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If the equation of the plane passing through the point (2,-1, 3) and perpendicular to the planes 3x - 2y + z = 9 and x + y + z = 9 is x + by + cz + d = 0, then d =

I : cos 52^(@) + cos 68^(@) + cos 172^(@)=1//2 II : 4 sin A cos^(3) A - 4 cos A sin^(3) A = cos 4A

Let f(x)=(x^2-ax-2)/(x^2+x+1) such that -3lt f(x)lt 2AA x in R and complete range is a is (p,s) , then the value of ((s-p)/2) is

Find the equation of circles determined by the following conditions. The centre at (3, 2) and circle is tangent to x-axis.

Compute the product A xx BA = {a,b} , B = {a,b,c}

The value of ("sin"(2pi)/9-"sin"(35pi)/(36))/("cos"(2pi)/9+"cos"(35pi)/36) is :-

Find the number of all integer-sided isosceles obtuse-angled triangles with perimeter 2008

From the top of aspier the angle of depression of the top and bottom of a tower of height h are theta and phi respectively. Then height of the spier and its horizontal distance from the tower are respectively.

Choose the correct answer int_0^(pi/2) log((4+3sinx)/(4+3cosx)) dx

Find the co-ordinates of the point on the curve y=x^(3)+3x^(2)-4x-12 at which the normal's inclination is -1/7. Also find the equation of the normal.

If (2, -3) is the foot of the perpendicular from (-4, 5) on a line, then the equation of the line is

Evalute the following integrals int (cot ("log x"))/(x)dx

Lt_(n rarr oo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4) + 2^(4))+....+(n^(3))/(n^(4)+n^(4))]

A right circular cylinder hasradius r = 10 cm and height h = 20 cm suppose that the radius of the cylinder is increased from 10 cm to 10.1 cm and the height does not change. Estimate the change in the volume of the cylinder . Also calculate the relative error and percentage error .

A random variable X has the following probability distribution. Find (i) k (ii) Mean (iii) P(0 lt X lt 5)

Let Z be the set of all integers and let R be a relation on Z defined by a R bhArr (a-b) is divisible by 3. then R is

Integrate the functions (x^(2)+1)logx

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P.,prove that 1/a,1/b,1/c are in A.P. given a+b+cne0.

Let a=hati+hatj+hatk, b=hati-hatj+hatkandc=hati-hatj-hatk be three vectors. A vector v in the plane of a and b, whose projection on c is (1)/(sqrt(3)), is given by

A solenoid of radius R number of turn per unit length n and length L has a current I=I_(0) cos omega t. The value of induced electric field at a distance of r outside the solenoid, is :

Al^(3+) and Cr^(3+) can be distinguishedby which of following reagent.

Which of the following reacts with NaOH to liberate a gas ?

Amount first hundred natural numbers how many are divisible by 2, 3 or 5

If vec(a) = 2 hat(i) - hat(j) + hat(k) and vec(b) = hat(i) - 2 hat(j) + hat(k)then projection of vec(b)'on ' vec(a) is

If alpha+ibeta=Tan^(-1)(z),z=x+iy and alpha is constant then the locus of z is

The position vectores of the vertices A,B, C of a delta ABC arehati- hatj- 3 hatk , 2hati+hatj - 2hatkand- 5 hati+ 2 hatj- 6 hatk respectively. The length of the bisector AD of the angleangle BAC, where D is on the line segments BC, is

Let P(1,-2,5) be the foot of the perendicular drawn from the origin to the plane pi_(1) and the same P be the foot of the perpendicular from (1,2,-1) to the planes, pi_(2). Then the acute angle between the planes pi_(1)andpi_(2) is

Integrate the functions (5x)/((x+1)(x^(2)+9))

Find the number of terms in the expansion of (x+y+z)^(20)

Find out which of the following statements have the same meaning: i. If Seema solves a problem then she is happy. ii. If Seema does not solve a problem then she is not happy. iii If Seema is not happy then she hasn't solved the problem. iv. If Seema is happy then she has solved the problem

Evaluate: int_(0)^(pi) (xsinx)/(1+cos^(2)x)dx

If f(x) =log=x^(2)logx on[1,e] , thenlog (greatest of f(x) - least of f(x) ) is equal to -

int _(-1)^(1)e^(x) dx

Find the derivative of y=sin(x+a)/(cosx).

Find the antiderivative (or integral) of the following functions by the method of inspection. sin2x-4 e^(3x)

cos^2 5^@-cos^2 15^@-sin^2 15^@+sin^2 35^@+ cos15^@ sin15^@- cos5^@ sin35^@=

The three urns having the numbers of white and black balls are given below : The probability of chosing every urn is equl. A ball is chosen randomly from the urn is found to be white. Then find the probability that the ball chosen was that form urn-2.

Find (dy)/(dx) of the functions (cos x)^(y) = (cos y)^(x).

Two chords of the circle x^(2)+y^(2)-2gx-2hy+g^(2)+h^(2)-c^(2)=0 are passing through the point (g,h+c) and the line y=x bisects these two chord. Then

A bag contains 10 White and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end at the seventh draw.

Integration of certainirrationalfunctions with theaid of trigonometricorhyperbolic substitutions I=intx^(2)sqrt(x^(2)-1)dx.

Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(i) ne, forall i in A, then number of such functions f are

Integration of certainirrationalfunctions with theaid of trigonometricorhyperbolic substitutions I=int(dx)/((x^(2)-2x+5)^((3)/(2))).

Verify the Rolle's theorem for each of the function in following questions: f(x)= x(x-1)^(2), " in" x in [0, 1]

Differentiate the following functions with respect to x. x^(y) + y^(x)= 1000

f:[0,3] rarr [1,29],f(x) =2x^(3)-15x^2+36x+1 then f is ........ function.

If S={omega^(a),omega^(b), omega^(c)}, omega is a non-real complex cube root of unity- T={{a,b,c): a,b,c in {1,2...20}, n(S)=3}. Coordinalty of set T is k, then (K)/(294)=.....

If a perpendicular drawn through the vertex O of the parabola y^2=4ax to any of its tangent meets the tangent at N and the parabola at M, then ON.OM=

Let A, B, C, D be four points with position vectors bar(a)+2bar(b), 2bar(a)-bar(b), bar(a) and 3bar(a)+bar(b) respectively. Express the vectors bar(AC), bar(DA), bar(BA) and bar(BC) interms of bar(a) and bar(b).

If A is matrix of order x*2 and B is of 2*y and (AB)' is of 4*3 then values of y,x are

If A is matrix of order x2 and B is of 2y and (AB)' is of 4*3 then values of y,x are