Mathematics JEE (Advanced) 2022 Paper 1 SECTION 1
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Questions and Answers

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?

    <p>$r &lt; q &lt; p$</p> Signup and view all the answers

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

    <p>Charge conservation in a circuit</p> Signup and view all the answers

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

    <p>$\frac{355}{864}$</p> 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?

    <p>π</p> 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))?

    <p>Undefined</p> Signup and view all the answers

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

    <p>900</p> Signup and view all the answers

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

    <p>Decreases the electric field strength</p> Signup and view all the answers

    When analyzing circuits, what does capacitance measure?

    <p>Ability to store electric charge</p> Signup and view all the answers

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

    <p>Voltage increases</p> Signup and view all the answers

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

    <p>|- sin 𝜃 -1 sin 𝜃 1 -sin 𝜃 sin 𝜋 1|</p> Signup and view all the answers

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

    <p>-1</p> Signup and view all the answers

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

    <p>Minimum and maximum values of g(𝜃)</p> Signup and view all the answers

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

    <p>-101</p> 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?

    <p>|PQ1| is perpendicular to SP1, and |PQ2| is perpendicular to SP2</p> Signup and view all the answers

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

    <p>-√3</p> Signup and view all the answers

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