Which of the following represents direction cosines of the line :
The general solution of the trigonometric equation tan2 θ = 1 is..........................
(a)`theta =npi+-(pi/3),n in z`
(b)`theta =npi+-pi/6, n in z`
(c)`theta=npi+-pi/4, n in z`
(d) `0=npi, n in z`
If `bara, barb, bar c` are the position vectors of the points A, B, C respectively and ` 2bara + 3barb - 5barc = 0` , then find the ratio in which the point C divides line segment AB.
Equation of a plane is `vecr (3hati-4hatj+12hatk)=8`. Find the length of the perpendicular from the origin to the plane.
Write the dual of the following statements:
(l) (p ∨ q) ∧ T
(2) Madhuri has curly hair and brown eyes .
If the lines `(x-1)/2=(y+1)/3=(z-1)/4 ` and `(x-3)/1=(y-k)/2=z/1` intersect each other then find value of k
Prove that three vectors `bara, barb and barc ` are coplanar, if and only if, there exists a non-zero linear combination `xbara+ybarb +z barc=0`
Show that the equation `x^2-6xy+5y^2+10x-14y+9=0 ` represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines.
Express the following equations in the matrix form and solve them by method of reduction :
2x- y + z = 1, x + 2y + 3z = 8, 3x + y - 4z =1
how that every homogeneous equation of degree two in x and y, i.e., ax2 + 2hxy + by2 = 0 represents a pair of lines passing through origin if h2−ab≥0.
find the symbolic fom of the following switching circuit, construct its switching table and interpret it.
if A, B, C, D are (1, i, I), (2, l ,3), (3; 2, 2) and (3, 3, 4) respetivly., then find the volume of the parallepiped with AB, AC and AD as concurrent edges
Find the equation of the plane passing through the line of intersection of planes 2x - y + z = 3 and 4x- 3y + 5z + 9 = 0 and parallel to the line
The integrating factor of linear differential equation `dy/dx+ysecx=tanx` is
(a)secx- tan x
(b) sec x · tan x
The equation of tangent to the curve y = 3x2 - x + 1 at the point (1, 3) is
Examine the continuity of the function
f(x) =sin x- cos x, for x ≠ 0
=- 1 ,forx=0
at the poinl x = 0
Evaluate : `intsec^nxtanxdx`
The probability mass function (p.m.f.) of X is given below:
|P (X= x)||1/5||2/5||2/5|
Ify y=f(u) is a differentiable function of u and u = g(x) is a differentiable function of x then prove that y = f (g(x)) is a differentiable function of x and
Obtain the differential equation by eliminating arbitrary constants A, B from the equation -
y = A cos (log x) + B sin (log x)
An open box is to be made out of a piece of a square card board of sides 18 cms. by cutting off equal squares from the comers and tumi11g up the sides. Find the maximum volume of the box.
If the function f (x) is continuous in the interval [-2, 2],find the values of a and b where
`=2x+1, for 0<=x<=1`
`=2bsqrt(x^2+3)-1, for 1<x<=2`
Find the area of the sector of a circle bounded by the circle x2 + y2 = 16 and the line y = x in the ftrst quadrant.