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Maths NCERT Exemplar Solutions Class 11th Chapter Six

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Class 12th

The number of all $3 * 3$ matrices, $A$ , with enteries from the set ${- 1,0, 1}$ such that the sum of the diagonal elements of $A A^{?}$ $^{}$ is 3 , is(Matrices)

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Raj Pandey

Contributor-Level 9

Let A=[a?]?. tr(AA?)=3.
Σa?² = 3.
Possible cases for non-zero elements are (1,1,1) or (-1,-1,-1) or (1,1,-1) etc.
Total combinations = ?C? * 2³ = 84 * 8 = 672.C? * 2³ = 84 * 8 = 672.

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Class 11th

The $_{}^{}$ $s u m ? \sum_{k = 1}^{20} ? (1 + 2 + 3 + \dots . k)$ is(Series)

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Raj Pandey

Contributor-Level 9

Sol. Σ? k(k+1)/2 = (1/2)Σ(k²+k) = (1/2)[ (5051101/6) + (5051/2) ]
The solution uses k=1 to 20.
(1/2)[ (202141/6) + (2021/2) ] = (1/2)[2870+210] = 1540

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Ncert Solutions Maths class 11th

The least positive value of ' $a$ ' for which the equation, $2 x^{2} + (a - 10) x + \frac{33}{2} = 2 a$ $^{} \frac{}{}$ has real root is

(Quadratic Equations)

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Raj Pandey

Contributor-Level 9

D≥0
(a-10)² - 4(2)(33/2 - 2a) ≥ 0
a²-4a-32 ≥ 0 ⇒ a∈(-∞, -4] U [8,∞)

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Class 11th

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that the most three of them are red is(Combinations)

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Raj Pandey

Contributor-Level 9

0 Red, 1 Red, 2 Red, 3 Red
Number of ways = ?C? + ?C?.?C? + ?C?.?C? + ?C?.?C? = 35+175+210+70=490

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Class 11th

Let the normal at a point $P$ on the curve $^{}^{}$ $y^{2} - 3 x^{2} + y + 10 = 0$ intersect the $y - a x i s$ at $(0, \frac{3}{2})$ $(\frac{}{})$ . If $m$ is the slope of the tangent at $P$ to the curve, then $| m |$ is equal to(2D)

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Raj Pandey

Contributor-Level 9

P=(x?,y?). 2yy'-6x+y'=0 ⇒ y' = 6x/(2y+1)
(y?-0)/(x?-3/2) = (1+2y?)/(6x?)
9-6y? = 1+2y? ⇒ y?=1. x?=±2. Slope = ±12/3 = ±4. |n|=4.

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2 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Six Exemplar Solution

(i) If $- 4 x \geq 12$ , then $x \dots - 3$ .

(ii) If $\frac{3}{4} - x \leq - 3,$ then $x \dots 4$ .

(iii) If $\frac{2}{x + 2} > 0,$ then $x \dots - 2$ .

(iv) If $x > - 5$ , then $4 x \dots - 20$ .

(v) If $x > y$ and $z < 0$ , then $- x z \dots - y z$ .

(vi) If $p > 0$ and $q < 0$ , then $p - q \dots p$ .

(vii) If $x + 2 > 5$ , then $x \dots - 7$ or $x \dots 3$ .

(viii)If $- 2 x + 1 \geq 9$ , then $x \dots - 4$ .

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} (i) - 4 x \geq 12 \Rightarrow x \leq - 3 \\ H e n c e, t h e f i l l e r i s (\leq) \\ (i i) I f - \frac{3}{4} x \leq - 3 \Rightarrow x \geq 3 x * \frac{4}{3} \Rightarrow x \geq 4 \\ H e n c e, t h e f i l l e r i s (\geq) \\ (i i i) I f \frac{2}{x + 2} > 0 \Rightarrow x > - 2 \\ H e n c e, t h e f i l l e r i s (>) \\ (i v) I f x > - 5 \Rightarrow 4 x > - 20 \\ H e n c e, t h e f i l l e r i s (>) \\ (v) I f x > y a n d z < 0, t h e n \\ x z < y z \Rightarrow - x z > - y z \\ H e n c e, t h e f i l l e r i s (>) \\ (v i) I f p > 0 a n d q < 0, t h e n \\ p - q > p \\ H e n c e, t h e f i l l e r i s (>) \\ (v i i) I f | x + 2 | > 5 t h e n \\ x + 2 < - 5 o r x + 2 > 5 \\ \Rightarrow x < - 5 - 2 o r x > 5 - 2 \\ \Rightarrow x < - 7 o r x > 3 \\ S o, x \in (- \infty, - 7) \cup (3, \infty) \\ H e n c e, t h e f i l l e r i s (<) o r (>) \\ (v i i i) I f - 2 x + 1 \geq 9 t h e n \\ \Rightarrow - 2 x \geq 9 - 1 \Rightarrow - 2 x \geq 8 \Rightarrow 2 x \leq - 8 \Rightarrow x \leq - 4 \\ H e n c e, t h e f i l l e r i s (\leq) \end{array}$

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2 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Six Linear Inequalities

(i) If $x < y$ and $b < 0$ , then $\frac{x}{b} > \frac{y}{b} .$

(ii) If $x y > 0$ , then $x > 0$ and $y < 0$ .

(iii) If $x y > 0$ , then $x < 0$ and $y < 0$ .

(iv) If $x y < 0$ , then $x < 0$ and $y < 0$ .

(v) If $x < - 5$ and $x < - 2$ , then $x \in (- \infty, - 5)$ .

(vi) If $x < - 5$ and $x > 2$ , then $x \in (- 5, 2)$ .

(vii) If $x > - 2$ and $x < 9$ , then $x \in (- 2, 9)$ .

(viii) If $? x ? > 5$ , then $x \in (- \infty, - 5) \cup (5, \infty) .$

(ix) If $? x ? \leq 4$ , then $x \in [- 4, 4] .$

(x) Graph of $x < 3$ corresponds to Fig 6.12.

(xi) Graph of $x \geq 0$ corresponds to Fig 6.13.

(xii) Graph of $y \leq 0$ corresponds to Fig 6.14.

(xiii) Solution set of $x \geq 0$ and $y \leq 0$ &nbs

...more

(i) If $x < y$ and $b < 0$ , then $\frac{x}{b} > \frac{y}{b} .$

(ii) If $x y > 0$ , then $x > 0$ and $y < 0$ .

(iii) If $x y > 0$ , then $x < 0$ and $y < 0$ .

(iv) If $x y < 0$ , then $x < 0$ and $y < 0$ .

(v) If $x < - 5$ and $x < - 2$ , then $x \in (- \infty, - 5)$ .

(vi) If $x < - 5$ and $x > 2$ , then $x \in (- 5, 2)$ .

(vii) If $x > - 2$ and $x < 9$ , then $x \in (- 2, 9)$ .

(viii) If $? x ? > 5$ , then $x \in (- \infty, - 5) \cup (5, \infty) .$

(ix) If $? x ? \leq 4$ , then $x \in [- 4, 4] .$

(x) Graph of $x < 3$ corresponds to Fig 6.12.

(xi) Graph of $x \geq 0$ corresponds to Fig 6.13.

(xii) Graph of $y \leq 0$ corresponds to Fig 6.14.

(xiii) Solution set of $x \geq 0$ and $y \leq 0$ corresponds to Fig 6.15.

(xiv) Solution set of $x \geq 0$ and $y \leq 1$ corresponds to Fig 6.16.

(xv) Solution set of $x + y \geq 0$ corresponds to Fig 6.17.

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Payal Gupta

Contributor-Level 10

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} (i) I f x < y a n d b < 0 \\ \Rightarrow \frac{x}{b} > \frac{y}{b} \\ H e n c e, s t a t e m e n t (i) i s F a l s e . \\ (i i) I f x, y > 0 t h e n x > 0, y > 0 o r x < 0, y < 0 \\ H e n c e, s t a t e m e n t (i i) i s F a l s e . \\ (i i i) I f x y > 0 t h e n x < 0, a n d y < 0 \\ H e n c e, s t a t e m e n t (i i i) i s T r u e . \\ (i v) I f x y < 0 t h e n x < 0, y > 0 o r x > 0, y < 0 \\ H e n c e, s t a t e m e n t (i v) i s F a l s e . \\ (v) I f x < - 5 a n d x < - 2 \Rightarrow x \in (- \infty, - 5) \\ H e n c e, s t a t e m e n t (v) i s T r u e . \\ (v i) I f x < - 5 a n d x > 2 t h e n x h a s n o v a l u e . \\ H e n c e, s t a t e m e n t (v i) i s F a l s e . \\ (v i i) I f x > - 2 a n d x < 9 \Rightarrow x \in (- 2, 9) \\ H e n c e, s t a t e m e n t (v i i) i s T r u e . \\ (v i i i) I f | x | > 5 t h e n x < - 5 o r x > 5 \\ \Rightarrow x \in (- \infty, - 5) \cup (5, \infty) \\ H e n c e, s t a t e m e n t (v i i i) i s F a l s e . \\ (i x) I f | x | \leq 4 t h e n - 4 \leq x \leq 4 \\ \Rightarrow x \in [- 4, 4] \\ H e n c e, s t a t e m e n t (i x) i s T r u e . \\ (x) T h e g i v e n g r a p h r e p r e s e n t s x \leq 3 \\ H e n c e, s t a t e m e n t (x) i s F a l s e . \\ (x i) T h e g i v e n g r a p h r e p r e s e n t s x \geq 0 \\ H e n c e, s t a t e m e n t (x i) i s T r u e . \\ (x i i) T h e g i v e n g r a p h r e p r e s e n t s y \geq 0 \\ H e n c e, s t a t e m e n t (x i i) i s &thins \end{array}$

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Maths NCERT Exemplar Solutions Class 11th Chapter Six Exemplar Solution

Choose the correct option for $x$ :

(a) $x \in (- \infty, - 2)$

(b) $x \in (- \infty, - 2]$

(c) $x \in (- 2, \infty]$

(d) $x \in [- 2, \infty)$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e g i v e n g r a p h r e p r e s e n t s a l l r e a l v a l u e s o f x l e s s t h a n a n d e q u a l t o - 2 . \\ S o, x \in (- \infty, - 2] \\ H e r e, t h e c o r r e c t o p t i o n i s (b) . \end{array}$

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New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Six Exemplar Solution

Choose the correct option for $x$ :

(a) $x \in (- \infty, \frac{7}{2})$

(b) $x \in (- \infty, \frac{7}{2}]$

(c) $x \in [\frac{7}{2}, \infty)$

(d) $x \in (\frac{7}{2}, \infty)$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e g i v e n g r a p h r e p r e s e n t s a l l t h e v a l u e s o f x l e s s t h a n \frac{7}{2} o n t h e r e a l n u m b e r l i n e . \\ S o, x \in (- \infty, \frac{7}{2}) \\ H e r e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Six Exemplar Solution

Choose the correct option for $x$ :

(a) $x \in (\frac{9}{2}, \infty)$

(b) $x \in [\frac{9}{2}, \infty)$

(c) $x \in (- \infty, \frac{9}{2}]$

(d) $x \in (- \infty, \frac{9}{2})$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e g i v e n g r a p h h a s a l l r e a l v a l u e s o f x g r e a t e r t h a n a n d e q u a l t o \frac{9}{2} . \\ S o, x \geq \frac{9}{2} \Rightarrow x \in [\frac{9}{2}, \infty) \\ H e r e, t h e c o r r e c t o p t i o n i s (b) . \end{array}$

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