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Centroid of the triangle is (3, 3) and orthocentre is (-3, 5). Then centre of the nine point circle is

If sinx=(3)/(5),cosy=-(12)/(13), where x and y both lie in second quadrant, find the value of sin(x+y).

Show that the statement 'For any real numbers a and b,a^(2)=b^(2) implies that a = b is not true' by giving counter example.

Statement P (n) : 10^(n) + 3(4^(n+2))+5 is divisible by n = ........

If log_(10)sinx+ log_(10)cosx+1 and log_(10)(sinx+cosx)=((log_(10)n)-1)/2, then the value of 'n/3' is _______

Consider the sets A = {1,2,3,4} and B = {3,4,5,6}.Find all possible subsets of A and B count the number of subsets of A. Verify the following result.If A contains n elements , then A will have 2^n subsets'.

The point (0,4) and (0,2) are the vertex and focus of a parabola. Find the equation of the parabola.

AA n in N, n^(2)(n^(4) -1) is divisible by

Calculate P_(95) for the following data

If tantheta+sintheta=mandtantheta-sintheta=n then m^(2)-n^(2) = …………

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then

In which of the following graphs is x=c the point of inflection ?

Statement -I : InDelta ABC , b cos ^(2) "" ( C)/(2)+ c cos ^(2) ""( B)/(2)= sStatement -IIDelta ABC , cot ""(A)/(2)= ( b+c)/( 2 ) rArr B = 90 ^(@) Which of the above statement is correct.

Calculate the mean deviatioin about median age for the age distribution of 100 persons given below:

If f(x)={{:((1-sin^(3)x)/(3 cos^(2)x),if x lt (pi)/(2)),(a,if x=(pi)/(2)),((b-(1-sinx))/(pi-2x)^(2),ifxgt(pi)/(2)):}is continuous at x =(pi)/(2)find a and

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : a multiple of 3 ?

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : a square number

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : a prime number

One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace (iii) a black card (i.e., a club or, a spade) (iv) not a diamond (v) not a black card.

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : not an odd number

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : an odd number

Nine counters numbered 2 to 10 are put in a bag . One counter isselected at random. What is the probility of getting a counter with : a number 5

Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.

Expand the following expressions : (2x+3y)^(5)

If x=5+2 sqrt(6) and tan theta=(1)/(2) ( sqrt(x)+(1)/(sqrt(x))) then sec^(2) theta+ sin^(2) theta=

If y = 1/xthen (dy)/(dx)+sqrt((1+y^4)/(1+x^4))=

The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for

cos^(2)(125^(@)-x)-cos^(2)(55^(@)+x)=

Findthe extremevaluesof thefollowingfunctionover R. (i) sin^(2) (60^(0)+ x)+ sin^(2) (60^(0)- x) (ii)cos (x+ (Pi)/(3) ) +2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv)cos 2 x+cos^(2) x (v )cos x cos ((2pi)/(3) + x)cos ((2pi)/(3)-x)

Let alpha=sin^(-1)(36/85), beta=cos^(-1)(4/5) and gamma=tan^(-1)(8/15) then

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

(n!)^(2) gt n^(n) is true for

Find Lt_(xtooo)((2x+3)/(3x-1)).

Simplify: sqrt(-4) + sqrt(-16)- sqrt(-25)

log ( 4x ^(2) - 9)

Find the mean and variance for each of the data :First n natural numbers .

ABCisan equitateral triangle of side 'a'. Then bar(AB).bar(BC)+bar(BC).bar(CA)+bar(CA).bar(AB)=

If cot^(-1)((n^(2)-10n+21.6)/pi) gt pi/6, n in N, then n can be

If a:b: c = 3: 5: 7then cos A : cos B : cos C

Sketch the graph of cos 2x in the intervals |0, pi]

Prove the following ("sin"x+"sin"3x)/(cosx-cos3x)="tan"2x

y = Cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] then (dy)/(dx) =

The origin shiftedto (1,2) then the equation y^(2) - 8x - 4y + 12 = 0 changes as y^(2) = 4axthen a =

Consider the experiment of rolling a die. Let A be the event 'getting a prime number', B be the event 'getting an odd number'. Write the sets representing the events (i) A or B (ii) A and B (iii) A but not B (iv) 'not A.

If y = x^(x) then dy/dx is:

Sum of the distances of a point from two per pendicular lines is 3. The area enclosed by the locus of the point is

baraxx{baraxx(baraxxbarb)}=

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))|is 8 the value of |2(a_(1),2b_(1),2c_(1)),(2a_(2),2b_(2),2c_(2)),(2a_(3),2b_(3),2c_(3))|