JEE, NEET, IOQM & School Practice Questions

Online practice questions for JEE, NEET, IOQM and school exams

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MathematicsClass XIIIT JEE AdvancedL4

QUESTION 1

QUESTION BYRamesh Chandra

IIT Kanpur Faculty | Mathematics & Physics | JEE Main & Advanced | 15+ Years Teaching Experience

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Challenge 2

QUESTION

Let

α a n d β

be the roots of

x^{2} - x - 1 = 0

, with

α > β

. For all positive integeres n, define

a_{n} = \frac{α^{n} - β^{n}}{α - β}, n \geq 1,

b1 = 1 and

b_{n} = a_{n - 1} + a_{n + 1}, n \geq 2

Then which of the following options is/are correct?

Your response

\sum n = 1 \infty \frac{b_{n}}{10^{n}} = \frac{8}{89}

$b_{n} = α^{n} + β^{n}$ for all $n \geq 1$

$a_{1} + a_{2} + a_{3} + . . . . . . . + a_{n} = a_{n + 2} - 1$ for all $n \geq 1$

$\sum n = 1 \infty \frac{a_{n}}{10^{n}} = \frac{10}{89}$

Hint

Answer key

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MathematicsClass XIIIT JEE AdvancedL4

QUESTION 2

QUESTION BYRamesh Chandra

IIT Kanpur Faculty | Mathematics & Physics | JEE Main & Advanced | 15+ Years Teaching Experience

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Challenge 2

QUESTION

Let $X = {(x, y) \in Z \times Z : \frac{x^{2}}{8} + \frac{y^{2}}{20} < 1 a n d y^{2} < 5 x}$ . Three distinct points P, Q and R are randomly chosen from

X

. Then the probability that P, Q and R form a triangle whose area is a positive integer, is

Your response

$\frac{71}{220}$

$\frac{73}{220}$

\frac{79}{220}

\frac{83}{220}

Hint

Answer key

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MathematicsClass XIIIT JEE AdvancedL6

QUESTION 3

QUESTION BYRamesh Chandra

IIT Kanpur Faculty | Mathematics & Physics | JEE Main & Advanced | 15+ Years Teaching Experience

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JEE Advamced Problem

QUESTION

Let $X = {(x, y) \in Z \times Z : \frac{x^{2}}{8} + \frac{y^{2}}{20} < 1 a n d y^{2} < 5 x}$ . Three distinct points P, Q and R are randomly chosen from

X

. Then the probability that P, Q and R form a triangle whose area is a positive integer, is

Your response

$\frac{71}{220}$

$\frac{73}{220}$

\frac{79}{220}

\frac{83}{220}

Hint

Answer key

Written solution

0Views 0Attempts —Correct

MathematicsClass XIIIIT JEE AdvancedL6

QUESTION 4

QUESTION BYRamesh Chandra

IIT Kanpur Faculty | Mathematics & Physics | JEE Main & Advanced | 15+ Years Teaching Experience

View profile

JEE Advamced Problem

QUESTION

Let $X = {(x, y) \in Z \times Z : \frac{x^{2}}{8} + \frac{y^{2}}{20} < 1 a n d y^{2} < 5 x}$ . Three distinct points P, Q and R are randomly chosen from

X

. Then the probability that P, Q and R form a triangle whose area is a positive integer, is

Your response

$\frac{71}{220}$

$\frac{73}{220}$

\frac{79}{220}

\frac{83}{220}

Hint

Answer key

Written solution

Video solution

Watch the teacher’s video explanation. Select the preview to play.

Open this video on YouTube ↗

0Views 0Attempts —Correct

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Online practice questions for JEE, NEET, IOQM and school exams

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Challenge 2

Hint

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Challenge 2

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JEE Advamced Problem

Hint

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JEE Advamced Problem

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Video solution

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Online practice questions for JEE, NEET, IOQM and school exams

Performance Dashboard

Choose your exam

Find your next “aha!” moment

Challenge 2

Hint

Answer key

Written solution

Challenge 2

Hint

Answer key

Written solution

Video solution

JEE Advamced Problem

Hint

Answer key

Written solution

JEE Advamced Problem

Hint

Answer key

Written solution

Video solution

Every attempt helps you grow

MATHSARC EDUCATION

Connect with us :

Investor Desk

CUSTOMER CARE

Useful Links

Visit YouTube

Think deeper.
Solve smarter.