Problem 2
The envelope of the family of straipht lines \(y=m x+a m^{2}\), (an being the parameter) is
Problem 3
The curvature of the circle \(x^{2}+y^{2}=25\) at the point \((3,4)\) is
Problem 6
A triangle of maximum area inscribed in a circle of radius \(r\) (a) is a right angled triangle with hypotenuse measuring \(2 r\) (b) is an equilateral triangle (c) is an isosceles triangle of height \(r\) (d) does not exist.
Problem 7
The extreme value of \((x)^{1 / x}\) is (a) \(\boldsymbol{e}\) (b) (1/e) (c) (e) \(^{\text {te }}\) (d) 1 .
Problem 8
The percentage error in computing the aren of an ellipse when an error of 1 per cent is made in measuring the major und rainor axes is (a) 0.2'ie (b) \(2 \%\) (c) 0.02*.
Problem 11
If the nermal to the curve \(y^{2}=5 x-1\) at the point \((1,-2)\) is of the form \(a x-5 y+b=0\), then \(a\) and \(b\) are (a) 4,14 (b) \(4,-14\) (c) \(-4,14\) \((d)-4,-14\)
Problem 12
The radius of curvature of the curve \(y=e^{x}\) at the point where it crosses the \(y\)-axis is (a) 2 (b) \(\sqrt{2}\) (c) \(2 \sqrt{2}\) (d) \(\frac{1}{2} \sqrt{2}\).
Problem 13
The equation of the asymptotes of \(x^{3}+y^{3}=3 a x y\), is (a) \(x+y-a=0\) (b) \(x-y+a=0\) (c) \(x+y+a=0\) (d) \(x-\dot{y}-a=0\).
Problem 15
Fnvelope of the family of lines \(x=m y+1 / m\) is \(\ldots\)
Problem 25
Envelope of the fumily of lines \(\frac{x}{t}+y t=2 \mathrm{c}\) (where \(t\) is the parameter) is \(\ldots\)
