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A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is (31)/(42), then determine the value of n.

Find the area of the region bounded by y^(2)=4ax between the lines x=a and x= 9a

Sum of coefficients of terms of even powers of x in (1 + x + x^2+ x^3)^5 is

Using differentials, find the approximate value of each of the up to 3 places of decimal. (26.57)^((1)/(5))

lim_(n to oo) (sqrt(1) + 2sqrt(2) + 3sqrt(3) + …… + nsqrt(n))/(n^(5//2)) is :

Solve (1+x^(2)y)(dy)/(dx) +2xy-4x^(2)=0

Let veca=2hati+hatj-2hatk and vecb=hati+hatj. Let vecc be a vector such that |vecc-veca|=3,|(vecaxxvecb)xxvecc| = 3 and the angle between vecc and veca xx vecbis 30^@ Find veca.vecc

If a=(hati+hatj+hatk), a.b=1 and axxb=hatj-hatk, then b is

Outof 7consonants and5vowelshowmanydifferentwordscan beformedeachconsistingof3 consonantsand 2vowels

Solve the following equations : tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x

If 4x - 5y + 33 = 0 and 20 x - 9y - 107 = 0 are two lines of regression, find the standard deviation of Y, the variance of x is 9.

10 % bulbs are defective produced by some factory. 5 bulbs are selected at random then ……… is the probability that bulb is without defect.

If P_(n) = cos^(n) theta + sin^(n) theta theta int [0,pi/2], n int (-infty, 2) then minimum of P_(n) will be

Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x)be its inverse. If int _(0)^(2pi)g (x) dx = api ^(2) + beta pi+ gamma, wherealpha, beta and gamma in R, then find the value of 2 (alpha + beta+ gamma).

Compute the area of the figure bounded by the straight lines x=0, x=2 and the curves y= 2^(x), y= 2x- x^(2)

If alpha, = underset(x rarr 0)("lim") (x.2^(x) - x)/(1 - cos x)and

y^(2)=4x, y^(2)=4(4-x)

Fill in the blanks : If veca=xhati+2hatj-3hatk and vecb=3hati+bhatj-9hatk are parallel then x=_(.........)

Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}|

If ** is a binary operation on the set R of all real numers difined by a**b=a+b-3 then find the identity element for **.

Findthe orderdegree, ( ifdefined) of thedifferentialequation .

The area bounded by the curves y=logx,y=2^(x) and the lines x=(1)/(2),x=2 is

Find the coefficient of x^2 in (7x^3 - (2)/(x^2))^9

The area enclosed between y^(2) = x and y=x is:

If f: R rarr R be an injective mapping and p, q,r are non-zero distinct real quantities satisfying f(p/r) = f((p-q)/(q-r)) and f(q/r) = f(r/p). If the graph of g(x)= px^(2)+qx+r passes thorugh M(1,6) then find the value of q.

Ifz and omega are two non-zero complex numbers such that |zomega| =1 and arg (z) - arg (omega) = (pi)/(2) then barz omega is equal to

vec(a)=hati+hatj+hatk,vec(b)=hati-hatj+hatk and vec( c )=hati+2hatj-hatk then the value of |{:(vec(a).vec(b),vec(a).vec(b),vec(a).vec( c )),(vec(b).vec(a),vec(b).vec(a),vec(b).vec( c )),(vec( c ).vec(a),vec( c ).vec(b),vec( c ).vec( c )):}| is .............

From the top of a 64 metres high tower, a stone is thrown upward vertically with the velocity of 48m/s. The greatest height (in metres) attained by stone, assuming the value of the gravitational acceleration g- 32 m//s^(2), is

An urn contains 5 white and 3 red balls. 3 red balls are drawn from box with replacement. If X represents numbers of red balls then obtain its probability distribution.

From a differential equation representing the given family of curves by eliminating the arbitrary constains a and b x/a + y/b = 1

If m is a positive integer, then [(sqrt(3)+1)^(2m)]+1, where [x] denotes greatest integer lex, must be divisible by

Find the Differential equation satisfying the family of curves y=ae^(3x)+be^(-2x),a and b are arbitrary constants.

Common chord of the circles x^2+y^2-4x-6y+9=0, x^2+y^2-6x-4y+4=0 is

In a cubicul hall ABCDPQRS with each side 10m, G is the centre of the walls BCRQ and T is the midpoint of the side AB, the angle of elevation of G at the Point T is

Find number of positive integer less than 2431 and prime to 2431.

Using elementary row transformations , find the inverse of [{:(4,5),(3,4):}]

Prove that 4 cos 12^(@)cos 48^(@)cos 72^(@)-cos36^(@)

There are 3 defective bulbs, in a group of 10 bulbs. If X is the number of defective bulbs in a random draw of 3 bulbs, then find its mean and variance.

Find the coefficient of x^(n) in the expansion of (x)/((2x+1)(x-2)) in powers of x specifying the interval in which the expansion is valid.

There are 30 questions in a multiple - choice test. A student gets 1 mark for each unattempted question, 0 mark for each wrong answer and 4 marks for each corrent answer. A student answered x question correctly and scored 60. Then the number of possible value of x is

If ""^(n)C_(r) denotes the number of combinations of n things taken r things at a time, then the expression ""^(n)C_(r+1)+""^(n+1)C_(r)+2""^(n)C_(r) is

If y=a^(1//2log_a(cosx)),"find"dy/dx.

For a vector bar(a),bar(a)xx vec( r )=bar(j) then bar(a).bar( r ) = ………….

If A = (a_(ij))_(3xx3) where a_(ij) = cos (i+j) then

In which of the following graphs is x =c point of inflection?

If (logx)/(a-b)=(logy)/(b-c)=(logz)/(c-a) then xyz=

Find the solution set of k so that y= is secant to the curve y=x^(2)+k.

If is a binary operation on the set R of all real numers difined by ab=a+b-3 then find the identity element for **.