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Coefficient of constant term in the expansion of (x^(3)+5(3)^(-logsqrt3sqrt(x^(3))))^(4) is

A problem of mathematics is given to three students and probability of solving the problem is(1)/(3), (1)/(3), (1)/(3) respectively. The probability that at least one of them solves the problem is …………

Show that the line passing through the points (4, 7, 8) and (2, 3, 4) is parallel to the line passing through the points (-1, -2, 1) and (1, 2, 5).

Find derivatives of the following functions.sec (tantheta)

Two medians drawn from acute angles of a right angled triangles intersect at an angle pi//6. If the length of the hypotenuse of the triangle is 3 units, then area of the traingle (in sq. units) is

If (3pi)/(2) lexle2pi " then :"sin^(-1) (sinx)= ...

Let K = 1 ^(@), then 2 sin 2K + 6 sin 6K + ….+ 180 sin 180 k isequal to

A unit vectorvec amakes angles pi/4\ a n d\ pi/3withhat i\ a n d\hat jrespectively and an acute angle thetawithhat kdotFind the angle thetaand components ofvec adot

If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is

Areaboundedby thecurvey=x^3the x-axisand theordinatesx=-2andx=1is

Using integration, find the area of the region bounded by the lines y=1+abs(x+1), x=-2, x=3 and y=0.

If vecA=3hati+4hatj, vecB=6hati+8hatj and vecC=15/sqrt2(hati-hatk) then a vector (vecP) having magnitude equal to the magnitude of vecA+vecB in the direction of sqrt2 vecC is :

If |z + barz| + |z - barz| = 2 then z lies on

{:("Column A","", "Column B"),("The perimeter of the triangle",,"The The circumference of the circle"):}

If there is an error of pm0.04 cm in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is 10 cm, is

cos(x-y)=3cos(x+y) then cotxcoty=

A square is inscribed in the circle x^(2)+y^(2)+2x+4y3=0. Its sides are parallel to the coordinates axes, then find the vertices of a square.

If vec(a)=3hati-hatj+2hatk,vec(b)=hati-3hatk and vec( c )=hati+2hatj then find (i) vec(a).vec(b)(ii) (vec(a)+vec(b)).vec( c ) (iii) (vec(a)-vec(b)).(vec(b)-vec( c )) (iv) (vec(a)+2vec(b)).vec(b) (v) (vec(a)-3vec( c )).(2vec(a)+vec(b))

The p.m.f. of a r.v. X is as follows : P(X=0)=3k^(3),P(X=1)=4k-10k^(2),P(X=2)=5k-1, P(X=x)=0" for any other values of x, then c.d.f. F (X)" is

Find the maximum area of an isosceles triangle inscribed in the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with its vertex at one end of the major axis.

In triangleABC the mid points of the sides AB,BC and CA are respectively (l,0,0),(0,m,0) and (0,0,n) . Then (AB^(2)+BC^(2)+CA^(2))/(l^(2) +m^(2)+n^(2))is equal to

By giving a counter example, show that the following statement 'if n is an odd integer, then n is prime' is false.

If Arg ((z+1)/(z-1))=pi/6then the locus of z = x + iy is

The mean and standard deviation of a distribution of weights of a group of 20 boys are 40 kg and 5 kg respectively. If two boys of weights 43 kg and 37 kg are excluded from this group, then the variance of the distribution of weights of the remaining group of boys is

Show that the lines y=0, sqrt(3y)-xy=sqrt(3) and sqrt(3y)+x-10=0 form a cyclic trapezium. Determine the centre and the radius of the circle and also the area of the trapezium.

Consider a parabola P touches coordinate axes at (4,0) and (0,3). if focus of parabola P is (a,b) then the value of b-a is

Evaluate the definite integrals int_(0)^((pi)/(4))(sinx+cosx)/(9+16sin2x)dx

For all integers, n ge 1 which of the following is divisible by 9.

Length of chord of parabola y^(2) =4axwhose equation is y-sqrt2 x + 4 sqrt2 a =0

Evalute the following integrals int sqrt(x)log xdx

If 0lt0ltpi/2" and "|{:(1+sin^(2)theta,cos^(2)theta,4sin4theta),(sin^(2)theta,1+cos^(2)theta,4sintheta),(sin^(2)theta,cos^(2)theta,1+4sintheta):}|=,"then "theta=

A matrix A has x rowsand x+5 column . A matrix B has y rows and 11 -y column . A matrix B has y rows and 11 - y column . If AB and BA are exist then the value of x and y are respectively ………..

Compute the area of the a surface generated by revolving about the x-axis an are of the curve x= t^(2) , y= (t)/(3) (t^(2)-3) between the points of intersection of the curve and the x-axis

show that the function is always differentiable .

Write bond-line structural formulas for (a) two primary (b) CH_(3)CHCH_(2)CH_(3)alcohols,a secondary alcohol, and (e) a tertiary alcohol - all having the molecular formula C_(4)H_(10)O

Iiv) If (2x^(3)+1)/((x-1)(x+1)(x+2))=A+(B)/(x-1)+(C)/(x+1)+(D)/(x+2), then find the value of A+B+C+D.

Problem of mathematics is given to three students and their respective probability of solving the problem is (1)/(3),(1)/(3) and (1)/(3). Find probability of an event that exactly one student can solve problem.

Draw the graph of y=cos^(-1)((1+x^(2))/(1+x^(2)))

Differentiate the functions with respect to x in Exerecises 1 to 8. 2sqrt(cot(x^2))

Four tickets marked 00, 01, 10 , 11 respectively are placed in a bag. A ticket is drawn at random five times being replaced each time. The probability that the sum of the numbers on the tickets is 22 is

Identify the planes containing the points ! (7,0,4),(2,-5,0),(0,sqrt2, -3)

Choose the correct answer int(dx)/(sin^(2)xcos^(2)x) equals

Where I denotes set of integers, then n(A cap B)=

If alpha, beta & gamma real numbers, then value of |(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1)| is equal to

Find the moment of inertia about the x-axis of the figure bounded by two parabolas with dimensions indicated in.

Find the region on the Argand plane on which z satisfies1lt|z-2i|lt3

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

Using the definition of definite integral as the limit of a sum evaluate int_(0)^(2)axdx where a is a constant.