List of practice Questions

What is point mutation? Give one example.
Briefly mention the contribution of T.H. Morgan in genetics.

Show that the function f: R* \(\to\) R* defined by f (x)= \(\frac {1} {x}\) is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R* ?  

Let R be the relation in the set N given by R={\((a,b):a=b−2,b>6\)}.Choose the correct answer
Let R be the relation in the set {1,2,3,4} given by R= {(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)}. Choose the correct answer.
Mention the advantages of selecting pea plant for experiment by Mendel.
How many eggs do you think were released by the ovary of a female dog which gave birth to 6 puppies?
How many eggs are released by a human ovary in a month? How many eggs do you think would have been released if the mother gave birth to identical twins? Would your answer change if the twins born were fraternal?
In our society the women are often blamed for giving birth to daughters. Can you explain why this is not correct?.
Find an anti derivative (or integral) of the following functions by the method of inspection: sin2x - 4e3x
A string is wound round the rim of a mounted flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord. Neglecting friction and mass of the string, the angular acceleration of the wheel is

For each of the differential equations given below, indicates its order and degree (if defined).

\((i) \frac {d^2y}{dx^2}+5x(\frac {dy}{dx})^2-6y=log\ x\)

\((ii)(\frac {dy}{dx})^3-4(\frac{dy}{dx})^2+7y=sin\ x\)

\((iii) \frac {d^4y}{dx^4}-sin(\frac {d^3y}{dx^3})=0\)

Find a particular solution satisfying the given condition:\(\frac {dy}{dx}-3y\  cot\ x=sin2x;\ y=2 \ when\  x=\frac \pi2\)
For the differential equations, find the particular solution satisfying the given condition:\(2xy+y^2-2x^2\frac{dy}{dx}=0;y=2\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\(\frac{dy}{dx}-\frac{y}{x}+cosec(\frac{y}{x})=0;y=0\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\([xsin^2(\frac{x}{y})-y]dx+xdy=0;y=\frac{π}{4},\)when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\(x^2dy+(xy+y^2)dx=0;y=1\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\((x+y)dy+(x-y)dy=0;y=1\) when \(x=1\)
Show that the given differential equation is homogeneous and solve:\((1+e^{\frac{x}{y}})dx+e^{\frac{x}{y}}(1-\frac{x}{y})dy=0\)
Show that the given differential equation is homogeneous and solve:\(y\,dx+xlog(\frac{y}{x})dy-2x\,dy=0\)
Show that the given differential equation is homogeneous and solve:\(x\frac{dy}{dx}-y+sinx(\frac{y}{x})=0\)
Show that the given differential equation is homogeneous and solve:\({xcos(\frac{y}{x})+ysin(\frac{y}{x})}y\,dx={ysin(\frac{y}{x})-xcos(\frac{y}{x})}x\,dy\)
Show that the given differential equation is homogeneous and solve:\(x\,dy-y\,dx=\sqrt{x^2+y^2}\,dx.\)
Show that the given differential equation is homogeneous and solve:\(x^2\frac{dy}{dx}=x^2-2y^2+xy\)
Show that the given differential equation is homogeneous and solve:\((x^2-y^2)dx+2xy\,dy=0\)