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If g''(x) is continuous for all x, g(0) = g'(1) = 1 and if int_0^1 x g^'' (x) dx vanishes, then g(1) is:

Find the length of the major axis, minor axis, latus rectum, eccentricity, centre, foci and the equations to the directrices of the ellipse. (i) 3x^(2) + y^(2) -6x -2 y -5 = 0

If f(x)=2x^(2), find (f(3.8)-f(4))/(3.8-4) :

Let a and p be the roots of equation x^2 + x - 3 = 0. Find the value of the expression 4p^2 - a^3.

The shortest distance between the lines 2x + y + z - 1 = 0 = 3x + y + 2z - 2 and x = y = z, is

An antiderivative of the integral inte^(x)((1-x)/(1+x))^(2)dx is

The points representing the complex numbers z for which |z+4|^2-|z-4|^2 = 8 lie on

The sum of the cofator of the elements in second column in |{:(7,9,1),(10,8,1),(12,10,1):}| is …….

The differential equation of the family of parabolas y^(2)=4ax where a is parameter is

Let f(x)=ax^(2)+x+3andf(x)ge0AAx inR,AAainA" where "AsubR. "Also "L=Lim_(xto oo) (x+1-sqrt(ax^(2)+x+3)). Which one of the following statement is incorrect ?

Evaluation of definite integrals by subsitiution and properties of its : If anti derivative of f(x)=(sinx)/(x) is F(x) then int_(1)^(3)(sin2x)/(x)dx=.........(xgt0)

A factory produces bulbs. The probability that any one bulb is defective is (1)/(50)and they are packed in 10 boxes. From a single box, find the probability that, (i) none of the bulbs is defective (ii) exactly two bulbs are defective (iii) more than 8 bulbs work properly.

(i) Solve :4 sin ^(-1) .(5)/(x) + sin ^(-1).(12)/(x)=(pi)/(2) (ii)slove :sin ^(-1).(5)/(x)+ sin ^(-1).(12)/(x) =(pi)/(2)

If the mean of the data7,8,9,7,lambda , 8,is 8then variance of the data is:

Lt_(xto0)(x^(2))/(int_(0)^(x)Tan^(-1)tdt)

If 10 coins are tossed, find the probability that no two or more consecutive heads occur.

Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the curve y=be^(-(x)/(a)) lies on Y-axis.

-a/6-a gt -4/3 Which of the following is equivalent to the inequal ity above?

Differentiate (1-tanx)/(1+tanx)

2(2x+3) -10 lt 6 (x-2)

If x satisfies the inequations2x - 7 lt 11 , 3x + 4 lt -5 , then x lies in the interval

If PN is the ordinate of a point P on the ellipse x^2/a^2+y^2/b^2=1 and the tangent at P meets the x-axis atT then show that (CN) (CT)=a^2 where C is the centre of the ellipse.

I : Ifcos A =(3)/(4) " then " cos""(A)/2 cos""(5A)/(2) =-7 II : Ifsin (120^(@) - alpha ) = sin(120^(@) - beta ) and 0 lt alpha , beta lt pi" then " alpha + beta + 60^(@)

Three are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put in the urn. A ball is drawn from the urn. Find the probability that it is white.

Using 6 different flags, how many different signals can be made by using atleast three flags, arranging on above the other ?

70 is 250% greater than what number?

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

Consider the following set ofreactions: CHCl_(2)COOH+NaOH to CHCl_(2)COONa+H_(2)O "" DeltaH_(1)=-12830 Cal HCl+NaOH to NaCl to NaCl+H_(2)O "" DeltaH_(2)=-13680 Cal. NH_(4)OH+HCl to NH_(4)Cl+H_(2)O "" DeltaH_(3)=-12270 Cal. Select the correct option(s) :

Let f be a real valued function defined as f: R to R f(x) =|x^(2) -6x +8| sin((x-2)Pi) + |e^(x) -1|sin x+|x^(2)|) The number of points of non-differentiability is

inttan^(-1)xdx=xtan^(-1)x+f(x)+C, " find "f(x).

Number of real solution of (x-1)(x+1)(2x+1)(2x-3)=15(1)is

The value of the integral I=int_(0)^(a) (x^(4))/((a^(2)+x^(2))^(4))dx is

If A is an orthogonal matrix , then |A| is :

In the matrix [{:(2,5,19,-7),(35,-2,(5)/(2),12),(sqrt(3),1,-5,17):}] , write : (i) The order of the matrix , (ii)The number of elements, (iii) Write the elements a_(13),a_(21),a_(33),a_(24),a_(23),

If (x^(2))/(x^(6)-1)=(A)/(x-1)+(B)/(x+1)+f(x) then find the value of f(2)

A bag A contains 3 white and 2 black balls and another bag B contains 2 white and 4 black balls. A bag and a ball out of it are picked at random. What is the probability that the ball is white?

Using the fact that sin (A +B) = sin A.cos B+ cos A sin B and the differentiation, obtain the sum formula for cosines.

if(-pi)/(2)lt thetalt pi/2andnthetane_0 pi/4 , thenvalueofcot((pi)/(4) + theta)cot((pi)/(4)- theta) is

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative.

I: The equation of the plane through the points (1, -2, 2), (3, 1, - 2) and perpendicular to the plane x + 2y – 3z = 5 is x + 16y – 11z + 37 = 0 II : The equation of the plane passing through (1, – 2, 4), (3, -4,5) and parallel to x-axis is y + 2z – 6= 0

If x = ( 2 + sqrt( 3))^(n), then find the value of x( 1- { x} ), where {x} denotesthe fractional part of x

Find the number of terms in the expansion of (3p+4q)^(14)

The surface area of the solid of revolutionof the region bounded by y=2x,x=0 and x=2 about x-axis is…..

Find derivatives of the following functions. (x^2 + 5)^8

int (cos x)/(3 cos x + 4 sin x )dx =

f:X to Y is onto, if and only if1. range of f=Y2. range of f neY3. range of f lt Y4. range of f ge Y

If |bar(x)|=|bar(y)|=2 and (bar(x)" "^(hat)bar(y))=theta then |bar(x)-bar(y)cos theta| = ………..

2lezle4 {:("Quantity A","Quantity B"),((2x)/(5),(5)/(22)):}

Let A = N xx N and be the binary opertion on A defined by (a,b) (c,d) = (a + c, b+d) Show that ** is commutative and associative.