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The value of intsec^2x /(cosec^2x)dxis

Differentiate (x^(2)-5x+8)(x^(3)+7x+9) in three ways mentioned below : (i) by using product rule (ii) by expanding the product to obtain a single polynomial. (iii) by logarithmic differentiation. Do they all give the same answer?

Find the angle between the cures given below : y^(2)=8x, 4x^(2)+y^(2)=32

If a_1,a_2,a_3,a_4 are the coefficients of 2nd, 3rd, 4th and 5th terms of (1+x)^n respectively then (a_1)/(a_1+a_2) , (a_2)/(a_2+a_3),(a_3)/(a_3+a_4) are in

Define * on N by m*n=1cm (m,n) Show that * is a binary operaitn which is commutative as well as associative

Normal diffusion capacity of gases in human lungs in order is :-

Let x,x_(1),x_(2),x_(3),x_(4),...,x_(8), be 10 real zeros, of the polynomial P(x)=x^(10)+ax^(2)+bx+c where a, b, c,in R. If the value of Q(x_(1))=(p)/(q), where p and q are coprime to each other. If Q(x_(1))=(x-x_(2))(x-x_(3))...(x-x_(8 ))andx_(1)=(1)/(2), then the value of q-p is.......

Letz_(1), alpha, betabe complex numbers of whichalpha and beta constants andz_(1) varies. Ifz_(2) is given in terms ofz_(1)by oneof the following equations, it is required to find z_(2) corresponding toz_(1) thenThe given figure illustrates(##AAK_T1_MAT_C01_E05_003_Q01.png" width="80%">

For each of the differential equations given in find a particular solution satisfying the given condition : (dy)/(dx)+2ytanx=sinx,y=0 when x=(pi)/(3)

If the axes are turned through 45^(@), find the transformed form of the equation 3x^(2)+3y^(2)+2xy=2.

Rectangle AKLD consists of 5 congruent rectangles , as shown in the figure below. Which of the following is the ratio of the length of bar(AK) to the length of bar(AD) ?

Show that |vec(a)|vec(b)+|vec(b)|vec(a) is perpendicualr to |vec(a)|vec(b)-|vec(b)|vec(a), for any to nonzero vectors vec(a) and vec(b).

Integrate the function (x+2)/(sqrt(x^(2)+2x+3))

If a point P moves such that the sum of the distance from P to the point A(1, -1) and B(-1, 1) is always 4, then the equation for the locus of P is

Find the equation of the circle which cuts the circle x^2 + y^2 + 4x - 6y + 11 = 0 and x^2 + y^2 - 10x - 4y + 21 = 0 rthogonally and has the diameter along the staight line 2x + 3y = 7.

The value of int (sinx)/(sin4x) dzx is

In [0,1], Lagrange's mean value theorem is not applicable to (a)f(x)={{:(1/2-x,xlt1/2),((1/2-x)^(2),xge1/2):} (b) f(x)={{:((sin)/(x),x ne 0),(1,x=0):} f(x)=x|x| (d) f(x)=|x|

If x= 3 sin t- sin (3t), y= 3 cos t- cos 3t, then find ((dy)/(dx))" at " t= (pi)/(3)

If the coefficients of 2nd , 3rd and 4th terms of the expansion of (1+x)^(2n) are in A.P. then the value of 2n^2 -9n + 7 is

Find the centre and radius of each of the circles whose equations are given below: (i) 3x^(2)+3y^(2)-5x-6y+4=0 (ii) 3x^(2)+3y^(2)+6x-12-1=0 (iii) x^(2)+y^(2)+6x+8y-96=0 (iv) 2x^(2)+2y^(2)-4x+6y-3=0 (v) 2x^(2)+2y^(2)-3x+2y-1=0 (vi) x^(2)+y^(2)+2x-4y-4=0 (vii) x^(2)+y^(2)-4x-8y-41=0

If 0 alpha ltbeta lt pi/2 then

If -2x ^(2)+ 5x-8 is multiplied by 4x-9, what is the coefficient of x in the resulting polynomial?

Two dice are rolled and given that the sum of them is atmost 11. Find the probability that they show even on both dice.

Evaluate int_(0)^((1)/(2)) (x^(7))/(sqrt(1-x^(4))) dx

Show that the function f(x)={:{(5-x"," x ge2),(x+1 "," x lt 1):}

Integrate thefunction in Exercise. (x)/(sqrt(x+4)),x gt -4

If |bar(a)|=4 and -3le lambda le 2, then the range of |lambda. bar(a)| is ………..

Which of the following is a homogeneous differential equation?

Let us define a relation R in R as aRb if a geb . Then, R is .......

Ify= tan^-1((1-x)/(1+x))+cot^-1((1-x)/(1+x)) then dy/dx ?

The points 2a + 3b - c, a - 2b + 3c, 3a + 4b - 2c, a - 6b + 6c are

Differentiate cos^2x+e^xcosx

int_(0)(pi//2) ( x dx)/(Sin x + Cos x)=

Which of following will form tri-bromo derivative of phenol ?

A gentlemen hosts a party of (m+n) guests and places 'm' at one round table and the remaining 'n' at the other round table. Number of ways the guests can be arranged is

Prove that the three lines drown from origin with direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3) are coplanar if [[l_1,m_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]]=0.

From a point (h,k) three normals are drawn to the parabola y^2=4ax. Tangents are drawn to the parabola at the of the normals to form a triangle.

From a point (h,k) three normals are drawn to the parabola y^2=4ax. Tangents are drawn to the parabola at the of the normals to form a triangle. The circumcentre O of triangle is

A is even ordered non singular symmetric matrix and B is even ordered non singular skew symmetric matrix such that AB = BA, then A^3B^3(B'A)^(-1)(A^(-1)B^(-1))'AB is equal to :

From a point (h,k) three normals are drawn to the parabola y^2=4ax. Tangents are drawn to the parabola at the of the normals to form a triangle. The condition for the equilateral is

The perpendicular bisectors of the sides of a triangle are concurrent.

Area bounded by curve y = tan pi x, x in [- (1)/(4) , (1)/(4) ] and X - axis is ….....

A baised coin with probability p,0lt p lt of heads is tossed until a head appears for the first time. If the probabilitythatthe numberof tosses requiredis even is 2/5, then p is equal to

[(d)/(dx) sec^(-1)x]_(x = -3)=…….

Mean of 100 observation is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. Then the correct means is

If alpha variable takes the discrete values alpha + 4, alpha - 7/2, alpha - 5/2 , alpha - 3, alpha- 2, alpha + 1/2 , alpha - 1/2, alpha + 5, (alpha> 0) then the median is

Find the direction cosines of the two lines which are connected by the relation l+m+n=0,mn−2nl−2lm=0

Evaluate the following lim_(xto2) (x -2)/(x^4-16)

Consider a 2xx2 matrix A=[a_(ij)] , where A_(ij)=(i+2j)^2/2 Write A

Define * on N by mn=1cm (m,n) Show that is a binary operaitn which is commutative as well as associative