SSLC Maths - Objective type Questions

Refer to this post for questions 27 to 33. These questions are of multiple choice type (choose the best answer).

27) The curved surface area of a sphere of radius 5, intercepted between two parallel planes of distance 2 and 4 on the same side from the centre is:

a) $ 20\pi $

b) $ 40\pi $

c) $ 10\pi $

d) $ 30\pi $



28) The arc length of the curve y = f(x) from x = a to x = b is:

a) $ \int_{a}^{b}\sqrt{(1+(\frac{\mathrm{d}y }{\mathrm{d} x})^2}\;\;dx $

b) $ \int_{a}^{b}\sqrt{(1+(\frac{\mathrm{d}x }{\mathrm{d} y})^2}\;\;dx $

c) $ 2\pi\int_{a}^{b}y\sqrt{(1+(\frac{\mathrm{d}y }{\mathrm{d} x})^2}\;\;dx $

d) $ 2\pi\int_{a}^{b}y\sqrt{(1+(\frac{\mathrm{d}x }{\mathrm{d} y})^2}\;\;dx $



29) Solution of $ \frac{\mathrm{d}y }{\mathrm{d} x} + mx=0 $, where m<0 is:

a) $ x=ce^{my} $

b) $ x=ce^{-my} $

c) $ x=my+c $

d) $ x=c $



30) The differential equation $ (\frac{\mathrm{d}y }{\mathrm{d} x})^2\;+\;5y^\frac{1}{3} = x $ is:

a) of order 2 and degree 1

b) of order 1 and degree 2

c) of order 1 and degree 6

d) of order 1 and degree 3



31) The equations of the latus rectum of $ \frac{x^2}{16}+\frac{y^2}{9}=1 $, are:

a) $ y=\pm \sqrt{7} $

b) $ x=\pm \sqrt{7} $

c) $ x=\pm \;7 $

d) $ y=\pm\; 7 $



32) The eccentricity of the hyperbola $ 12y^2-4x^2-24x+48y-127=0 $ is:

a) 4

b) 3

c) 2

d) 6



33) The length of the latus rectum of the rectangular hyperbola xy = 32 is :

a) $ 8\sqrt{2} $

b) $ 32 $

c) $ 8 $

d) $ 16 $

Refer to the question ranges here 1-6 , 7-12 , 13-19 and 20-26 .