Geometry and Analytical Mathematics Quiz
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Questions and Answers

Which shape is described by the equation x^2 + y^2 = 3?

  • Parabola
  • Circle (correct)
  • Ellipse
  • Hyperbola
  • If a particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution, what is the angle of projection ($\theta$) when the particle is projected at the maximum height equal to 4R?

  • $75^\circ$
  • $60^\circ$ (correct)
  • $30^\circ$
  • $45^\circ$
  • What is the center of the circle with the equation x^2 + y^2 = 3?

  • (3, 3)
  • (0, 3)
  • (3, 0)
  • (0, 0) (correct)
  • A galvanometer with a resistance of 50 ohms can be converted into a voltmeter to measure up to 100V by connecting a resistor in series. What should be the resistance of this additional series resistor?

    <p>19950 ohms</p> Signup and view all the answers

    If a line passes through the point of intersection of a circle and a parabola in the first quadrant, which quadrant(s) can this point lie in?

    <p>First Quadrant</p> Signup and view all the answers

    If the de Broglie wavelengths of a proton and an alpha particle are $\lambda$ and $2\lambda$ respectively, what is the ratio of their velocities?

    <p>1:2</p> Signup and view all the answers

    In a Vernier caliper where 10 main scale divisions coincide with 11 Vernier scale divisions, and each main scale division is 5 units, what is the least count of the instrument?

    <p>$\frac{10}{11}$ units</p> Signup and view all the answers

    In which quadrant can the centers Q1 and Q2 of circles C1 and C2 lie if the line they lie on intersects the y-axis?

    <p>First Quadrant</p> Signup and view all the answers

    In a series LCR circuit where the capacitance changes from C to 4C while keeping the resonance frequency unchanged, how should the inductance change?

    <p>Reduced by L/3</p> Signup and view all the answers

    What is the shortest distance between two lines L1 and L2 at points P and Q respectively called?

    <p>Perpendicular Distance</p> Signup and view all the answers

    If (α, β, γ) is the midpoint of a line segment PQ, what is 2(α + β + γ)?

    <p>(0, 6, 0)</p> Signup and view all the answers

    What is the position of the particle when the time is t = 4s?

    <p>28 m</p> Signup and view all the answers

    At what time does the velocity of the particle reach its maximum value?

    <p>3 s</p> Signup and view all the answers

    What is the magnitude of the force acting on the particle when its acceleration is zero?

    <p>$45, \text{N}$</p> Signup and view all the answers

    What is the total charge that flows through the conductor from t = 0s to t = 2s?

    <p>120 C</p> Signup and view all the answers

    What is the ideal lift force acting on the plane during level flight?

    <p>$7,200, \text{N}$</p> Signup and view all the answers

    If the air density is doubled, what will be the new lift force acting on the plane?

    <p>$6,480, \text{N}$</p> Signup and view all the answers

    What is the correct reagent for the conversion CH3(CH2)5–C–OC2H5 to CH3(CH2)5CHO?

    <p>CH3MgBr, H2O</p> Signup and view all the answers

    Which of the following reagents is NOT correctly matched with its respective conversion?

    <p>CH3COCH2COOC2H5 → CH3C(OH)CH2COOC2H5: DIBAL-H, H2O</p> Signup and view all the answers

    In Kjeldahl’s method for estimation of nitrogen, what role does CuSO4 play?

    <p>Oxidising agent</p> Signup and view all the answers

    Which statement about Potassium hydrogen phthalate (KHP) as a primary standard is true?

    <p>KHP is a primary standard often employed in standardizing sodium hydroxide solutions</p> Signup and view all the answers

    What is the correct order of Vant' Hoff factor (i) for the NaCl solutions with concentrations 0.1 M, 0.01 M, and 0.001 M?

    <p>$i_A &lt; i_C &lt; i_B$</p> Signup and view all the answers

    According to the given reactions and reagents list, which sequence correctly matches the conversions with the corresponding reagents?

    <p>A-(III), B-(IV), C-(II), D-(I)</p> Signup and view all the answers

    Which of the following statements is correct regarding aminobenzene and aniline?

    <p>Statement I is correct but Statement II is incorrect</p> Signup and view all the answers

    Which of the following complexes is homoleptic?

    <p>[Fe(NH3)4Cl2]+</p> Signup and view all the answers

    In the given reaction sequence, which compound will most easily be attacked by an electrophile?

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

    Ionic reactions with organic compounds primarily proceed through:

    <p>Heterolytic bond cleavage</p> Signup and view all the answers

    Arrange the bonds in order of increasing ionic character in the molecules LiF, K2O, N2, SO2, and ClF3.

    <p>N2 &lt; SO2 &lt; ClF3 &lt; K2O &lt; LiF</p> Signup and view all the answers

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