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Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen

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2 months ago

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

Let y = mx + c, m > 0 be the focal chord of y² = -64x, which is tangent to ${(x + 10)}^{2} + y^{2} = 4 .$ Then, the value of $4 \sqrt[]{2} (m + c)$ is equal to………….

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

Let $A = (\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}) a n d B = 7 A^{20} - 20 A^{7} + 2 I,$ where I is an identity matrix of order 3 * 3. If B = $[b_{i j}],$ then b₁₃ is equal to……………

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Raj Pandey

Contributor-Level 9

$A = [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}]$

B = 7A20 – 20A7 + 2l

$A^{2} [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 1 & - 2 & 1 \\ 0 & 1 & - 2 \\ 0 & 0 & 1 \end{matrix}]$

$A^{3} = [\begin{matrix} 1 & - 2 & 1 \\ 0 & 1 & - 2 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 1 & - 3 & 3 \\ 0 & 1 & - 3 \\ 0 & 0 & 1 \end{matrix}]$

$A^{4} = [\begin{matrix} 1 & - 3 & 3 \\ 0 & 1 & - 3 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 1 & - 4 & 6 \\ 0 & 1 & - 4 \\ 0 & 0 & 1 \end{matrix}]$

$a_{13} o f A, A^{2}, A^{3}, . . . . . . .$

are 0, 1, 3, 6,.

For 0, 1, 3, 6, .

$S_{n} = 0 + 1 + 3 + 6 + . . . . + t_{n}$

$S_{n} = 0 + + 3 + . . . . + t_{n - 1} + t_{n}$

$t_{n} = 1 + 2 + 3 + . . . + (t_{n} - t_{n - 1})$

$= \frac{(n - 1) . n}{2}$

$b_{13} = 7 (190) - 20 (21) + 0$

= 1330 – 420 = 910

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2 months ago

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

Let $A = (\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}) a n d B = 7 A^{20} - 20 A^{7} + 2 I,$ where I is an identity matrix of order 3 × 3. If B = $[b_{i j}],$ then b₁₃ is equal to……………

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New question posted

3 months ago

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

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Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

The sum of probabilities of two students getting distinction in their final examinations is 1.2.

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} Since, t h e t w o g i v e n e v e n t s a r e n o t r e l a t e d t o t h e s a m e S a m p l e s p a c e . \\ ∴ T h e s u m o f p r o b a b i l i t i e s o f t w o s t u d e n t s g e t t i n g d i s t i n c t i o n i n t h e i r f i n a l \\ m a y b e 1.2 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' T r u e' \end{array}$

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3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

The probability of the occurrence of event A is 0.7 and that of the occurrence of event B is 0.3, but the probability of the occurrence of both is 0.4.

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} H e r e, P (A) = 0.7, P (B) = 0.3 \\ ∴ P (A \cap B) = P (A) * P (B) \\ = 0.7 * 0.3 = 0.21 \\ B u t t h e g i v e n p r o b a b i l i t y i s 0.4 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' \end{array}$

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3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

The probability of the intersection of two events A and B is always less than or equal to the probability of A.

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} H e r e, P (A \cap B) \leq P (A) W h i c h i s a l w a y s t r u e . \\ H e n c e, t h e g i v e n s t a t e m e n t i s' T r u e' \end{array}$

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3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

If A and B are two candidates seeking admission in an engineering college, the probability that A is selected is 0.5, and the probability that both A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.7?

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} G i v e n t h a t P (A) = 0.5 a n d P (A \cap B) \leq 0.3 \\ N o w P (A) * P (B) \leq 0.3 \\ \Rightarrow 0.5 * P (B) \leq 0.3 \\ \Rightarrow P (B) \leq \frac{0.3}{0.5} \\ \Rightarrow P (B) \leq 0.6 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' \end{array}$

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3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

The probabilities that a typist will make 0, 1, 2, 3, 4, or 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11.

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} S u m o f a l l p r o b a b i l i t i e s = 1 \\ ∴ P (0) + P (1) + P (2) + P (3) + P (4) + P (5) = 0.12 + 0.25 + 0.36 + 0.14 + 0.08 + 0.11 \\ = 1.06 > 1 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' . \end{array}$

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3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen Exemplar Solution

The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get a compartment is 0.96.

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Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} L e t E b e t h e e v e n t t h a t t h e s t u d e n t w i l l p a s s \\ a n d F b e t h e e v e n t t h a t h e w i l l g e t c o m p a r t m e n t \\ ∴ P (E) = 0.73, P (F) = 0.13 a n d P (E \cup F) = 0.96 \\ ∴ P (E \cup F) = P (E) + P (F) - P (E \cap F) \\ = 0.73 + 0.13 - 0 [? P (E \cap F) = 0] \\ = 0.86 \\ B u t P (E \cup F) = 0.96 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' . \end{array}$

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