Mathematics: Deviation and Set Theory Quiz
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Questions and Answers

In the isosceles triangle ∆ABC with ∠C = 90° and AC = 5 cm, what is the length of side AB?

  • 10 cm (correct)
  • 2.5 cm
  • $5 oot{2}$ cm
  • 5 cm
  • In triangle ∆ABC, if AD is the bisector of ∠BAC and AB = 8 cm, BD = 6 cm, DC = 3 cm, what is the length of side AC?

  • 4 cm (correct)
  • 6 cm
  • 8 cm
  • 3 cm
  • Which of the following probability statements is incorrect?

  • $0 ext{le} P(A) ext{le} 1$
  • $P(A) > 1$ (correct)
  • $P(A) + P(A') = 1$
  • $P( othing) = 0$
  • What is the shape of a shuttlecock used for playing badminton?

    <p>a hemisphere and a cone</p> Signup and view all the answers

    If the equation of a straight line is x = 11, what can be said about this line?

    <p>parallel to X-axis</p> Signup and view all the answers

    In a lucky draw where 135 tickets were sold and Kamalam's winning probability is 1/9, how many tickets did Kamalam buy?

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

    What is the Highest Common Factor (HCF) of the quadratic expressions 𝒙² - 𝟐𝒙 - 𝟐𝟒 and 𝒙² - 𝒌𝒙 - 𝟔 if (𝒙 - 𝟔) is their HCF?

    <p>5</p> Signup and view all the answers

    In a matrix, if the number of columns and rows are not equal, it is classified as a:

    <p>Rectangular matrix</p> Signup and view all the answers

    Where is a tangent line to a circle perpendicular to the radius?

    <p>Point of contact</p> Signup and view all the answers

    What is the variance of the first 20 natural numbers?

    <p>32.25</p> Signup and view all the answers

    In Euclid’s division lemma for positive integers a and b, what condition must the remainder r satisfy in the equation a = bq + r?

    <p>$0 ≤ r &lt; b$</p> Signup and view all the answers

    What is the probability of drawing a Rs.500 or Rs.200 note from a purse containing notes of Rs.2000, Rs.500, and Rs.200 denominations?

    <p>$4/5$</p> Signup and view all the answers

    In the given function f(x) = (x + 1)^3 - (x - 1)^3, what type of function does it represent?

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

    If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal, what is the value of (a, b)?

    <p>(2, -2)</p> Signup and view all the answers

    For the identity function {(a, 8), (6, b)}, what are the values of a and b respectively?

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

    What is the sum of the exponents of the prime factors in the prime factorization of 1729?

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

    If the first term of an arithmetic progression is 1 and the common difference is 4, which of the following will be a term of this A.P.?

    <p>10091</p> Signup and view all the answers

    What is the point of intersection between 3x - y = 4 and x + y = 8?

    <p>(3, 5)</p> Signup and view all the answers

    What is the correct formula for the function f(x) = √(1 + x^2)?

    <p>None of these</p> Signup and view all the answers

    If the HCF of 65 and 117 can be expressed as 65m - 117, what is the value of m?

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

    What is the value of (13 + 23 + 33 + ... + 153) - (1 + 2 + 3 + ... + 15)?

    <p>14280</p> Signup and view all the answers

    What is the curved surface area of a right circular cone with a height of 15 cm and base diameter of 16 cm?

    <p>110π cm^2</p> Signup and view all the answers

    What is the volume, in cm^3, of the largest sphere that can be cut off from a cylindrical log with a base radius of 1 cm and height of 5 cm?

    <p>(10/3)π</p> Signup and view all the answers

    If the radius of the base of a right circular cylinder is halved while keeping the same height, what is the ratio of the volume of the new cylinder to the original cylinder?

    <p>1 : 4</p> Signup and view all the answers

    In statistics, the sum of all deviations of the data from its mean is ____.

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

    For the sets A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}, and D = {5, 6, 7, 8}, which statement is true?

    <p>(𝑩 × 𝑫) ⊂ (𝑨 × 𝑪)</p> Signup and view all the answers

    When selecting a page at random from a book, what is the probability that the digit at the unit place of the page number chosen is less than 7?

    <p>3/10</p> Signup and view all the answers

    If the standard deviation of a data set is 3, what is the new variance if each value is multiplied by 5?

    <p>225</p> Signup and view all the answers

    If the probability of getting a job for a person is x/3 and the probability of not getting the job is 2/3, what is the value of x?

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

    In a scenario where two poles of heights 6 m and 11 m stand vertically on a plane ground with a distance of 12 m between their feet, what is the distance between their tops?

    <p>13 m</p> Signup and view all the answers

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