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MathematicsClass XIIJEE Main - EngineeringL2

QUESTION 1

QUESTION BYRamesh Chandra

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

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Matrix Match No 1

QUESTION

For real numbers 𝛼, 𝛽, 𝛾, 𝛿 and 𝜇 , consider the matrix

(\begin{matrix} α & \frac{1}{\sqrt{2}} & - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & β & \frac{1}{\sqrt{3}} \\ γ & δ & μ \end{matrix})

. Suppose that 𝑀𝑀𝑇= 𝐼 , where 𝑀𝑇 is the transpose of the matrix 𝑀, and 𝐼 is the 3×3 identity matrix. Let

u \to = α i + \frac{1}{\sqrt{3}} j + γ k

,

v \to = \frac{1}{\sqrt{2}} i + β j + δ k

and

w \to = - \frac{1}{\sqrt{2}} i + \frac{1}{\sqrt{3}} j + μ k

.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List I

The value of $γ^{2} + δ^{2}$ is
If $x u \to + y v \to + z w \to = j$ for some real numbers 𝑥, 𝑦 and 𝑧, then the value of 𝑥 is
The value of $| u \to \cdot (v \to \times w \to) |$ is
The value of $| u \to \times (v \to \times w \to) |$ is

List II

0
1
$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
$\frac{5}{6}$

Your response

Choose the correct matching combination

A.

P → (5) Q → (4) R → (2) S → (1)

B.

P → (4) Q → (5) R → (1) S → (2)

C.

P → (5) Q → (3) R → (2) S → (1)

D.

P → (5) Q → (4) R → (1) S → (2)

Hint

Answer key

Written solution

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10Views 1Attempts 100%Correct

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

A.

$\frac{71}{220}$

B.

$\frac{73}{220}$

C.

\frac{79}{220}

D.

\frac{83}{220}

Hint

Answer key

Written solution

Video solution

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9Views 1Attempts 0%Correct

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

A.

$\frac{71}{220}$

B.

$\frac{73}{220}$

C.

\frac{79}{220}

D.

\frac{83}{220}

Hint

Answer key

Written solution

10Views 1Attempts 100%Correct

PsychologyClass IICentral GovernmentL5

QUESTION 4

QUESTION BYRamesh Chandra

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

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Test True/False

QUESTION

Consider the image and answer the following True/False questions

Question image

Your response

Evaluate each statement

Statement 1

Is there are 8 students in total in the picture?

\int 01 x^{2} d x

TrueFalse

Statement 2

There are 2 boys in the picture

v = u + a t

TrueFalse

Statement 3

Sun rises in the west

N_{2} + 3 H_{2} ⇌ 2 N H_{3}

TrueFalse

Hint

Answer key

Written solution

Video solution

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11Views 1Attempts 0%Correct

MathematicsClass XIIIT JEE AdvancedL4

QUESTION 5

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

A.

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

B.

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

C.

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

D.

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

Hint

Answer key

Written solution

14Views 2Attempts 0%Correct

MathematicsClass XIIIIT JEE AdvancedL6

QUESTION 6

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

A.

$\frac{71}{220}$

B.

$\frac{73}{220}$

C.

\frac{79}{220}

D.

\frac{83}{220}

Hint

Answer key

Written solution

Video solution

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

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9Views 2Attempts 50%Correct

MathematicsClass IXCBSE - Central Board of Secondary EducationL4

QUESTION 7

QUESTION BYRamesh Chandra

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

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Multi Option Correct

QUESTION

Lets test Multi option question Answer B, C.

$\sum i = 1 n a_{i}$	$v = u + a t$	$10 m s^{- 1}$
$SO 4 2 -$	$H_{2} O$	${CH}_{4} + 2 O_{2} \to {CO}_{2} + 2 H_{2} O$

So this is final multi correct

Question image

Your response

A.

$\int 01 x^{2} d x$

B.

v \to = \frac{d r \to}{d t}

C.

F \to = m a \to

D.

\frac{a + b}{c + d}

Hint

Answer key

Written solution

Video solution

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8Views 1Attempts 0%Correct

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Matrix Match No 1

List I

List II

Hint

Answer key

Written solution

Video solution

Challenge 2

Hint

Answer key

Written solution

Video solution

JEE Advamced Problem

Hint

Answer key

Written solution

Test True/False

Hint

Answer key

Written solution

Video solution

Challenge 2

Hint

Answer key

Written solution

JEE Advamced Problem

Hint

Answer key

Written solution

Video solution

Multi Option Correct

Hint

Answer key

Written solution

Video solution

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