Senior Secondary School Mathematics for Class 11 by R S Aggarwal | 9789350271476 | 9350271478

Mathematics

Senior Secondary School Mathematics for Class 11

1195 SOLVED PROBLEMS

Question: 20.8.3

Reduce the equation √3x+y+2=0 to the normal form x cos α+y sin α=p, and hence find the values of α and p. ...

Verified Answer:

We have

\begin{aligned}\sqrt{3} x+y+2=0 \Ri...

Question: 17.2.1

Find the principal solutions of each of the following equations: (i) sin x=1/2 (ii) cos x=1/√2 (iii) tan x=1/√3 ...

Verified Answer:

(i) The given equation is

\sin x=\frac{1}{...

Question: 15.4.19

Prove that cot 2x cot x-cot 3x cot 2x-cot 3x cot x=1. ...

Verified Answer:

We have

\begin{aligned}& \cot 3 x=\cot ...

Question: 28.6.1

Differentiate: (i) e^x/x (ii)(2x+3/x²-5) (iii) e^x/(1+sin x) ...

Verified Answer:

(i)

\frac{d}{d x}\left(\frac{e^{x}}{x}\rig...

Question: 28.7.5

If y=cos² x², find dy/dx. ...

Verified Answer:

y=\left(\cos x^{2}\right)^{2}

. Pu...

Question: 28.7.10

Differentiate (i) √1+x/1-x (ii) x/√1-x² ...

Verified Answer:

(i) Let

y=\sqrt{\frac{1+x}{1-x}}

....

Question: 28.7.9

Differentiate e^ax cos (b x+c) . ...

Verified Answer:

Using the product rule, we have

\begin{arra...

Question: 28.7.8

Differentiate sin 2x cos 3x . ...

Verified Answer:

By using the product rule, we have

\begin{a...

Question: 28.7.7

If y=sin (√sin x+cos x), find dy/dx . ...

Verified Answer:

Putting

(\sin x+\cos x)=t

and [la...

Question: 28.7.6

Differentiate √1-tan x/1+tan x. ...

Verified Answer:

Let

y=\sqrt{\frac{1-\tan x}{1+\tan x}} [/l...