Mathematics Tes...

The area (in square units) bounded by the curves y² = 4x and x² = 4y in the plane is

The length of the tangent from (0,0) to the circle 2x² + 2y² + x - y + 5 = 0 is

If the line 3x-4y=λ touches the circle x²+y²-4x-8y-5=0, λ  can have the values

The differential equation which represents the family of plane curves y=exp. (cx) is

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Tangents are drawn from the point (17,7) to the circle x²+y²=169.
Statement-1:
The tangents are mutually perpendicular.
Statement-2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x²+y²=338.

The value of a for which the system of equations

a³x+(a+1)³y+(a+2)³z = 0
ax+(a+1)y+(a+2)z = 0
x+y+z = 0

has a non-zero solution, is

The chance of getting a doublet with 2 dice is

If cov. (x, y) = 0, then ρ(x, y) equals

The two opposite vertices of a square on xy-plane are A(-1,1) and B(5,3), the equation of other diagonal (not passing through A and B) is

If the normal to the curve y=f(x) at the point (3,4) makes an angle 3π/4 with the positive x-axis, then f'(3)