According to ques: \[P\text{ }\left( n \right)\text{ }=\text{ }n\text{ }\left( n\text{ }+\text{ }1 \right)\] is even. Hence, \[P\text{ }\left( 3 \right)\text{ }=\text{ }3\text{ }\left( 3\text{...
Answers: (i) If we read the complete sentence it becomes x and the letter x comes before ‘e’ in the English alphabet. Thus, the letters before the letter ‘e’ are a,b,c,d. ∴ Roster form = {a,b,c,d}...
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question, the given integral can be solved as
Answer: According to the question the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integral can be solved as
Answer:- According to question, the given integrals can be solved as (i) (ii)
(i) (ii) Answer:- According to question, the given integrals can be solved as (i) (ii)
(i) (ii) Answer:- According to question, the given integrals can be solved as (i) (ii)
(i) (ii) Answer: According to question, the given integrals can be solved as (i) (ii)
Answer: Given, According to question, the given integrals can be solved as (i) (ii)
and 
are connected parametrically by the equations given in Exercise 
without eliminating the parameter, find dy/dx.Solution: The provided functions are $x=a \sec \theta$ and $y=b \tan \theta$ $\frac{d x}{d \theta}=a \sec \theta \tan \theta$ and $\frac{d y}{d \theta}=\sec ^{2} \theta$ So now, $\frac{d y}{d...
where 
is defined by: 
Solution: The function provided is $f(x)=\left\{\begin{array}{lll}x+1, & \text { if } & x \geq 1 \\ x^{2}+1, & \text { if } & x<1\end{array}\right.$ As we all know that,...
for ![x \in[1,2]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f408866b9dc82cffe3b69c6d0861f6c9_l3.png "Rendered by QuickLaTeX.com")
Solution: (i) $f(x)=x^{2}-1$ for $x \in[1,2]$..........(1) Provided here, $f(x)$ is a polynomial function. Then, $f(x)$ is continuous and derivable on the real line. Therefore $f(x)$ is continuous...
in the following exercise 
Solution: The provided function is: $y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right),-1<x<1$ Let's take $x=\tan \theta$, we obtain $y=\cos^{-1}\quad[(2 \tan\ \theta) /(1+\tan^ 2$$\theta)]$...
in the following exercise 
Solution: The provided function is $2 x+3 y=\sin y$ On derivating the function with respect to $\mathrm{x}$, we have $\frac{d}{d x}(2 x)+\frac{d}{d x}(3 y)=\frac{d}{d x} \sin y$ $2+3 \frac{d y}{d...
Let consider the centre of the circle is O. Given in the question- OP = radius = $5cm$ OQ = $13cm$ At point P, a tangent if formed such that the line passing through O intersects it at point Q....
Ages (in years):5 – 1515 – 2525 – 3535 – 4545 – 5555 – 65No of students:6112123145 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. ...
$x:$$5$$6$$7$$8$$9$$f:$$4$$8$$14$$11$$3$ Solution: $x$$f$$fx$$5$$4$$20$$6$$8$$48$$7$$14$$98$$8$$11$$88$$9$$3$$27$$N=40$$\sum{fx=281}$ Mean $=\sum{fx/n=281/40}$ $\therefore $ Mean...