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Questions and Answers

Which of the following is not a quadratic equation?

  • 5x^2 = 90
  • x^2 + 4x = 11 + x^2
  • x^2 = 4x
  • 2x - x^2 = x^2 + 5 (correct)

    • Find the values of a, b, and c for the given quadratic equation : x^2 + 5x = -(3 - x)

    a = 1, b = 6, c = 3

    If $x = 1$ and $-1$ are the roots of the equation x^2 + 4x - 5 = 0, then the given values are the roots of the equation.

    True

    The sum of the first n even natural numbers is ?

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

    The sum of all odd numbers from 1 to 150 is ?

    <p>5625</p> Signup and view all the answers

    If the 9th term of an A.P. is 0, then what is the 29th term?

    <p>2 times of the 19th term</p> Signup and view all the answers

    If the investment in shares is ` 2000/, find total investment.

    <p>20000</p> Signup and view all the answers

    If the rate of GST on stainless steel utensils is 18%, then the rate of State GST is ______ %.

    <p>9</p> Signup and view all the answers

    What is the amount of dividend received per share of face value ` 10 and dividend declared is 50%?

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

    A trader from Surat, Gujarat sold cotton clothes to a trader in Rajkot, Gujarat. The taxable value of cotton clothes is ` 2.5 lacs. What is the amount of GST at 5% paid by the trader in Rajkot?

    <p>12500</p> Signup and view all the answers

    The total value of a mutual fund scheme is ` 200 crores and 8 crore units are issued. Find the NAV of one unit.

    <p>25</p> Signup and view all the answers

    If NAV of one unit is 25, then how many units will be alloted for the investment of 10,000?

    <p>400</p> Signup and view all the answers

    If n(A) =2, P(A) = 1/5, then n(S) = ?

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

    The probability of any event is from 0 to 1 or 0% to 100%.

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

    A box contains 5 red, 8 blue, and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?

    <p>8/16</p> Signup and view all the answers

    The probability of getting a white ball is [blank]?

    <p>3/4</p> Signup and view all the answers

    The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.

    <p>1/6</p> Signup and view all the answers

    The probability of getting the same digit on the upper face of a die when it is rolled twice is?

    <p>1 / 6</p> Signup and view all the answers

    If two dice are rolled simultaneously, find the probability of getting at least one tail.

    <p>3/4</p> Signup and view all the answers

    A two-digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - multiple of 4.

    <p>1/5</p> Signup and view all the answers

    A bag contains 50 cards. Each card bears only one number from 1 to 50. One card is drawn at random from the bag. Write the sample space. Also write the events A, B, and find the number of sample points in them. (i) Condition for event A: the number on the card is divisible by 6. (ii) Condition for event B: the number on the card is a complete square.

    <p>S = {1,2,3, . . . , 49, 50}, n(S)=50, A = {6, 12, 18, 24, 30, 36, 42, 48} , n(A)=8, B = {1, 4, 9, 16, 25, 36, 49}, n(B)=7</p> Signup and view all the answers

    A sanitation committee of 2 members is to be formed from 3 boys and 2 girls. Write sample space ‘S’ and number of sample points n(S). Also write the following events in set form and number of sample points in the event. (i) Condition for event A: at least one girl must be a member of the committee. (ii) Condition for event B: Committee must be of one boy and one girl. (iii) Condition for event C: Committee must be of boys only. (iv) Condition for event D: At the most one girl should be a member of the committee.

    <p>S= {B1B2,B1B3,B2B3,B1G1,B1G2,B2G1,B2G2,B3G1,B3G2,G1G2}, n(S) = 10 (i) A = {B1G1,B1G2,B2G1,B2G2,B3G1,B3G2, G1G2} , n(A) = 7 (ii) B = {B1G1,B1G2,B2G1,B2G2,B3G1,B3G2}, n(B) =6 (iii) C = {B1B2,B1B3,B2B3}, n(C)=3 (iv) D = {B1B2,B1B3,B2B3,B1G1,B1G2,B2G1,B2G2,B3G1,B3G2}, n(D) = 9</p> Signup and view all the answers

    Two dice are rolled, write the sample space ‘S’ and number of sample points n(S). Also, write the events and number of sample points in the events according to the given condition. (i) Sum of the digits on the upper face is a prime number. (ii) Sum of the digits on the upper face is a multiple of 5. (iii) Sum of the digits on the upper face is 25. (iv) Digit on the upper face of the first die is less than digit on the second die.

    <p>S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}, n(S) = 36 (i) E = {(1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (5,6), (6,1), (6,5)}, n(E)= 15 (ii) F= {(1,4), (2,3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}, n(F) = 7 (iii) G = { }, n(G)=0 (iv) H = {(1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)}, n(H) = 15</p> Signup and view all the answers

    In a random experiment of tossing a coin, what are the possible outcomes?

    <p>The possible outcomes are Heads and Tails.</p> Signup and view all the answers

    In the sequence 2, -2, -6, -10, ..., what is the value of 'd'?

    <p>-4</p> Signup and view all the answers

    Find the value of 'd', the common difference in the sequence 5, 12, 19, 26, ...

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

    A card is drawn at random from a pack of 52 playing cards. What is the probability of drawing a heart?

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

    Given a set S = {1, 2, 3, 4, 5, 6}, what is the probability of getting an odd number?

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

    Suppose a bag contains 4 balls of the same size. Three are white and one is black. If you pick one ball at random, what is the probability of getting a white ball?

    <p>3/4</p> Signup and view all the answers

    What is the probability of getting a head when a coin is tossed?

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

    What is the probability of drawing a card with the number 5 from a deck of 52 cards?

    <p>1/13</p> Signup and view all the answers

    What is the probability of getting a head on the second coin when two coins are tossed simultaneously?

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

    What is the probability of getting a head when two coins are tossed simultaneously?

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

    What is the probability of drawing a queen from a pack of 52 cards?

    <p>1/13</p> Signup and view all the answers

    In a random experiment of rolling a die, how many outcomes are possible?

    <p>6</p> Signup and view all the answers

    A bag contains 3 red, 3 white, and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is not red?

    <p>2/3</p> Signup and view all the answers

    If one die is rolled, what is the probability of getting a prime number on the upper face?

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

    If two coins are tossed simultaneously, list the possible outcomes.

    <p>The possible outcomes are HH, HT, TH, and TT.</p> Signup and view all the answers

    Study Notes

    Mathematics Part-I, Standard Ten

    • This textbook covers Algebra, Graph, Financial planning and Statistics.
    • It introduces topics studied in ninth standard in greater detail.
    • A new tax system, GST, is introduced in Financial Planning.
    • Each chapter contains solved examples and practice questions.
    • Some questions in practice sets are marked as challenging for talented students.

    The Constitution of India, Chapter IV A

    • This chapter details the Fundamental Duties of citizens of India.
    • Article 51A outlines duties, including those towards the Constitution, ideals, and institutions, national flag, and national anthem.
    • Also included are duties related to upholding sovereignty, unity and integrity, national service, promoting harmony, and renouncing practices derogatory to women.
    • Duties are further listed that protect and improve the environment.
    • Duties for safeguarding against violence are also included.
    • Duties to strive for excellence with collective activity are included.
    • Lastly duties to ensure and provide opportunities for education is included, to children of parents/guardians between the ages of six and fourteen years.

    Other Information

    • The provided documents include mathematical formulas, details of mathematical and scientific concepts.
    • It has tables related to solution of simultaneous linear equations and quadratic equations, mathematical practicals to be performed etc.

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