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If 'X' has a binomial distribution with parameters n=6, p and P(X=2)=12, P(X=3)=5 then P=

One vertex of a triangle of given species is fixed and another moves along circumference of a fixed circle. Prove that the locus of the remaining vertex is a circle and find its radius.

Differentiate the following w.r.t. x : e^(x) + e^(x^2)+"……….."+e^(x^5).

int (1)/(sqrt(4-5x))dx=

If |bar(a)|=|bar(b)|, then necessarily it implies bar(a)=+-bar(b).

Find n in the binomaial[ root (3)(2) + (1) /root(3)(3)]^(n) ,if the ratio of 7th term from beginning to 7th term from the end is 1/6.

Which of the following is/are true? (you may use f(x)=In((Inx))/(Inx)

Circle touching y-axis and centre (3,2) is

thevalueof""^50C_(4) +underset( r=1)overset( 6 )sum""^(56 - r)C_(3) is

Find the period of (a) (|sin4x|+|cos 4x|)/(|sin 4x-cos 4x|+|sin 4x+cos 4x|) (b) f(x)="sin"(pi x)/(n!)-"cos"(pi x)/((n+1)!) (c ) f(x)=sin x +"tan"(x)/(2)+"sin"(x)/(2^(2))+"tan"(x)/(2^(3))+ ... +"sin"(x)/(2^(n-1))+"tan"(x)/(2^(n))

Let (a,b,c)ne(0,0,0). The pair of equations which does not represent a straight line is:

Find the middle term (s) in the expansion of (I) (1+2x)^(12) (II) (2y-(y^(2))/(2))^(11)

Find r(X,Y) from the tworegression equation 3x=y and 4y=3x.

The inverse point of (1,2) origin w.r.t. the circle x^(2)+y^(2)-4x-6y+9=0 is

Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, pi} with replacement. Now a circle is drawn taking (p,q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

Find the perpendicular distance of the point (2, 1, 3) from the line (x-1)/(3)=(y-3)/(1)=(z-4)/(-5)

int_(0)^(1)(dx)/(x+sqrt(x))=

If two lines (x-2m)/(2m+5)=(y)/(8m)=(z-4)/(2) and (x-m)/(m-2)=(y)/(-1)=(z-2m)/(1-3m) are parallel for some m inR, then distance between them is:

O is the origin and B is a point on the x-axis at a distance of 2 units from the origin. Match the following lists.

A spherical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^(3)//min. The rate at which the diameter is decreaseing when the diameter is 10 cms is ..

If int((sqrt(x))^(5))/((sqrt(x))^(7)+x^(6))dx = a log ((x^(k))/(x^(k)+1))+c

Evaluate the following integrals : int_(0)^(pi/4)cos^(4)xdx

A student has to answer 10 out of 13 questions inan examination. The number of ways in which he can answer if he must answeratleast 3 of the first five questions is276b. 267c. 80d. 1200

The number of ways in which 19 different objects can be divided into two groups of 13 and 6 is

Find the value of lambda such that the vectors bar(a)=2bar(i)+lambda bar(j)+bar(k) and bar(b)=bar(i)+2bar(j)+3bar(k) are orthogonal …….

Find the area of the circle x^(2) + y^(2) = a^(2) using integration.

If omega ne 1" and "omega^(3)=1, the (a omega+b + c omega^(2))/(a omega^(2)+b omega+c)+(a omega^(2)+b+c omega)/(a+b omega+c omega^(2)) is equal to

Findthe areaof theregionbounded by theliney= 3x +2 ,the x -axisand theordinatesx=-1 and x=1.

If the first and the (2n+1) -th terms pf AP, GP and HP are equal and their n-th terms are respectively a , b , c then always

Assertion (A) : A fair coin is tossed n times. If the probablities of getting 4,5 and 6 heads be in A.P then n is equal to 7,14 Reason (R ) : If .^(n)C_(r+1), .^(n)C_(r ), .^(n)C_(r+1) are in A.P then (n-2r)^(2)=n+2 The correct answer is

ABC is a triangle with 1 as its incentre. The radii ofthe incircles of the triangles BIC, AIB and AIC are r_1,r_2" and "r_3 respectively. Prove that AI+BI+CI= (a(r-r_1))/(2r_1) + (b(r-r_2))/(2r_2)+(c(r-r_3))/(2r_3).

{:("Column A","in the figure,"Delta ABC"is inscribed in the circle.The triangle does not contain the center of the circle O","Column B"),(x,,90):}

Find the second order derivatives of the functions given in Exercises 1 to 10. tan^(-1) x.

Translate "Jamini will be rewarded if and only if he is punctual" propositions into symbolic form, stating the prime components

Find the area enclosed between the curves y= x^(2)-5x and y= 4-2x

Integrate the following int(dx)/(sqrt(11-4x^2)

A bag contains n coins of which five of them are counterfeit with heads on both sides and the rest are fair coins. If one coin is selected from the bag and tossed, the probability of getting head is 5//8 then n=

Method of integration by parts : int cos^(2)xdx=....

The cartesian equation of the plane passing through A and perpendicular to vec(AB) where 3i + j + 2k, I - 2j + 4k are the position vectorsof A,B respectively

A fair die is rolled. Consider the events E={1,3,5}, F = {2,3} and G={2,3,4,5}. FindP(E/G) and P(G/E)

{:(" "Lt),(n rarr oo):} {sum_(r=1)^(n)1/n e^(r//n)}=

((ds)/(dt))^(4) + 3s(d^(2)s)/(dt^(2)) = 0

Two cards are drawn at random from a pack of 52 cards . The probability that one of them is black and other is red is

For the reaction .............

If z=(sqrt3-i)/(2) then (i^(101)+z^(101))^(103)=