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If A is a 3 xx 3 matrix and |A| = 2, then |Adj (Adj A)|Adj(Adj A) =

int_(0)^(2pi) sqrt(1-cos 2x)/(2)dx=

Solve the following linear programming problem graphically : Maximise Z = 4x + y "…(1)" subject to the constraints : x+y le 50 "…(2)" 3x+y le 90"…(3)" x ge 0, y ge 0"...(4)"

A funtion f , R-{0} rarr R is defined as f(x)={{:(x^(2)+3x-7",",xgt0),(h(x)",",xlt0):}If f (x) is an odd funtion, then h(x)=

Shortest distance between the linesbar (r )= (1 , 2, 1 ) + lambda (1,-1,1) and bar(r ) = (2,-1,-1) + mu (2,1,2)is

Reactify the mistakes if any. The vector vec0 has unique direction.

int_(0)^((pi)/(2)) (3 tan x + 4 cot x)/(tan x + cot x)dx

The solution of the differential equation ydx-(x+2y^(2))dy=0 is x=f(y). If f(f-1)=1, then f(1) is equal to :

Let f(x)=(sin4pi[x])/(1+[x]^(2)), where [x] is the greatest integer lex, then :

When the axes are rotated through an angle alpha, find the transformed equation of xcos alpha+ysin alpha=p.

The origin is shifted to (2,3) and then the axes are rotated through angle theta in the counter clock sense. If the equation 3x^(2) + 2xy + 3y^(2) - 18x -22y + 50=0 is transformed to 4x^(2) + 2y^(2) -1=0, then the angle theta =

Find the mean about the mean for the following data . (##VIK_MAT_IIA_QB_C08_SLV_003_Q01.png" width="80%">

Find the particular solution of the differential equation 3e^(x) tan y dx + (1 + e^(x)) sec^(2) y dy=0, when x= 0, y= pi

It is given that 10% of the electric bulbs manufactured by a company are defective. In a sample of 20 bulbs, find the probability that more than 2 are defective.

Differentiate with respect to x: (sin x)^(x) + sin^(-1)sqrt(x)

consider the function f(X) =x+cosx -a values of a for which f(X) =0 has exactly one negative root are

{:(" "Lt),(n rarr oo):}[(1)/(na)+(1)/(na+1)+(1)/(na+2).......+(1)/(nb)]=

A and B seek admission in I.I.T. The probability that A is selected is 0.5 and the probability that both A and B are selected is atmost 0.3. The probability of B getting selected is atmost is

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2.

The probability that a person chosen at random is left handed (in hand writing) is 0.1 what is the probability that in a group of ten people there is one and only one who is left handed.

If f(x)={((sin3x)/(e^(2x)-1),,,x!=0),(k-2,:,x=0):} is Continuous at x=0, then k=

Let f(x) (1-cos4x)/(x^(2)),g(x)=(sqrtx)/((sqrt(16+sqrtx))-4)and q(x)=(e^(2x)-x^(x)+1)/(x^(2x+e^(x)+1)),(x in R). lim_(x to 0)q(x)=

If |bar(a)xx bar(b)|^(2)+|bar(a).bar(b)|^(2)=144 and |bar(a)|=4, then |bar(b)| is equal to ……………….

If x,y,z in R. xgtygtz and D= |{:((x+1)^2,(y+1)^2,(z+1)^2),(x,y,z),(1,1,1):}| , then D is ………

int_(0)^(pi//4) (dx)/(2+sin^(2)x)=

Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

Evaluate the definite integral in exercise overset(5) underset(4) int e^(x)dx

int_(r//6)^(pi//4)(dx)/(sin2x)=

How many middle terms (x+2z)^(4n +1) possesses ?

The vector equation of the line joining the pionts hat(i) - 2hat (j)+ hat k and -2 hat j + 3 hatk........

For |x| lt 1, the coefficient of x^r in the expansion of ((1+x)^2)/((1-x)^3) is

Differentiate (x^2-5x+8)(x^3+7x+9)by using product rule

Prove that : Expand 5sqrt(5) in increasing powers of (4)/(5).

Evaluate the following integrals int ((sec 2x - 1)/(sec 2x + 1)) dx

Matrix multiplication is commutative .

The product of the perpendicular distances drawn from the points (3,0) and (-3,0) to the tangent of the ellipse (x^(2))/(36)+(y^(2))/(27)=1" at "(3,(9)/(2)) is

For the equation 2x-1=-sqrt(2-x), find the sum of the roots.

If the integral int_(b)^(oo)(sqrt(sqrtx+a)-sqrtx)-sqrt(sqrtx-sqrt(x-b)))dx is finite, then

If A , B are event such that P(A)=0.6, P(B)=0.4 and P(A cap B)=0.2, then find P(B | A^c)

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int_(a)^(b) x dx

If x% of y is 10, which of the following is equal to y% of x?

A 1 kg block is a given a velocity of 15 m//s towards right over a very long rough plank of mass 2kg placed on a smooth horizontal surface as shown in figure. The correct graph showing linear momentum of 1 kg (i.e P_(1)) andand 2 kg (i.eP_(2)) versus time is

Statement-1:It is impossible for a system to undergo a cyclic process whose sole effects are flow ofheat into the system froma hot reservior and perform and equivalent amount of work by the system on the surroundin. Statement-2 : First law of thermodynamics is invalid for a cyclic process.

If a line has direction ratios 2, -1, -2, determine its direction cosines.

Evaluate the definite integrals int_(0)^(pi/2)(2sinx+3)dx

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k= 3, 4, 5 otherwise X takes the value -1. The expected value of X, is ……….

The vector equation of the line passing through the points (1,-2,5) and (-2,1,3) is

If the angle 2 theta is acutethen the acute angle between the pair of straight lines x^(2) (cos theta - sin theta) + 2xy cos theta + y^(2) (cos theta + sin theta) = 0is