JEE (Main)-2023 Exam Instructions
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Questions and Answers

The distance between points C1 and C2, represented by 'd', is calculated as d = C1C2 = (9 − 3)2 + ( ______ - 3 )2

(-3/2)

What is the final value of 'd' after carrying out the calculations?

38

What does the symbol 'r1' represent in the given context?

  • The radius of the circle centered at point C1 (correct)
  • The distance between the origin and point C1
  • The radius of the circle centered at the origin
  • The radius of the circle centered at point C2
  • The equation r1 + r2 = C1C2 suggests that the two circles intersect at two distinct points.

    <p>False (B)</p> Signup and view all the answers

    Based on the given information, how many common tangents can be drawn to the two circles?

    <p>3 (C)</p> Signup and view all the answers

    Match the following terms with their corresponding definitions:

    <p>d = The distance between the centers of the two circles r1 = The radius of the circle centered at point C1 r2 = The radius of the circle centered at point C2 C1C2 = The distance between the centers of the two circles</p> Signup and view all the answers

    What is the final simplified expression for f(y)?

    <p>(81 + y^2)/(19 - y^2)</p> Signup and view all the answers

    The function f(y) is defined for all real values of y.

    <p>False (B)</p> Signup and view all the answers

    What is the value of 𝜆 in the equation –3x + y + 13z = 𝜆, given that x = –3, y = 2, and z = 0?

    <p>11 (B)</p> Signup and view all the answers

    The distance between the point (–3, 2, 0) and the plane 2x – 2y + z = 11 is 7.

    <p>True (A)</p> Signup and view all the answers

    What is the cross product of vectors n1 and n2?

    <p>4iˆ + 3 ˆj – 12kˆ</p> Signup and view all the answers

    The ______ between the point and the plane is calculated using the formula: d = |ax + by + cz + d|/√(a² + b² + c²), where (a, b, c) is the normal vector of the plane and (x, y, z) is the point, and d is the constant in the plane equation.

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

    Match the following equations to their corresponding variables:

    <p>–x + 2y – 9z = 7 = Equation (i) –x + 3y + 7z = 9 = Equation (ii) –2x + y + 5z = 8 = Equation (iii) –3x + y + 13z = 𝜆 = Equation (iv)</p> Signup and view all the answers

    The equation ( 2iˆ + 3 jˆ – 12kˆ )  ( 4iˆ + 3 ˆj – 12kˆ ) = 8 is used to solve for 𝜆.

    <p>True (A)</p> Signup and view all the answers

    What is the total number of possible numbers that can be formed with the sum of digits equal to 24?

    <p>1 (C)</p> Signup and view all the answers

    What is the equation of the plane that passes through the point (-3, 2,0)?

    <p>2x – 2y + z = 11</p> Signup and view all the answers

    The range of the function f(y) is given as (– 0.125, 1.125]. Therefore, the value of (\beta - \alpha) is equal to ______.

    <p>1.25</p> Signup and view all the answers

    The number of possible numbers that can be formed with a sum of digits equal to 12 is 12.

    <p>False (B)</p> Signup and view all the answers

    Match the following expressions with their corresponding values based on the given information.

    <p>(\alpha) = -0.125 (\beta) = 1.125 (\beta - \alpha) = 1.25 24((\beta - \alpha)) = 30</p> Signup and view all the answers

    What is the value of 2(a + b + c) if (p_1 = 20) and (p_2 = 210) in the expression (a + bx + cx^2 = \sum_{i=10}^{20} p_i x^i)?

    <p>15</p> Signup and view all the answers

    The given differential equation involves a function x that is a function of y, denoted as x(y). This means that x is the ______ variable and y is the ______ variable.

    Signup and view all the answers

    The set (Re(\frac {z^2}{3z - 5z})) where (Re(z)) is the real part of (z), equals the interval ((\alpha), (\beta)]. What is the value of 24((\beta - \alpha))?

    <p>30 (A)</p> Signup and view all the answers

    The total number of possible numbers that can be formed with the sum of digits equal to 3, 9, 12, 15, 18, and 21 is 10.

    <p>False (B)</p> Signup and view all the answers

    The value of the expression (a - b) + (a^2 - ab + b^2) + (a^3 - a^2b + ab^2 - b^3) + ... is given by the formula ______ .

    <p>((a + b)/(1 - a/b)) * (a^2 - b^2 + a^3 + b^3 + a^4 - b^4 + ...)</p> Signup and view all the answers

    What is the simplified expression for (a + b)/(1 - a/b) * (a^2 - b^2 + a^3 + b^3 + a^4 - b^4 + ...)?

    <p>(a^2 + b^2)/(1 - a^2/b^2)</p> Signup and view all the answers

    Which of the following equations represents the plane P?

    <p>7x + 9y - 10z - 27 = 0 (B)</p> Signup and view all the answers

    The point B lies on the plane P.

    <p>True (A)</p> Signup and view all the answers

    What is the value of  + 3, where  and  are the direction ratios of the line AB?

    <p>7</p> Signup and view all the answers

    Match the following terms with their corresponding values:

    <p>a = 1/2 b = 1/3  = -1/6  = 7  = 6</p> Signup and view all the answers

    The equation of the plane P is given by ______x + ______y + ______z + ______ = 0.

    <p>7, 9, -10, -27</p> Signup and view all the answers

    The line AB intersects the plane P at a single point.

    <p>True (A)</p> Signup and view all the answers

    A single slit of width 'a' is illuminated by monochromatic light of wavelength 600 nm. The value of 'a' for which the first minimum appears at θ = 30° on the screen is:

    <p>1.2 µm (D)</p> Signup and view all the answers

    The work done in moving a charge of 2 coulomb between two points having a potential difference of 150 volts is ______ joules.

    <p>300</p> Signup and view all the answers

    For a voltmeter to be accurate, its internal resistance should be very high compared to the resistance of the circuit it is connected to.

    <p>True (A)</p> Signup and view all the answers

    What is the condition for the first minimum in a single-slit diffraction pattern?

    <p>The path difference between the waves from the two edges of the slit is equal to one wavelength.</p> Signup and view all the answers

    Which of the following conditions would result in a higher internal resistance for an ammeter?

    <p>For ammeter r ≈ 6 Ω (B)</p> Signup and view all the answers

    What is the primary type of equation represented in the content?

    <p>Differential equation (A)</p> Signup and view all the answers

    The variable 'x' is independent of 'y' in the given differential equation.

    <p>False (B)</p> Signup and view all the answers

    In the given differential equation, what is the expression that represents the integration bounds?

    <p>0 to 2</p> Signup and view all the answers

    The differential equation mentioned is valid for values of y such that y > ______.

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

    Match the following components of the differential equation with their descriptions:

    <p>dx = Represents a small change in x dy = Represents a small change in y log_e(y + 2) = Natural logarithm of (y + 2) e^4t = The exponential function of 4 times t</p> Signup and view all the answers

    Study Notes

    JEE (Main)-2023 (Online) Phase-2 Exam Instructions

    • Time: 3 hours
    • Total Questions: 90
    • Total Marks: 300
    • Sections: Mathematics, Physics, Chemistry (each with 30 questions)
    • Sections (further divided): Each subject has two sections (A and B)
    • Section A (Mathematics, Physics, Chemistry): 20 multiple choice questions, 4 options. Each correct answer worth 4 marks and 1 mark deducted for a wrong answer.
    • Section B (Mathematics, Physics, Chemistry): Numerical value answers, attempt 5 out of 10. Each correct answer worth 4 marks, and 1 mark deducted for a wrong answer. Round off answer to the nearest integer.

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    Prepare for the JEE (Main)-2023 Phase-2 exam with this detailed instructional quiz. It provides information about the exam structure, scoring, and the types of questions included in Mathematics, Physics, and Chemistry sections. Test your knowledge and understanding of the exam format and rules.

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