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Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The n umber of arithmetic means is

Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The value of Sigma_(r=1)^(n) G_ris

I : If a = I +j - k, b = 2i - 3j + 2k, c = 13 I - 7j + 3k then [a b c] = 0 II : If a,b,c are mutually perpendicular unit vector then [a b c]^(2) = 1

Evaluate intxsqrt(1 + x - x^(2))dx

A box contains 19 screws, 3 of which are defective, Two screws are drawn at random with replacement. Find the probability that neither of the two screws is defective.

Using elementary transformation find the inverse of the matrix : A=((1, -3,2),(3, 0, 1),(-2, -1, 0))

Number of ways of forming a committee of 6 members out of 5 Indians. 5 Americans and 5 Australians such that there will be atleast one member from each county in the committee is

The mid point of the chord 2x+5y=12 of the ellipse 4x^(2) + 5y^(2) = 20 is

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

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

int (x^(2)+1)/(x^(4)+x^(2)+1)dx=

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

If a diameter of a hyperbola meets the hyperbola in real points then

Match the following lists:

For what values of x is the rate of increase of x^(3)-2x^(2)+3x+8 is twice the rate of increase of x..

If |z-3+i| = 4 then the locus of z = x +iy is

Is the function defined by f(x)= |x|, a continuous function?

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

(1-omega)(1-omega^2)(1-omega^4)(1-omega^5)=9

Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

(1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……oo=

The sum to n terms of the series 1+ 5 ((4n +1)/(4n - 3)) + 9 ((4n +1) /( 4n -3)) ^(2) + 13 ((4n +1)/( 4n -3)) ^(3) + ((4n + 1 )/( 4n -3)) ^(2)+ ……. is .

For any value oftheta if the straight lines x sin theta + (1-cos theta ) y = a sin theta and xsin theta -(1+ cos theta)y + a sin theta = 0 intersect at P(theta) thenthe locus of P(theta)is a

If the length of three sides of a trapezium other than base are equal to 10 cm. Than find the area of trapezium when it is maximum.

State whether the following statements are true or false . Justify . If ** is commutative binary operation on N, then a"*" (b"*" c)=(c"*"b)"*"a.

Evaluate int (x cos^(-1)x)/(sqrt(1-x^(2))dx

Consider the lines represented by equation (x^(2) + xy -x) xx (x-y) =0 forming a triangle. Then match the following lists:

Let p, q in R. "If " 3 - sqrt(3) is a root of thequadratic equation x^(2) + px + q = 0 , then

Iff(x)={:{((x -1)/(2x^(2) - 7 x +5) ," for "x ne 1) , (-1/3 , " for "x = 1):} thenf (1)is equal to

The probability of three mutually exclusive events A, B and C are given by 2/3, 1/4, 1/6 respectively Is this statement a)True? b)False? c)Cannot be said? d)Data not sufficient?

If barb and barc are two non-collinear vectors, then number of solution (x,y) in x,y in [0,10], satisfying the equation bara.[barb+barc] = 5 and bara xx (barb xx barc) = (x^2 -2x+7) barb+(siny)barc is :

Match the relation for derivatives given in List II with the relation given in List I and then choose the correct code.

If 3hat(i)+hat(j)-2hat(k)andhat(i)-3hat(j)+4hat(k) are the diagonals of a parallelogram, then the area of the parallelogram is

Phenol and benzoic acid can not be separated by

n^(th) term of log_(e )(6//5) is

If the relation R:A rarr B where A={1,2,3,4} and B={1,3,5}is defined by R={(x,y),xlty,x in A,y in B} then ROR^(-1) is

Evaluate the determinants below in examples number 1 and 2 |{:(2,4),(-5,-1):}|

A monument ABCD stands at A on a level ground. At a point P on the ground the portions AB, AC, AD subtend alpha, beta, gamma respectivelyl. If AB = a, AC = b, AD = c, AP = x and alpha + beta + gamma = 180^(@) "then x"^(2) is equal to

The logically equivalent statement of p toqis

Show that the position vector of the point P, which divides the line joining the points A and B having position vectors veca and vecb internally in ratio m:n is (mvecb+nveca)/(m+n)

If the mapping f(x) = mx + c, m gt 0maps [-1,1] onto [0,2], thentan ( tan^(-1). 1/7 + cot ^(-1) 8 + cot ^(-1) 18) is equal to

Solve(dy)/(dx)=(3x+y+4)^(2)

Show that the position vector of the point P, which divides the line joining the points A and B having position vector a and b internally in the ratio: m:n is (mvecb + nveca)/(m+n)

If the square of the length of the tangents from a point P to the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b^(2), x^(2)+y^(2)=c^(2) are in A.P. then a^(2),b^(2),c^(2) are in

Represent graphically : (i) A displacement of 50 km., 30^(@) West of Sout. (ii) A displacement of 70 km., 40^(@) West of North. (iii) A displacement of 50 km., 45^(@) North of East.

x+(x^(3))/(3)+(x^(5))/(5)+(x^(7))/(7)+….oo=

Solve :cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)

State whether the following statements are true or false . Justify . If ** is commutative binary operation on N, then a"" (b"" c)=(c""b)""a.