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Differentiate w.r.t.x the function in Exercises 1 to 11. (3x^(2)-9x+5)^(9)

Coefficient of x^10 in 10^x is

Two events A and B are such that P(A)=(1)/(4),P(A|B)=(1)/(4) and P(B|A)=(1)/(2) Consider the following statements : (I) P (overline(A)|overline(B))=(3)/(4) (II) A and B are mutually exclusive (III) P(A |B)+P(A|overline(B))=1 Then

The total number of ways of selecting 3 balls from a bag containing 7 balls is

The optimal value of the objective function in a LPP is attained at points-

An object moves in x-y plane such that it starts from origin with initial velocity vecu=3hati+4hatj(m/s) and an acceleration veca=2hati(m//s^2), It's distance from origin at t=1 s is :

Let S and S^(1)be the foci of an ellipse . At any point P on the ellipse ifSPS^(1) lt 90 ^(@)thenits eccentricity :

Orthocentre of the triangle formed by the lines xy-3x-5y+15=0 and 3x+5y=15 is

A speaks 3 out of 5 times. He throws an unbiased die and reports it is a six. Let p be the probability that it is actually a six, then 6.5p = ______

Let A = {1,2,3},B={5,6.7} then find AcapB

If alpha, beta and gamma are real numbers, then : Delta=|(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1)| ie equal to :

whichof the following is//aretrue for Delta= |{:(a^(2),,1,,a+c),(0,,b^(2)+1,,b+c),(0,,b+c,,c^(2)+1):}| ?

Integrate the following functions sqrt(x^2+4x+6)

If {:|( x,2),(18,x) |:}= {:|( 6,2),( 18,6)|:} , then x is equal to

If f(x)={:{(1+sin x"," 0 le x lt pi//2),(""1 "," x lt0):} then show that f(0) =|x| does not exist.

If A_(g)^(-)rarrA_(g)^(+2)+3e^(-), triangleH_(2)=550 kj//mol^(-1) then EGE of A is(in kj//mol^(-1))

If ~q vv pis F, then which of the following is correct?

A boy is flying a kite of a height of 40 ft. If the kite moves horizontally away from the boy at the rate of 5 ft. //sec., paid out at the rate of

The value of sin(cos^-1(3/5)) is:

Statement -1 : The equation |x|+|y|=2 represents a parallelogram.Statement - 2 : Lines x+y=2 and x+y=-2 are parallel. Also lines x-y=2 and -x+y=2 are parallel.

Observe the following statements : Asseration (A) : f(x)=2x^3-9x^2+12x-3 is increasing outside the interval (1,2) Reason (R ) : f^1(x)lt0" for "x in (1,2) Then which of the following is true

The two vectors veca =2hati+hatj+3hatk and vecb =4hati-lamdahatj+6hatkare parallel, iflamda is equal to:a) 2 b) -3 c)3 d) -2

Match the following Lists . {:("List - I","List - II"),((1)(1.2)/(1!)+(2.3)/(2!)+(3.4)/(3!)+...oo,(a) 3e),((2)2/(3!)+4/(5!)+6/(7!)+...oo,(b)(e(e^2-1))/2),((3) 4(1+1/(2!)+(2)/(3!)+(2^2)/(4!)+......oo),(c) e^2+1),((4)1+(1+3)/(2!)+(1+3+3^2)/(3!)+....,(d)5e):}

Evaluate the following determinants: [[16,19,13],[15,18,12],[14,17,11]]

The solution of (dy)/(dx) + ((y^(2) + y + 1)/(x^(2) + x+1)) = 0 is

A={a_(1),a_(2),a_(3)}, B={b_(1),b_(2),b_(3)}. A one-one mapping is selected at random from the set of mappings from A to B. The probability that it satisfies the condition f(a_(i)) ne b_(i) is

If A=[{:(a,0,0),(0,a,0),(0,0,a):}] then |adjA| = …….

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC. Given AH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of HD.HF is

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC. Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of R is

If C denotes the binomial coefficient .^(n)C_(r) then (-1)C_(0)^(2)+2C_(1)^(2)+5C_(2)^(2)+……+(3n-1)C_(n)^(2)=

int (dx)/((x+1)sqrt(4x+3))=

Evaluate the following integrals int_(-2)^3x^4dx

Two blocks on horizontal ground are connected by a spring. At an instant, acceleration of 3kg while being pulled by 10N force is 2 m//s^2

int_(0)^(a) (f(x)+f(-x))dx=

Country X has a four-digit postal code assigned to each town, such that the first digit is non-zero, and none of the digits is repeated. {:("Quantity A","Quantity B"),("The number of possible postal","4,500"),("codes in country X",):}

If A=[(cosalpha,sinalpha),(-sinalpha,cosalpha)]prove that A.A^(T)=1 Hence find A^(-1)

What is the remainder when 3^(257) is divided by 80

If a, b, c are in G.P then the value of the determinant Delta= [[a, b, ax+by],[b ,c ,b x+c y],[a x+b y, b x+c y, 0]] is

Find the value of (-64)^(1//6).

A pair of fair dice is rolled repeatedly. Find the probability of getting doublet 4th time in the 9th trail.

(x-3)/(-1) =(y-4)/(2)=(z+2)/(1) "and" (x-1)/(1)=(y+7)/(3) =(z+2)/(2)

Let f and g be function defined by f(theta) = cos^(2)theta and g(theta) = tan^(2)theta. Suppose alpha and beta satisfy 2f(alpha) - g(beta)=1, then the value of 2f(beta) -g(alpha) is ………….

Two pair of balanced dice is tossed four times. If random variable X denotes equal numbers obtained on dice, find mean.

a manhas4 friends , inhowmanywayscan heiniviteone ormorethemto dinner?

Find axis, Vertex, focus and equation of directrix for x^(2)-6x-12y-3=0.

Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], where 0 lethetale2pi Then

The normal of the circle (x- 2)^(2)+ (y- 1)^(2) =16 which bisects the chord cut off by the line x-2y-3=0 is