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By finding the area of a regular polygon of n sides inscribed in a circle of radius r ,show that the area of the circle ispi r ^(2)

If the inverse of implication p rarr q is defined as ~p rarr ~q, then the inverse of the proposition (p ^^ ~q) rarr r is not equivalent to : I : ~r rarr p vv q II : ~p vv ~q rarr ~r III : r rarr p ^^ ~q The true statements in the above are :

If a, b, c are three noncollinear points then r = (1 - p - q) a + pb + qc represents If a, b are two points then r = (1 - p) a + p b represents

The radius of a circular disc is given as 24cm with a maximum error in measurement of 0.02 cm. (i) Use differentials to estimate the maximum error in the calculated area of the disc. (ii) Compute the relative error.

Evaluate: int_(0)^(pi//4)(dx)/(4+5cos^(2)x) .

If (1 + cos theta - isin theta) ( 1+ cos 2 theta + isin 2 theta) = x +iy then x^(2) + y^(2) =

If f(x) is a polynomial of degree 'n' with rational co-efficients and 1+2i,2-sqrt(3) and 5 are three roots of f(x)=0, then the least value of 'n' is

If the coefficient of x^((n^(2)+n-18)/2) in (x-1)(x^(2)-2)(x^(3)-3)(x^(4)-4)….(x^(n)-n), where (nge8) is k, then k is equal to ___________

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx

For any two vectors bara" and "barb show that |bara+barb|le|bara|+|barb| (triangle inequality).

The slope of the tangent to the curve y=6+x-x^2 at (2,4) is

int_(0)^(pi//4)(tan^(4) x + tan^(2) x ) dx=

Let f : R to R be the Signumb Function defined as f (x) = {{:(1",", x gt 0), ( 0"," , x =0), ( -1 "," , x lt 0):} and g : Ro to R be the Greatest Integer Function given by g (x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0,1]?

What are the value of p,q,r, and s for the following reaction ""pO_(3) + qHI to rI_(2) + sH_(2)O

If 3 is a root of x^(2)+kx-24=0, it is also a root of

A random variable x had its range {0, 1, 2} and the probabilities are given by P(x=0)=3k^(3), P(x=1)=4k-10k^(2), P(x=2)=5kk-1 where k is constant then k =

A and B are two events such that P(A) = p_(1), P(B) = p_(2), P(A nn B) = p_(3) then find {:((a),P(A^(C) nn B),(b),P(A^(C)uu B)),((c),P(A^(C) nn B^(C)),(d),P(A^(C) uu B^(C))):}

Find, by intregration , the volume of the solid generated by revolving about y-axis the region bounded between the curve y=(3)/(4)sqrtx^(2)-16,x ge4, the y-axis and the lines y=1 and y=6

Find (dy)/(dx) of the functions given in Exercises 12 to 15. y^(x)= x^(y).

Find delta f and dfwhen f(x) = In (1+x), x = 1, deltax = 0.04

A tree, in each year grows 5 cm less than it grew in the previous year. If it grew half a metre in the first year,then the height of the tree (in metres) when it ceases to grow,is

Obtain the equation of straight lines : Whose perpendicular distance from origin is 2 such that the perpendicular from origin has indication 150.

IFC(2n, 3): C (n,2) = 12: 1, thenn=

If alpha , beta , gamma are the roots of the equationx^(3) + 3x^(2) + 8x - 2=0 then the value of(4 + alpha^(2)) ( 4 + beta^(2)) (4 + gamma^(2))=

A committee of five is to be chosen from a group of 8 people which included a married couple. The probability for the selected committee which may or may not have the married couple is

If int log_(10)xdx = K.xlogf(x) + c then K.f(x) =

Find int (e^x(1+x))/(cos^2(e^x x)) dx

Simplify (-30)/(5)-(18-9)/(-3)

If x,y in (0,30) such that [(x)/(3)]+[(3x)/(2)]+[(y)/(2)]+[(3y)/(4)]=(11)/(6)x+(5)/(4)y (where [x] denotes greatest integer le x), then number of ordered pairs (x,y) is

Find the shortest distance between two lines whose vector equations are vec(r) = (hat(i) + 2 hat(j) + 3 hat(k))+lambda(hat(i)- 3hat(j) + 2 hat(k)) and vec(r) = (4 hat(i) + 5 hat(j) + 6 hat(k))+ mu (2 hat(i)+3 hat(j) + hat(k)).

vec(a) is perpendicular to vec(b)+vec(c),vec(b) is perpendicular to vec(c)+vec(a)andvec(c) is perpendicular to vec(a)+vec(b). If |vec(a)|=2,|vec(b)|=3and|vec(c)|=6, then |vec(a)+vec(b)+vec(c)|-2=

A natural number is chosen at random from the first 100 natural numbers. The probability that x+(100)/(x) gt 50 is

Evaluate : int (sqrt(x^(2) + 1) ( log (x^(2) + 1) - 2 log x))/( x^(4)) dx

(1^(2))/(1!)+(1^(2)+2^(2))/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+....=

Find the area of the region bounded by y= x^(2) and y=2

{:(" " Lt),(x rarr0):}(int_(0)^(x) sin^(3) t dt)/(x^(4))=

(dy)/(dx) = xy + x + y +1 has the solution

If both the rootsof the quadratic equation x^(2) + 2 (a +2) + x + 9a - 1 = 0 are negative, then a lies in the set

The switching circuit for the statement [p ^^ (q vv r) ] vv (~p vv s) is

Find the area of the region bounded by x^2=36y y axis y=2 and y=4.

The shortest distance· between the two· lines (x- 4) / 1 = (y+ 1) / 2 =z/- 3 and(x- 1)/ 2 =(y- 1) / 4 =(z- 2 )/- 5

Two person A , B in order cut a pack of cards replacing them after each out. The person who first cuts a club shall prize. The probabilities of their winning are

A point P lies on a line through Q(1,-2,3) and is parallel to the line (x)/(1)=(y)/(4)=(z)/(5). If P lies on the plane 2x+3y-4z+22=0, then segment PQ equal to

A vertical tower CP subtends the same angle theta, at point B on the horizontal plane through C, the foot of the tower, and at point A in the vertical plane. If the triangle ABC is equilateral with length of each side equal to 4 m, the height of the tower is

Volume of solid obtained by revolving the area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1about major and minor axes are in tha ratio……

Evaluate int x ^(3) . e ^(5x) dx.

Let l,r,c and v represent inductance, resistance, capacitance and voltage, resistance,capacitance and voltage, respectively. The dimension of (l)/(rcv) in SI units will be :