# Recent questions and answers in Math

### In Young’s double slit experiment, the two slits $0.15\;m$ apart are illuminated by monochromatic light of wavelength 450nm.$The screen is$1.0\;m$away from the slits. 1. Find the distance of the second a) bright fringe b) dark fringe from the central maximum. 2. How will the fringe pattern change, if the screen is moved away from the slits? ### Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle $\alpha$ is $\large\frac{4}{27}\pi h^3\tan^2 \alpha$. ### Differentiate ‘Cry’ and ‘cry’ ### If A is a square matrix of order 3 such that |adj A|=64. Find |A'|. ### A square matrix A, of order 3, has | A | = 5, find | A.adj.A |. ### If A is square matrix of order 3 such that | adj.A |=81, find | A |. ### If A is an invertible matrix of order 3 and |A|=5 then find [adj.A]. ### A small manufacturer has employed 5 skilled men 10 semi - skilled men and makes an article in two qualities deluxe model and an ordinary model. The making of a deluxe model requires 2 hrs work bt skilled man and 2 hrs work by a semi skilled man. The ordinary model requires 1 hr by a skilled man and 3 hrs by a semi skilled man. By union rules no mam may work more than 8 hrs per day. The manufactures clear profit on deluxe model is Rs.15 and an orsinary model is Rs. 10. How many of each type should be made in order to maximize his total daily profit. ### Find the equation of the plane which contains the line of intersection of the planes$ \overrightarrow r. (\hat i + 2\hat j + 3\hat k ) -4 = 0 \overrightarrow r. (2\hat i + \hat j - \hat k ) + 5 = 0$and which is perpendicular to the plane$\overrightarrow r. (5\hat i + 3\hat j - 6\hat k ) + 8 = 0 $. ### Three persons,A,B and C,fire at a target in turn,starting with A.Thier probability of hitting the target are 0.4,0.3 and 0.2 respectively.The probability of two hits is ### Let * be a binary operation on set Q of rational numbers defined as a*b = $\large\frac{3ab}{7}$. Write the identity for * , if any. ### (a)Draw a circuit diagram of an n-p-n transmitter with its emitter base function forward biased and base collector junction reverse biased. Describe briefly its properties (b) Explain how a transistor in active state exhibits a low resistance at its emitter base junction and high resistance at its base collector junction . ### A matrix A, of order 3 x 3, has determinant 4 find the value of |3A|. ### Find the equation of the plane passing through the points ( 1, 2, 3 ) and (0, -1, 0 ) and parrallel to the line, $\large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3}$. ### Which one of the following is a bird flu virus? ### In a metre bridge experiment a student observed a balance point at the point J, where AJ = l. Draw the equivalent Wheatstone Bridge circuit diagram for this setup The values of R and X are both doubles and then interchanged. What would be the new position of the balance point? If in this set up, the galvanometer and battery are interchanged at the balance position, how will the balance point get affected? ### Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation. ### Two bags A and B contain 4 white and 3 black balls and 2 white,2 black balls respectively. From bag A, two balls are transferred to bag B. Find the probability of drawing (a) 2 white balls from Bag B? (b) 2 black balls from bag B? (c) 1 white and 1 black ball from bag B? ### Find the equation of a line passing through the point (2,1,3) and perpendicular to the lines$ \large\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$and$\large\frac{x}{-3}=\frac{y}{2}=\frac{z}{5} $. ### Relation R in the set of Z of all integers defined as R = {(x, y) : x-y is an integer }. ### Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values X has the following form, where k is some unknown constant. $p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right.$ (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours? ### Write the number of all one-one functions from the set A = { a, b, c} to itself. ### Give an account of Hershey and Chase experiment. What did it conclusively prove? If both DNA and pro ### During reproduction, the chromosome number (2n) reduces to half (n) in the gametes and again the ori ### find intervals in which function given by f(x) = sin 3x where x belongs [0, pi/2] is 1 increasing 2 decreasing ### If the points$(1,1,p)$and$(-3,0,1)$are at equidistant from the plane$\overrightarrow {r} . (3 \hat {i} +4 \hat {j} -12 \hat {k}) + 13 = 0, \$ then find the value of p.

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