Mathematics JEE (Advanced) 2022 Paper 1 SECTION 1

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What is the probability of $X_2$ being greater than $Y_2$?

$\frac{77}{432}$

$\frac{11}{16}$ (correct)

$\frac{3}{8}$

$\frac{5}{16}$

If $x = y$, what is the total score of player $P_1$ and $P_2$ after playing the third round?

10 points each

7 points each (correct)

2 points each

5 points each

Which option correctly pairs the probability with the corresponding event?

(IV) → Probability of $X_3 > Y_3$

(III) → Probability of $X_3 = Y_3$

(I) → Probability of $X_2 less Y_2$ (correct)

(II) → Probability of $X_2 less Y_3$

If $p, q, r$ are nonzero real numbers in a harmonic progression, what is a possible relationship between them?

$r < q < p$ Signup and view all the answers

In the system of linear equations provided, what does the equation $10x + 100y + 1000z = 0$ represent?

Charge conservation in a circuit Signup and view all the answers

What is the probability of $X_3 > Y_3$ happening?

$\frac{355}{864}$ Signup and view all the answers

In the given mathematics problem, what is the value of 2√2 cos^−1(√2/2) + sin^−1(π/4) + tan^−1(2) + 3π/2?

π Signup and view all the answers

For the functions 𝑓(𝑥) = sin(𝜋𝑥)/12 and 𝑔(𝑥) = 2 log_e(√𝑥 - √𝛼) / log_e(𝑒√𝑥 - 𝑒√𝛼), what is the value of limₓ→𝛼⁺ 𝑓(𝑔(𝑥))?

Undefined Signup and view all the answers

In the pandemic study, if data was collected from 900 persons, what number of data points were gathered?

900 Signup and view all the answers

In an electric field, what effect does a dielectric material have when placed within the field?

Decreases the electric field strength Signup and view all the answers

When analyzing circuits, what does capacitance measure?

Ability to store electric charge Signup and view all the answers

What happens to the voltage across a charging capacitor as it reaches its maximum capacity?

Voltage increases Signup and view all the answers

What is the determinant of the square matrix 𝐹(𝜃)?

|- sin 𝜃 -1 sin 𝜃 1 -sin 𝜃 sin 𝜋 1| Signup and view all the answers

What is the value of the function 𝑔(𝜋/2)?

-1 Signup and view all the answers

What are the roots of the quadratic polynomial 𝑝(𝑥)?

Minimum and maximum values of g(𝜃) Signup and view all the answers

What is the value of 3(𝛼 + 𝛽) based on the given position vectors of Q and S?

-101 Signup and view all the answers

What is the relation between the points P, Q1, Q2, and S based on the tangents drawn to the parabola?

|PQ1| is perpendicular to SP1, and |PQ2| is perpendicular to SP2 Signup and view all the answers

What is the value of √f(0) based on the given function g(𝜃)?

-√3 Signup and view all the answers

Mathematics JEE (Advanced) 2022 Paper 1 SECTION 1

Podcast Beta

Questions and Answers

What is the probability of $X_2$ being greater than $Y_2$?

If $x = y$, what is the total score of player $P_1$ and $P_2$ after playing the third round?

Which option correctly pairs the probability with the corresponding event?

If $p, q, r$ are nonzero real numbers in a harmonic progression, what is a possible relationship between them?

In the system of linear equations provided, what does the equation $10x + 100y + 1000z = 0$ represent?

What is the probability of $X_3 > Y_3$ happening?

In the given mathematics problem, what is the value of 2√2 cos^−1(√2/2) + sin^−1(π/4) + tan^−1(2) + 3π/2?

For the functions 𝑓(𝑥) = sin(𝜋𝑥)/12 and 𝑔(𝑥) = 2 log_e(√𝑥 - √𝛼) / log_e(𝑒√𝑥 - 𝑒√𝛼), what is the value of limₓ→𝛼⁺ 𝑓(𝑔(𝑥))?

In the pandemic study, if data was collected from 900 persons, what number of data points were gathered?

In an electric field, what effect does a dielectric material have when placed within the field?

When analyzing circuits, what does capacitance measure?

What happens to the voltage across a charging capacitor as it reaches its maximum capacity?

What is the determinant of the square matrix 𝐹(𝜃)?

What is the value of the function 𝑔(𝜋/2)?

What are the roots of the quadratic polynomial 𝑝(𝑥)?

What is the value of 3(𝛼 + 𝛽) based on the given position vectors of Q and S?

What is the relation between the points P, Q1, Q2, and S based on the tangents drawn to the parabola?

What is the value of √f(0) based on the given function g(𝜃)?

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Mathematics JEE (Advanced) 2022 Paper 1 SECTION 1

Podcast Beta

Questions and Answers

What is the probability of $X_2$ being greater than $Y_2$?

If $x = y$, what is the total score of player $P_1$ and $P_2$ after playing the third round?

Which option correctly pairs the probability with the corresponding event?

If $p, q, r$ are nonzero real numbers in a harmonic progression, what is a possible relationship between them?

In the system of linear equations provided, what does the equation $10x + 100y + 1000z = 0$ represent?

What is the probability of $X_3 > Y_3$ happening?

In the given mathematics problem, what is the value of 2√2 cos^−1(√2/2) + sin^−1(π/4) + tan^−1(2) + 3π/2?

For the functions 𝑓(𝑥) = sin(𝜋𝑥)/12 and 𝑔(𝑥) = 2 log_e(√𝑥 - √𝛼) / log_e(𝑒√𝑥 - 𝑒√𝛼), what is the value of limₓ→𝛼⁺ 𝑓(𝑔(𝑥))?

In the pandemic study, if data was collected from 900 persons, what number of data points were gathered?

In an electric field, what effect does a dielectric material have when placed within the field?

When analyzing circuits, what does capacitance measure?

What happens to the voltage across a charging capacitor as it reaches its maximum capacity?

What is the determinant of the square matrix 𝐹(𝜃)?

What is the value of the function 𝑔(𝜋/2)?

What are the roots of the quadratic polynomial 𝑝(𝑥)?

What is the value of 3(𝛼 + 𝛽) based on the given position vectors of Q and S?

What is the relation between the points P, Q1, Q2, and S based on the tangents drawn to the parabola?

What is the value of √f(0) based on the given function g(𝜃)?

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JEE(Main) -2023 Test: Physics, Chemistry &amp; Mathematics Paper - 1

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