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If the pair of lines﻿ ax^(2) + 2hxy + by^(2)+ 2gx + 2fy + c = 0﻿ intersect on the y-axis then﻿

There are two parallel lines, one having 10 points and the other having 5 points. The number of triangles formed with vertices as these points is

Find the approximate value of f(3.02), where f(x)=3x^(2)+5x+3.

int x^(x) ( 1 + log x ) dx =

A and B are two events of a trial, P(A) = 0.4, P(B) = p, P(A uu B) = 0.7. Find p if A and B are independent.

If "Cos"^(-1)P/a+"Cos"^(-1)q/b=alpha, then prove that (p^(2))/(a^(2))-(2pq)/(ab).cos alpha+(q^(2))/(b^(2))=sin^(2)alpha

Show that the function given by f(x)=(log x)/(x) has maximum at x = e.

(sinx+icosx)^(n)

Integrate the following functions 1/(x(logx)^m , xgt0

Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vector such that rtimesa=b and r*c=1, then

{{:(3x -9y=-6),(1/2x-3/2y=c):} If the system of linear equations above has infinitely many solutions, and c is a constant, what is the value of c ?

Form the differential equation of the family of circles touching the y- axis at origin.

If the set A contains 5 elements and the set B contains 6 elements, then the number ofone-one and onto mappings from A to B is

Prove that (1^(2))/(3).^(n)C_(1)+(1^(2) + 2^(2))/(7).^(n)C_(2)+(1^(2)+2^(2)+3^(2))/(7).^(n)C_(3)+"...." +(1^(2)+2^(3)+"....."+n^(2))/(2n+1).^(n)C_(n) = (n(n+3))/(6)2^(n-2).

Find the matrix A satisfying the matrix equation : [{:(2,1),(3,2):}]*A*[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}]

IF lengthof xreactangleis decreasingat therateof3 cm/ minuteand thewidthis increasingat therateof2 cm /minute, whenx=10cm andy=6cm . Find therateof changeof I.The perimeter II. The areaof thereactange

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)x(1-x)^(5)dx=..........

Evaluate the following integrals inte^(x)(2-x)^(2)/((1-x)sqrt(1-x))dx

If the distance s travelled by a particle in time ti is given by s=t^2-2t+5, then its acceleration is

Solve the following differential equations. (dy)/(dx)+(2y)/(x)=2x^(2)

If the angle between the normal to the planes is (pi)/(2), then

Evaluation of definite integrals by subsitiution and properties of its : int_(-4)^(4)|x+2|dx=.......

In which one of the following compounds electron densityon phenyl ring is maximum

Find the 7^("th")" term of "(1-(x^(2))/(3))^(-4)

Solve : sin (cos^(-1) (1/(sqrt(1-x^(2)))))= cos (tan^(-1) (4/3))

int (2x + sin 2x)/(1 + cos 2x)dx =

If overline(a), overline(b), overline(c) are non-coplanar and m, n are real numbers, the [[moverline(a), moverline(b), 3overline(c)]]-[[moverline(b), overline(c), noverline(a)]]-[[noverline(c), noverline(a), 2overline(b)]]=0 is true for

A bag contains n balls, one of which is white. The probability that A and B speak truth are P_(1) and P_(2), respectively. One ball is drwn from the bag and A and B both assert that it is white. Find the probability that drawn ball is actually white.

If origin and (3, 2) are contained in the same angle of the lines 2x + y – a = 0, x – 3y + a = 0, then 'a' must lie in the interval

If n persons are sitting in a row. Find the number of ways of selecting 2 persons so that they are not adjacent to each other .

Equation of the hyperbola with latus rectum (22)/(5) and eccentricity 6/5 is

Two wire of equal length, one of copper and the other of steel, are strecthed side by side by the same tension. So that they produce the same note, their diameters should bear a ratio.(rho_(Cu)=8.9 gm/cc and rho_("steel")=7.7 gm/cc)

How many words can be formed using the letters of the word ASSESSMENT if each word begin with A and end with T?

(i) A pair of dice are rolled. What is the probability that they sum to 7 given that neither die shows a 2 ? (ii) A pair of dice is thrown. Find the probability that either of the dice shows 2 when their sum is 6.

Find int[sqrt(cotx)+sqrt(tanx)]dx

To the circle x^(2)+y^(2)=16 tangent at the point theta=(pi)/3 is

If R, is the set of all non - negative real numbers prove that the function f:R_(+) to [-5, infty]" defined by "f(x)=9x^(2)+6x-5 is invertible. Write also f^(-1)(x).

Statement 1 The equation of the director circle to the ellipse 4x^(2)+9y^(2)=36 is x^(2)+y^(2)=13 Statement 2 The locus of the point of intersection of perpendicular tangents to an ellipse is called the director circle.

The switching circuit for the symbolic form (p vv q) ^^ [~p vv (r ^^ ~ q)] is

Show that C_0 n^2 + C_1 (2-n)^2 + C_2 (4-n)^2 + .... + C_n (2n-n)^2 = n.2^n

If a tangent of slope 2 of the ellipse(x^(2))/( a^(2)) +(y^(2))/( b^(2)) =1is normal to the circle x^(2) +y^(2) +4x +1=0,then the maximum value of ab is

Probability of independent events is P(A_(i))= (1)/(i+1). Where i = 1, 2, 3 ... n, probability of an event that at least one event occurs is ...............

Consider the following frequency table . (i)Find the mean (ii) Find the mean deviation about the mean.

For which value of x, the function f(x)= (e^(sin x))/(4-sqrt(x^(2)-9)) is discontinuous?

If the lines : L_(1):x=1+s,y=-3-lambdas,z=1+lambdas & L_(2):x=(t)/(2),y=1+t,z=2-t with the parameters s & t respectively are coplanar then lambda=

Which of the following option(s) is/are incorrect?

If A is a square matrix of order 3 such that |A^(T)| = 5, then value of |2A|=a) 25 b) 10 c) 20 d) 40

Find direction cosines of the line passing through the poins P(-2, 4, -5) and C(1, 2, 3).

If the pair of lines ax^(2) + 2hxy + by^(2)+ 2gx + 2fy + c = 0 intersect on the y-axis then

Find the matrix A satisfying the matrix equation : [{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}]