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Number of solutions of the equation sin^4x-cos^2xsinx+2sin^2x+sinx=0in0lt=xlt=3piis_____

Consider the circle x^(2)+(y-1)^(2)=9, (x-1)^(2)+y^(2)=25. They are such that

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is (1)/(2), (1)/(3) and (1)/(4). Probability that the problem is solved is ………

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is (1)/(2),(1)/(3) and (1)/(4) . Probability that the problem is solved is ........

Let U (x) and V(x)be two differentiablefunction. Given(U(x))/(V(x))=7,if(U'(x))/(V'(x))=pand[(U(x))/(V(x))]=q then the value of(p+q)/(p-q)is_

Evaluate the following integrals intlog(1+x^(2))dx

Evaluate the following integrals int cos (log x) dx

If I_(n)= int (log x)^(n)dx then I_(n)+nI_(n-1)=

Express with rational denominator(x+sqrt(-1))^2/(x-sqrt(-1))-((x-sqrt(-1^2)))/(x+sqrt(-1))

For the function f(x)=int_(0)^(x^(2))(-t^(2)/4)(4-t)dt

Find the second order derivatives of the following functions: 3 sin 4x-4sin^(3) 4x

In Z the set of all integers, the inverse of -7 w.r.t. '**' defined by a**b=a+b+7 for all a, bin Z is

If tan^(-1) x + tan^(-1) y + tan ^(-1) z = (pi)/(2) , then value of xy + yz + zxa) -1 b) 1 c) 0 d) None of these

Integrate the rational functions 1/((e^(x)-1)) [Hint : Put e^(x) = t]

Let A={x_(1),x_(2),x_(3)....,x_(7)},B={y_(1)y_(2)y_(3)}. The total number of functions f:AtoB that are onto and ther are exactly three elements x in A such that f(x)=y_(2), is equal to

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=(z-6)/(-5) are perpendicular, find the value of k.

The tagents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B,the other end of the diameter, through, A. The sum of focal distance of any point on the curce is

The tagents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B,the other end of the diameter, through, A. Which of the following does not change by changing the radius of the circle ?

The tagents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B,the other end of the diameter, through, A. The locus of the intersection of AO and BT is a conic whosee eccentricity is

Find the values of x and y from the following equation , 2[{:(x,5),(7,y-3):}]+[{:(3,-4),(1,2):}]=[{:(7,6),(15,14):}].

Let f(x) = |(cosx,sinx,cosx),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x)| then the value of f'(pi/2) is :

The mean of 20 observations is 15. On Checking it was found that two observations were wrongly copied as 3 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct means is

If sum of n terms of a sequence is given by S _(n) = 2n ^(2) - 4n, find its 50^(th) term.

If bar(x)=(-1,4,-2),bar(y)=(-4,16,-8) then |bar(x)+bar(y)|…………|bar(x)|+|bar(y)|

Differentiate the functions with respect to x in Exerecises 1 to 8. sin (ax+b)

There is an error of pm0.04 cm in the measurement of the diameter of a sphere. When the radius is 10 cm, the percentage error in the volume of the sphere is

If p, q and r are three logical statements then the truth value of the statement (p^^~q)vv(qrarr r), where p is true,is

find the following definite trigonometric integral as limit of sums. overset(pi)underset(0) int sinx dx

Value of the Delta=|{:(,a^(3)-x,a^(4)-x,a^(5)-x),(,a^(5)-x,a^(6)-x,a^(7)-x),(,a^(7)-a,a^(8)-x,a^(9)-x):}| then the value of Delta_(1)-Delta_(2) is

If 1 , omega , omega^(2) are the cube roots of unity, then prove that 1/(2 + omega) - 1/(1+2 omega) = 1/(1 + omega) .

If the coefficient of x^(5) in the expansion of (ax^(2)+(1)/(bx))^(13) is equal to the coefficient of x^(-5) in the expansion of (ax-(1)/(bx^(2)))^(13), then ab =

Find the equation of the circle with centre C and redius r where. C= (1,7) , r =5/2

If f(x )=0hasarepreatedrootalphathenanotherequationhavingalphaas rootis

If P(A) = 1/2, P(B) = 7/12 and P(not A or not B) = 1/4, then A and B are independent events.

If a, b and c are unit vectors then abs(a-b)^(2)+abs(b-c)^(2)+abs(c-a)^(2) does not exceed.

p : If end digit of an integer is 5 then end digit of its square is also 5. Statement p is same as the

Find the number of natural numbers less than 10^7 which have exactly 77 divisors.

Evaluate the following integrals (vi) int_(0)^(1) (1)/(sqrt(x+1)+sqrt(x))dx

If the system of homogeneous equations (a-1)x+(a+2)y+az=0, (a+1)x+ay+(a+2)z=0and ax+(a+1)y +(a-1)z=0has a non -tivial solution, then find the value of a .

If int (1)/((x + 100) sqrt(x + 99)) dx = f (x) + c then f(x) =

if has set of all valuesof theparameter 'a' for which the function f(x) = sin 2x -8 (a+1) sin x + (4a^(2) +8a -14) x increases for allx in R and hasno critical points for all x in R" is " (-oo , -m -sqrt(n))uu (sqrt(n) ,oo) then (m^(2) +n^(2)) is (where m,n are prime numbers):

Prove that f(x)=5x-3 is continuous at x=0

Statement I The circle x^(2) + y^(2) - 6x - 4y - 7 = 0 touches y-axis Statement II The circle x^(2) + y^(2) + 6x + 4y - 7 = 0 touches x-axis Which of the following is a correct statement ?

ABCDEF is a regular hexagone. AB+AC+AD+AE+AF=lambda AD then lambda = ………….

If |z,|=1,|z_(2)|=2,|z_3|=3 and |9z_1z_2+4z_1z_3+z_2z_3|=12, then the value of |z_1+z_2+z_3| is

int sqrt((cos x - cos^(3) x)/(1 -cos^(3) x))dx =

Find the locus of the point whose polars with respect to the circles x^(2)+y^(2)-4x-4y-8=0 and x^(2)+y^(2)-2x+6y-2=0 are mutually perpendicular.

Find the equation of parabola whose Vertex is (2,3) latus rectum is 8 and axis is parallel to x-axis

In Z the set of all integers, the inverse of -7 w.r.t. '' defined by ab=a+b+7 for all a, bin Z is