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- Question 2, Exercise 2.3 @math-11-kpk:sol:unit02
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... gn} This gives, $A$ is non-singular and $A^{-1}$ exists. Now \begin{align} & \left[\begin{matrix} 4 & ... n} This gives, $A$ is non-singular and $A^{-1}$ exists. Now \begin{align}&\left[ \begin{matrix} 3 & -... n} This gives, $A$ is non-singular and $A^{-1}$ exists. Now \begin{align}&\left[\begin{matrix} 1 & 2
- Question 7, Exercise 10.2 @math-11-kpk:sol:unit10
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... 2\tan 2\alpha =R.H.S.\end{align} =====Question 7(xi)===== Prove the identity $\tan \dfrac{\alpha }{2}... ac{\alpha }{2}=R.H.S.\end{align} =====Question 7(xii)===== Prove the identity $\dfrac{\cos ec\theta -... c{\theta }{2}=R.H.S.\end{align} =====Question 7(xiii)===== Prove the identity ${{\cos }^{2}}\dfrac{
- Question 4 Exercise 4.5 @math-11-kpk:sol:unit04
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... $a_1=0.63, \quad r=0.01<1$.\\ Therefore the sum exists and is given by\\ \begin{align}S_{\infty}&=\df... 5, r=0.01<1$.\\ Thus the sum of the given series exists and given by $$S_{\infty}=\dfrac{a_1}{1-r}$$,\... =0.123, \quad r=0.001<1 \end{align} Thus the sum exists and is given by\\ \begin{align}S_{\infty}&=\df
- Question 1, Review Exercise 1 @math-11-kpk:sol:unit01
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... -5i}{z+5i}|=1$, then $z$ lies on * (a) $X-axis$ * (b) $Y-axis$ * %%(c)%% line $y=5$ * (d) None of these \\ <btn type="link" collapse=
- Question 2 and 3 Exercise 3.3 @math-11-kpk:sol:unit03
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... os ^1(0.2971)=72.72^{\circ}=73^{\circ}\text{(approximately)}\end{align} =====Question 3(iii)===== Fin... ow \theta&=\cos ^1(-0.1601)=99^{\circ}\text{(approximately)}\end{align} ====Go To==== <text align="l
- Question 13 & 14 Exercise 4.5 @math-11-kpk:sol:unit04
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... ac{x}{3}<1$ because $0<x<3$. Thus infinite sum exists and is given by $S_{\infty}=\dfrac{a_1}{1-r}$,... =10+19.84375\\ S&=29.84375\quad \text{ feet approximately}\\ S&=29\dfrac{27}{32}\text{ft}\end{align}
- Question 5 and 6 Exercise 7.3 @math-11-kpk:sol:unit07
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... $\frac{1}{x^3}$ may be neglected, then find approximate value of: $$ \frac{x \sqrt{x^2-2 x}}{(x+1)^2}... =1-\frac{3}{2}+ \end{aligned} $$ Hence the spproximate value of $\frac{x \sqrt{x^2-2 x}}{(x+1)^2}$ i
- Question 14 & 15, Exercise 2.2 @math-11-kpk:sol:unit02
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... stion 14===== Show that inverse of square matrix exists. Then it is unique. ====Solution==== ==
- Question 7 & 8 Exercise 3.3 @math-11-kpk:sol:unit03
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... \sqrt{2} \hat{i}+\hat{j}+\hat{k}$ makes with $y$ axis. ====Solution==== Let $\vec{a}=\sqrt{2} \hat{i}+
- Question 8 Exercise 4.4 @math-11-kpk:sol:unit04
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... \sqrt{4-9}= \pm \sqrt{5}i\end{align} It does not exists. ====Go To==== <text align="left"><btn ty
- Question 3 Exercise 6.4 @math-11-kpk:sol:unit06
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... $$ Here $6$ question to be correct are at least maximum may be eight correct. so the possible oulcome
- Question 5 & 6 Review Exercise 7 @math-11-kpk:sol:unit07
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board... m in the expansion which is 252. Q6 Find an approximation of $(0.99)^5$ using the first three terms o
- Unit 07: Mathmatical Induction and Binomial Theorem (Solutions)
- $n$ is a rational number. * Determine the approximate values of the binomial expansions having indi
- Question 1, Exercise 1.1 @math-11-kpk:sol:unit01
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board
- Question 2 & 3, Exercise 1.1 @math-11-kpk:sol:unit01
- is is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board