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- Unit 01: Complex Numbers (Solutions)
- Unit 02: Matrices and Determinants (Solutions)
- Unit 04: Sequences and Seeries
- Unit 05: Polynomials
- Unit 08: Fundamental of Trigonometry
- Unit 09: Trigonometric Functions
- Question 1, Exercise 1.1
- Question 2, Exercise 1.1
- Question 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3, Exercise 1.2
- Question 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 10, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3, Exercise 1.3
- Question 4, Exercise 1.3
- Question 1, Exercise 1.4
- Question 2, Exercise 1.4
- Question 3, Exercise 1.4
- Question 4, Exercise 1.4
- Question 5, Exercise 1.4
- Question 6(i-ix), Exercise 1.4
- Question 6(x-xvii), Exercise 1.4
- Question 7, Exercise 1.4
- Question 8, Exercise 1.4
- Question 9, Exercise 1.4
- Question 10, Exercise 1.4
- Question 1, Review Exercise
- Question 2, Review Exercise
- Question 3, Review Exercise
- Question 4, Review Exercise
- Question 5, Review Exercise
- Question 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 1, Exercise 2.1
- Question 2, Exercise 2.1
- Question 3, Exercise 2.1
- Question 4, Exercise 2.1
- Question 1, Exercise 2.2
- Question 3, Exercise 2.2
- Question 3, Exercise 2.2
- Question 4, Exercise 2.2
- Question 5, Exercise 2.2
- Question 6, Exercise 2.2
- Question 7, Exercise 2.2
- Question 8, Exercise 2.2
- Question 9, Exercise 2.2
- Question 10, Exercise 2.2
- Question 11, Exercise 2.2
- Question 12, Exercise 2.2
- Question 13, Exercise 2.2
- Question 1, Exercise 2.3
- Question 2, Exercise 2.3
- Question 3, Exercise 2.3
- Question 4, Exercise 2.3
- Question 5, Exercise 2.3
- Question 6, Exercise 2.3
- Question 7, Exercise 2.3
- Question 1, Exercise 2.5
- Question 2, Exercise 2.5
- Question 3, Exercise 2.5
- Question 1, Exercise 2.6
- Question 2, Exercise 2.6
- Question 3, Exercise 2.6
- Question 4, Exercise 2.6
- Question 5, Exercise 2.6
- Question 6, Exercise 2.6
- Question 7 and 8, Exercise 2.6
- Question 9 and 10, Exercise 2.6
- Question 1, Review Exercise
- Question 2 and 3, Review Exercise
- Question 4 and 5, Review Exercise
- Question 1 and 2, Exercise 4.1
- Question 3 and 4, Exercise 4.1
- Question 5 and 6, Exercise 4.1
- Question 7 and 8, Exercise 4.1
- Question 9 and 10, Exercise 4.1
- Question 11 and 12, Exercise 4.1
- Question 13 and 14, Exercise 4.1
- Question 15 and 16, Exercise 4.1
- Question 17 and 18, Exercise 4.1
- Question 19 and 20, Exercise 4.1
- Question 21 and 22, Exercise 4.1
- Question 1, Exercise 4.2
- Question 2, Exercise 4.2
- Question 3 and 4, Exercise 4.2
- Question 5 and 6, Exercise 4.2
- Question 7 and 8, Exercise 4.2
- Question 9 and 10, Exercise 4.2
- Question 11 and 12, Exercise 4.2
- Question 13, Exercise 4.2
- Question 14 and 15, Exercise 4.2
- Question 16 and 17, Exercise 4.2
- Question 1 and 2, Exercise 4.3
- Question 3 and 4, Exercise 4.3
- Question 5 and 6, Exercise 4.3
- Question 7 and 8, Exercise 4.3
- Question 9 and 10, Exercise 4.3
- Question 11 and 12, Exercise 4.3
- Question 13 and 14, Exercise 4.3
- Question 15 and 16, Exercise 4.3
- Question 17, 18 and 19, Exercise 4.3
- Question 20, 21 and 22, Exercise 4.3
- Question 23 and 24, Exercise 4.3
- Question 25 and 26, Exercise 4.3
- Question 1 and 2, Exercise 4.4
- Question 3 and 4, Exercise 4.4
- Question 5, 6 and 7, Exercise 4.4
- Question 8 and 9, Exercise 4.4
- Question 10 and 11, Exercise 4.4
- Question 12 and 13, Exercise 4.4
- Question 14 and 15, Exercise 4.4
- Question 16 and 17, Exercise 4.4
- Question 18 and 19, Exercise 4.4
- Question 20 and 21, Exercise 4.4
- Question 22 and 23, Exercise 4.4
- Question 24 and 25, Exercise 4.4
- Question 26 and 27, Exercise 4.4
- Question 28 and 29, Exercise 4.4
- Question 30, Exercise 4.4
- Question 1 and 2, Exercise 4.5
- Question 3 and 4, Exercise 4.5
- Question 5 and 6, Exercise 4.5
- Question 7 and 8, Exercise 4.5
- Question 9 and 10, Exercise 4.5
- Question 11, 12 and 13, Exercise 4.5
- Question 14, Exercise 4.5
- Question 15, Exercise 4.5
- Question 16, Exercise 4.5
- Question 1 and 2, Exercise 4.6
- Question 3 & 4, Exercise 4.6
- Question 5 & 6, Exercise 4.6
- Question 7 & 8, Exercise 4.6
- Question 9 & 10, Exercise 4.6
- Question 11, Exercise 4.6
- Question 12, Exercise 4.6
- Question 1 and 2, Exercise 4.7
- Question 3 and 4, Exercise 4.7
- Question 5 and 6, Exercise 4.7
- Question 7 and 8, Exercise 4.7
- Question 9 and 10, Exercise 4.7
- Question 11, 12 and 13, Exercise 4.7
- Question 14, 15 and 16, Exercise 4.7
- Question 17 and 18, Exercise 4.7
- Question 19 and 20, Exercise 4.7
- Question 19 and 20, Exercise 4.7
- Question 21 and 22, Exercise 4.7
- Question 23 and 24, Exercise 4.7
- Question 25 and 26, Exercise 4.7
- Question 27 and 28, Exercise 4.7
- Question 29 and 30, Exercise 4.7
- Question 1 and 2, Exercise 4.8
- Question 3 and 4, Exercise 4.8
- Question 5 and 6, Exercise 4.8
- Question 7 and 8, Exercise 4.8
- Question 9 and 10, Exercise 4.8
- Question 11 and 12, Exercise 4.8
- Question 13, 14 and 15, Exercise 4.8
- Question 1, Exercise 5.1
- Question 2 and 3, Exercise 5.1
- Question 4 and 5, Exercise 5.1
- Question 6 and 7, Exercise 5.1
- Question 8 and 9, Exercise 5.1
- Question 10, Exercise 5.1
- Question 1 and 2, Exercise 5.2
- Question 3 and 4, Exercise 5.2
- Question 5 and 6, Exercise 5.2
- Question 7 and 8, Exercise 5.2
- Question 1, Exercise 5.3
- Question 2, Exercise 5.3
- Question 3, Exercise 5.3
- Question 4, Exercise 5.3
- Question 5, Exercise 5.3
- Question 6, Exercise 5.3
- Question 2, Review Exercise
- Question 1, Review Exercise
- Question 2 & 3, Review Exercise
- Question 4 & 5, Review Exercise
- Question 6 & 7, Review Exercise
- Question 8, Review Exercise
- Question 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 1, Exercise 8.1
- Question 2, Exercise 8.1
- Question 3, Exercise 8.1
- Question 4, Exercise 8.1
- Question 5 and 6, Exercise 8.1
- Question 7, Exercise 8.1
- Question 8, Exercise 8.1
- Question 9, Exercise 8.1
- Question 10, Exercise 8.1
- Question 11, Exercise 8.1
- Question 12, Exercise 8.1
- Question 13, Exercise 8.1
- Question 14, Exercise 8.1
- Question 1, 2 and 3 Exercise 8.2
- Question 4 Exercise 8.2
- Question 5 Exercise 8.2
- Question 6 Exercise 8.2
- Question 7 Exercise 8.2
- Question 8(i, ii & iii) Exercise 8.2
- Question 8(iv, v & vi) Exercise 8.2
- Question 8(vii, viii & ix) Exercise 8.2
- Question 8(x, xi & xii) Exercise 8.2
- Question 8(xiii, xiv & xv) Exercise 8.2
- Question 8(xvi, xvii & xviii) Exercise 8.2
- Question 8(xix, xx, xxi & xxii) Exercise 8.2
- Question 1(i, ii, iii & iv) Exercise 8.3
- Question 1(v, vi, vii & viii) Exercise 8.3
- Question 1(ix, x & xi) Exercise 8.3
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- Question 3(xi, xii & xiii) Exercise 8.3
- Question 4 Exercise 8.3
- Question 1, Review Exercise
- Question 2, Review Exercise
- Question 3, Review Exercise
- Question 4, Review Exercise
- Question 5 and 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 9, Review Exercise
- Question 10, Review Exercise
- Question 1, Exercise 9.1
- Question 2, Exercise 9.1
- Question 3, Exercise 9.1
- Question 4(i-iv), Exercise 9.1
- Question 4(v-viii), Exercise 9.1
- Question 5(i-v), Exercise 9.1
- Question 5(vi-x), Exercise 9.1
- Question 6, Exercise 9.1
- Question 7 & 8, Exercise 9.1
- Question 9, Exercise 9.1
- Question 10, Exercise 9.1
- Question 2 and 3,Review Exercise
- Question 4, Review Exercise
- Question 1,Review Exercise
- Question 2 and 3, Review Exercise
- Question 4, Review Exercise
- Question 5 and 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 9, Review Exercise
- Question 10(i-v), Review Exercise
- Question 10(vi-x), Review Exercise
- Question 10(xi-xv), Review Exercise
Fulltext results:
- Unit 04: Sequences and Seeries
- is is a forth unit of the book "Model Textbook of Mathematics for Class XI" published by National Book F... "default" title="Exercise 4.1 (Solutions)"> * [[math-11-nbf:sol:unit04:ex4-1-p1|Question 1 & 2]] * [[math-11-nbf:sol:unit04:ex4-1-p2|Question 3 & 4]] * [[math-11-nbf:sol:unit04:ex4-1-p3|Question 5 & 6]] * [
- Unit 01: Complex Numbers (Solutions)
- == Unit 01: Complex Numbers (Solutions) ===== {{ :math-11-nbf:sol:math-11-nbf-sol-unit01.jpg?nolink&400x335|Unit 01: Complex Numbers (Solutions)}} This is a first unit of the book Model Textbook of Mathematics for Class XI published by National Book Fo... "default" title="Exercise 1.1 (Solutions)"> * [[math-11-nbf:sol:unit01:ex1-1-p1|Question 1]] * [[mat
- Unit 08: Fundamental of Trigonometry
- = Unit 08: Fundamental of Trigonometry ====== {{ :math-11-nbf:sol:math-11-nbf-unit-08.jpg?nolink&477x400|Unit 08: Fundamental of Trigonometry}} This is a eight unit of the book "Model Textbook of Mathematics for Class XI" published by National Book F... "default" title="Exercise 8.1 (Solutions)"> * [[math-11-nbf:sol:unit08:ex8-1-p1|Question 1]] * [[mat
- Unit 02: Matrices and Determinants (Solutions)
- is is a second unit of the book Model Textbook of Mathematics for Class XI published by National Book Fo... "default" title="Exercise 2.1 (Solutions)"> * [[math-11-nbf:sol:unit02:ex2-1-p1|Question 1]] * [[math-11-nbf:sol:unit02:ex2-1-p2|Question 2]] * [[math-11-nbf:sol:unit02:ex2-1-p3|Question 3]] * [[math-1
- Unit 05: Polynomials
- ====== Unit 05: Polynomials ====== {{ :math-11-nbf:sol:math-11-nbf-unit-05.jpg?nolink|Unit 05: Polynomials}} This is a fifth unit of the book "Model Textbook of Mathematics for Class XI" published by National Book F... "default" title="Exercise 5.1 (Solutions)"> * [[math-11-nbf:sol:unit05:ex5-1-p1|Question 1]] * [[mat
- Unit 09: Trigonometric Functions
- is is a ninth unit of the book "Model Textbook of Mathematics for Class XI" published by National Book F... "default" title="Exercise 9.1 (Solutions)"> * [[math-11-nbf:sol:unit09:ex9-1-p1|Question 1]] * [[math-11-nbf:sol:unit09:ex9-1-p2|Question 2 ]] * [[math-11-nbf:sol:unit09:ex9-1-p3|Question 3]] * [[math-
- Question 3, Exercise 9.1 @math-11-nbf:sol:unit09
- tric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... & -1\leq \cos 4x \leq 1 \,\, \forall \,\, x\in \mathbb{R} \\ \implies & -7\leq 7 \cos 4x \leq 7 \\ \end{align*} Thus domain $= ]-\infty, \infty[ = \mathbb{R}$ Range $=[-7,7]$. =====Question 3(ii)====... q \cos \frac{x}{3} \leq 1 \,\, \forall \,\, x\in \mathbb{R} \\ \end{align*} Thus domain $= ]-\infty, \in
- Question 5 and 6, Exercise 4.2 @math-11-nbf:sol:unit04
- nce and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... align*} \begin{array}{ccc} a_1& + 27d &= -73\\ \mathop{}\limits_{-}a_1 &\mathop+\limits_{-} 16d &= \mathop-\limits_{+}40 \\ \hline & 11d &= -33\\ \end{array}&\\ \implies \boxed{d =
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- d Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... begin{array}{cccc} 2x_1&-3 x_{2}&+4 x_{3}&=0\\ \mathop+\limits_{-}2x_1&\mathop-\limits_{+}4x_2&\mathop+\limits_{-}6x_3&=0 \\ \hline &x_2&-2x_3 &=0\\ \end{array} \\ \implies &x_2=2
- Question 3, Exercise 1.2 @math-11-nbf:sol:unit01
- omplex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... an. ====Question 3(i)==== Prove that for $z \in \mathbb{C}$. $z$ is real iff $z=\bar{z}$. **Solution.** Let $$z=a+ib\quad \text{where}\quad a,b\in \mathbb{R}\, ... (1)$$ First suppose that $z$ is real, ... al. ====Question 3(ii)==== Prove that for $z \in \mathbb{C}$. $\dfrac{z-\bar{z}}{z+\bar{z}}=i\left(\dfra
- Question 3, Exercise 1.4 @math-11-nbf:sol:unit01
- omplex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... tan ^{-1}\left(\frac{b}{a}\right)+2 k \pi, k \in \mathbb{Z}$ ** Solution. ** Let $z_r=x_r+iy_r$, $r=1,... eta_n = \theta + 2k\pi, \quad \text{where } k\in \mathbb{Z}.\,\, -- (3) $$ Taking square on both sides o... eta_r = \theta + 2k\pi, \quad \text{where } k\in \mathbb{Z}, $$ implies $$\sum_{r=1}^{n} \tan ^{-1}\left
- Question 8, Exercise 1.4 @math-11-nbf:sol:unit01
- omplex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... icle from mean position when amplitude is $0.004 \mathrm{~mm}$ and angle is: $\dfrac{\pi}{4}$ ** Soluti... icle from mean position when amplitude is $0.004 \mathrm{~mm}$ and angle is: $\dfrac{\pi}{3}$ ** Soluti... icle from mean position when amplitude is $0.004 \mathrm{~mm}$ and angle is: $\dfrac{\pi}{6}$ ** Soluti
- Question 7, Exercise 2.2 @math-11-nbf:sol:unit02
- d Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... n{bmatrix} x & 0 \\ y & 1 \end{bmatrix}.$$ We use mathematical induction to prove the given fact. For C-... n & 1-2 n \end{bmatrix} $ ** Solution. ** we use mathematical induction. Put $n = 1$ \begin{align*} A^... 1 - 2(k + 1) \end{array}\right] \end{align*} By mathematical induction, the formula \[ A^n = \left[\b
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- d Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... y}{cccc} 2x_1&+\frac{7}{11} x_{2}&+ x_{3}&=0\\ \mathop+\limits_{-}2x_1&\mathop+\limits_{-}3x_2&\mathop-\limits_{+}x_3&=0 \\ \hline &-\frac{26}{11}x_2&+2x_3 &=0\\ \end{array} \\ \i
- Question 3 and 4, Exercise 4.2 @math-11-nbf:sol:unit04
- nce and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Fo... in{align*} \begin{array}{ccc} a_1 & + 8d &= -1\\ \mathop{}\limits_{-}a_1 &\mathop+\limits_{-} 2d &= \mathop{}\limits_{-}14 \\ \hline & 6d &= -15\\ \end{array}&\\ \implies \boxed{d = -