 0, then the angle between the lines is |
|
Answer» `cos^(-1) ((1)/(6))` |
|
| 27053. |
Choose the correct answer: The probability that a student is not a swimmer is (1)/(5) out of five students, four are swimmers is |
|
Answer» `""^(5)C_(4)((4)/(5))^(4)(1)/(5)` |
|
| 27054. |
If I_(1) = int_(x)^(1) (1)/(1+t^(2))dt and I_(2)=int_(1)^(1/x) (1)/(1+t^(2))dt for x gt0, then |
|
Answer» `I_(1)=I_(2)` |
|
| 27055. |
Evalute the following integrals int sin^(2)x dx on R |
|
Answer» |
|
| 27056. |
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%? |
|
Answer» |
|
| 27057. |
Formthe differential equation of the family of circles having centre on y-axis and radius 3 units. |
|
Answer» |
|
| 27058. |
Find the vector equation of the plane passing through the points (1, -2, 5) (0, -5, -1) and (-3, 5, 0). Transform the vector equation into cartesian equation. |
|
Answer» |
|
| 27059. |
Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are collinear. |
|
Answer» |
|
| 27060. |
Show that the locus of the foot of the perpendicular drawn from centre on any tangent to the ellipse b^2x^2+a^2y^2=a^2b^2 is the curve (x^2+y^2)^2=a^2x^2+b^2y^2 |
|
Answer» |
|
| 27061. |
write the negation of following statements Every living person is not 150 year old |
| Answer» Solution :There EXISTS a living PERSON who is 150 years OLD | |
| 27062. |
Find the equation of the circle with centre C and radius r where C = (-7, -3) , r= 4 |
|
Answer» |
|
| 27063. |
Solution of the differential equation 2 y sin x (dy)/(dx) = 2 sin x cos- y^(2) cos x satisfying y(pi//2) = 1 is given by |
|
Answer» `y^(2) = SIN X` |
|
| 27064. |
whenfourlettersare insertedin tofourcovers (onein each ) A =eventthat onlyone lettersgoesto thepropercover . B = eventthat exactlythreelettersgo to thepropercovers . C=eventthat lllettersgo topropercoversand then ...... is true |
|
Answer» `p toA , Q to c, R to B` |
|
| 27065. |
If A and B are two independent events, and P(A)=1//4, P(B)=1//3 then find P(A-B)uu(B-A)). i.e., propbability of occurrence of exactly one of the events A and B. |
|
Answer» |
|
| 27066. |
Centre of the circle circumscribed in a rectangle formed by the lines x^(2)-8x+12=0 and y^(2)-14y+40=0 is |
|
Answer» (4,7) |
|
| 27067. |
Express in the form a+bi (1+i)/(1-i) |
|
Answer» SOLUTION :`(1+i)/(1-i)=((1+i)^2)/2=(1-1+2i)/2` `=i=0+i` |
|
| 27068. |
Let A, B and C be three events and suppose that simultaneous occurrence of A and B implies the occurrence of C, then |
|
Answer» `P(C) GE P(A)+P(B)` |
|
| 27070. |
Write the direction ratio'sof thevector veca=hati+hatj-2hatk andhence calculate its direction cosines. |
|
Answer» |
|
| 27072. |
Calculate the range and its coefficient for the following data 100, 80, 200, 150, 250, 300 |
|
Answer» |
|
| 27073. |
If alpha, beta, gammaare roots of x^(3) - ax^(2) + bx + c = 0 then (alpha^(2) + 1) (beta^(2) + 1)(gamma^(2) + 1) = |
|
Answer» `(C - a)^(2) + (B - 1)^(2) ` |
|
| 27074. |
Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+z ^(2) =1 and z ^(2) +zx+x^(2) =3. If the value of xy + zx can be expressed as sqrt((p)/(q)) where p and q are relatively prime positive integral find the value of p-q, |
|
Answer» |
|
| 27075. |
Evaluate i. lim_(xto0)(tanx-sinx)/(sin^(3)x) ii. lim_(xto0)(cos2x-1)/(cosx-1) |
|
Answer» (II) 4 |
|
| 27076. |
If A is a 3xx3 skew -symmetric matrix with real entries and trace of A^(2) equals zero then |
|
Answer» A=O |
|
| 27077. |
A bag contain 5 balls. Two balls are drawn and found them to be red. Find the probability that all the balls are red. |
|
Answer» |
|
| 27078. |
Find the coefficient of x^(3) in the expansion of ((1+3x^(2))^(3//2))/((3+4x)^(1//3)). |
|
Answer» |
|
| 27079. |
A company manufactures two typesof toysA and B type A requires5 munutes each fro cuttingh and 10 minutes each and 8 minutes each for assemblinghe earns a profitof Rs 50 eachon typeA andRs 60 eachson type B |
|
Answer» |
|
| 27080. |
The sum of coefficients of integral powers of x in the binomial expansion of (1-2 sqrtx)^50 is |
|
Answer» `(1)/(2) (3^50 +1)` |
|
| 27081. |
A cooperative society oof farmer has 50 hectares of land to grow crops A and B.The profits from crops A and B per hectare are estimated as ₹.10,500 and ₹. 9,000 respectively.To control weeds, a liquid pesticide has to be used for crops A and B at the rate of 20 litres and 10 litres per hectare,respectively.Further not more than 800 litres of pesticide should be used in order to protect fish and wildlife using a pond which collects drainage from this land.Keeping in mind that the protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each crop so as to maximize the total profit?Form an LPP from the above and solve it graphically.Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance in environment? |
|
Answer» |
|
| 27082. |
Equation of the line 2x + z - 4 = 0 = 2y + z in symmetric form is |
|
Answer» `(X)/(1)=(y+2)/(1)=(z-4)/(-2)` |
|
| 27083. |
Ifsintheta= 3sin( theta + 2 alpha), thenthe valueoftan(theta+ alpha) + 2 tan alphais |
| Answer» ANSWER :D | |
| 27084. |
Equation of line passing through the points (1,2,3) ,(2,-1,2) is |
|
Answer» `(x-2)/(2) =(y-2)/(-1) =(z-3)/(2)` |
|
| 27085. |
Let n be even postiive integer such thatn/2 is odd and letalpha_(0) ,alpha_(1) ,……..,alpha_(n+1) be the complex roots of unityof order n. prove that overset(n/1)underset(k=0)(II)(a+balpha_(k)^(2))=(alpha^(n/2)+b^(n/2))^(2) for any complex numbers a and b |
| Answer» | |
| 27086. |
Evaluate the definite integrals int_(0)^(pi/4)(sinxcosx)/(cos^(4)x+sin^(4)x)dx |
|
Answer» |
|
| 27087. |
If n is a natural number, then the number of non-negative integral solutions of x+y+z=n is |
|
Answer» `(N(n-1))/(2)` |
|
| 27088. |
Evaluate int_(0)^(2pi) [ sin x + cos x] dx where [ ] denotes the G.I.F. |
|
Answer» |
|
| 27089. |
The shortest distance between the lines r=3i+5j+7k +lambda (i+2j+k) and r=-i-j-k+mu (7i-6j+k) is |
|
Answer» `(16)/(5sqrt5)` |
|
| 27090. |
Evalute the following integrals int (x^(2))/(x^(2) - 4) dx |
|
Answer» |
|
| 27091. |
Find the following integrals. int_0^(pi/2)frac(sinx)(1+cos^2x)dx |
|
Answer» SOLUTION :Put COSX = 1. Then dt = -sinx dx `gt sinx dx = -dt` ALSO X = 0 `gt t = 1` and x = `pi/2 gt t = 0 therefore `int_0^(pi/2) sinx/(1+cos^2 x) dx = int_1^0 (-dt)/(1+t^2)` =`-[tan^-1 t]_1^0 = -[0-pi/4] = pi/4` |
|
| 27092. |
Iflog_("sin"(pi)/(4)) sin x gt 0 , x in [ 0. 4pi). Themfind the region of x satisfying the inequality . |
|
Answer» Solution :We have , ` log_("sin"(pi)/(4)) sin x gt 0 ` `rArr log_((1)/(sqrt(2))) sin x gt 0 ` ` rArr (sin x ) LT ((1)/(sqrt(2)))^(0) as 0 lt (1)/(sqrt(2)) lt 1` `rArr (sin x) lt 1 "but sin" x gt 0 ` ` rArr 0 lt sin x lt 1 ` `rArr x in (,(pi)/(2)) cup((pi)/(2) , pi)cup(2pi, (5pi)/(2)) cup ((5pi)/(2) ,3pi)`. |
|
| 27094. |
For the plane prod = x + y +z – 4= 0, the point (1, 2, 3) lie in the |
| Answer» Answer :A | |
| 27095. |
Three screws are drawn at random from a lot of 50 screws, 5 of which are defective. Find the probability of the event that all 3 screws are non-defective assuming that the drawing is a) with replacement b) without replacement. |
|
Answer» |
|
| 27097. |
Negative of the statement: All the students completed their homework. |
| Answer» SOLUTION :There EXISTS a STUDENT who has not COMPLETED his HOMEWORK. | |
| 27098. |
Which of the following matrice is invertible? [[1,0,1],[2,-2,1],[3,2,4]] |
|
Answer» Solution :LET A=`[[1,0,1],[2,-2,1],[3,2,4]]` `therefore absA=[[1,0,1],[2,-2,1],[3,2,4]]` =`1[[-2,1],[2,4]]+1[[2,-2],[3,2]]` =-8-2+4+6=0 `therefore` This MATRIX A is not INVERTIBLE. |
|
| 27099. |
A square plate contract at the uniform rate of 0.01cm //sec, then, when the radius is 20 cm , vloume of the sphere is increasing at the rate of |
|
Answer» `1.6 pi C.c //SEC`. |
|
| 27100. |
Show that the average value of the function f(x), continuous on the interval [a,b], is the limit of the arithmetic mean of the values of this function taken over equal intervals of the argument x. |
|
Answer» |
|