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A regularpolygonof nsideshas170digonals . Then n=

Let f (x) = sin x - ax and g (x) - sin x - bx, where 0 lt a,b, lt 1 Suppose that the number of real roots of 1 (x)=0 is greater than that of g (x) =0in [ -2pi, 2pi], then

The maximum value of logx/x, 0

A die is rolled n times, where n is at least 3. {:("Quantity A","Quantity B"),("The probability that at least",(1)/(2)),("one of the throws yields a 6",):}

Let A =[a, oo) denotes domain, then f:[a, oo) to B, f(x) =2x ^(3)+6 will have an inverse for then smallest real values of a, if:

A is a set containing n elements. Two subsets P and Q of A are chosen at random. (P and Q may have elements in common). The probability that P nn Q= phi is

How many onto functions can be defined from a set A onto another set B where n(A) = 5 and n(B) = 4.

The probability that Ahits a target is 1//4 and the probability that B hits the target is 1//3. If each of then fired once, what is the probability that the target will be hit atleast once ?

The tangent at P on the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 meets one of the asymptote in Q. Show that the locus of the mid point of PQ is a similar hyperbola.

Ifalpha , beta, gammaarethe rootsofx^3 +px^2 +qx +r=0then thevalueof(1 + alpha^2) (1+ beta^2) (1+ gamma^2) is

Oxyhaemoglobin work as a :-

What is the area of the parallelogram whose sides are vectors 2overset^i+overset^j and 2overset^j+overset^k ?

Match the following lists and then choose the correct code.

Find the equation of circles determined by the following conditions.The centre at (-2, 3) and passing through origin.

Solve graphically: Maximize z= 8000x + 12000y subjected to 9x + 12y le 180, x + 3y le 30, x ge 0^(') y ge 0

Show that the equation of the normal to the curve x = acos^(3) theta , y = a sin ^(3) theta at 'theta' is x cos theta - y sin theta = a cos 2 theta .

A rectangular hyperbola of latus rectum 4 units passes through (0,0) and has (2,0) as its one focus. The equation of locus of the other focus is

The vibrations produced in the ear drum are transmitted through the ear ossicles to the fluid filled inner ear via -

Find the area of the region in the first quadrant enclosed by x-axis, line x = sqrt3y and the circle r^(2)+ y^(2) = 4.

A double decker bus can accomodate 75 passengers 35 in the lower deck 40 in the upper deck. The number of ways the passengers can be accomodated if 5 want to sit only in lower deck and 8 want to sit only in upper deck is

If two out of the three vectors a,b,c are unit vectors, a + b + c = 0 and 2.(a.b + b.c +c.a) + 3 = 0, then the third vector is of length

If f(x) = ||x| - 1|, then draw the graph of f(x) and fof(x) and also discuss their continuity and differentiability. Also, find derivative of (fof)^(2)"at x" = (3)/(2)

If alpha gt 1 , then int (dx)/(x^(2) + 2 alpha x + 1) =

If the function f(x)= (1)/(x+2), then find the points of discontinuity of the composite function y= f {f(x)}

If the curve (x ^(2))/(a ^(2)) + ( y ^(2))/(k^(2) a ^(2)) =1 and (x -g) ^(2) + (y -f)^(2) =r ^(2) intersect each other orthogonally and if P (a cos theta,ka sin theta) be a point of intersection of the above curves, then

Consider f : R rarr Rgiven by f(x) = 4x +3. Show that f is invertible. Find inverse of f .

Let three sets be defined as A={x|cos2x + cosx+1=0} B={x|cos2x + 3sinx=2} ( c) {x|secx + tanx = cosx} The number of elements in A cap B cap C is

Prove that f(x)=sin x+3^(1/2) cos x has maximum value at x=(pi)/(6)

If f(x)=={{:((sin(x))/({x})",",{x} ne 0),(k",",{x}0):}, where {x} denotes factional part of x, then f(x) will be continuous

Prove that {1,2,3,4,5,6,……} set are equivalent.

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to "........."

The planes : 2x – y + 4z = 5 and 5x – 2.5 y + 10 z = 6 are

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

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. then the value of E(X) is

PQ is a double ordinate of the parabolay^2 = 4ax . Tangents are drawn to parabola at P and Q, which meets the y axis at S, R respectively. If area of trapezium PQRS is equal to24a^2 , then angle subtended by RS at the focus of parabola is:

The plane is passing through A(2,-1,3) and it is parallel to bar a = (3,0,-1) and barb = (-3,2,2). The equation of this plane is ...........

A : if semivertical angle of a cone is 45^@ and height of the cone is 20.025 then approximate value of its volume is 10pi cubic units. R : If semivertical angle of a cone is alpha and height is h then volume of cone is pi/3 h^3 tan^2 alpha

Number of 4 digitnumbers b_(1)b_(2)b_(3)b_(4) such thatb_(1) gt b_(2) gt b_(3) gt b_(4) is equal to

Integrate the following intsec^2(4x)dx

r : Two polygons are congrunent then they are equal in shape and size Statement r can be interpreted as

Evaluate the following integrals : int_(0)^(pi)(1)/(1+sinx)dx

If the position vectors of P, Q, R and S are 2hati+hatj, hati-3hatj, 3hati+2hatj and hati mu+hatj respectively and PQ"||"RS, then the value of mu is

Find all points of discontinuityof f, where f is defined by f(x) = {{:((|x|)/(x)," if "x ne0),(0," if "x= 0):}

Let f _(n)(x) = (sin x )^(1//pi) , x in R, then:

Find the equation of the circumeircle of the triangles formed by the straight lines x + y = 6, 2x+ y= 4 and x+ 2y = 5

Four bad apples are mixed accidentally with 20 good apples. If 3 apples are drawn one by one with replacement then mean of number of good apples is

Form the differential equation representing the family of curvesgiven by (x - a)^(2) + 2y^(2) = a^(2),where a is an arbitrary constant.

Evaluate the definite integrals int_(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2x))dx

Find int(x^(2)+1)/(x^(2)-5x+6)dx