Algebra Class 10 - Section A Quiz

Section A

Question 1
- 1. Between -2 and -3
  - The number lies on the number line between -2 and -3.
- ** 2. 10**
  - The sum of all interior angles of an n-sided polygon is (n-2) x 180 degrees.
  - Since the polygon is regular, all interior angles are equal to 140 degrees.
  - So, (n-2) x 180 = 140 x n. Solving for n, we get n = 10.
- 3. 110 degrees
  - Let the smaller angle be x degrees. Then the larger angle is (2x - 30) degrees.
  - The sum of opposite angles of a parallelogram is 180 degrees. So, x + (2x-30) = 180.
  - Solving for x, we get x = 70 degrees. Therefore, the larger angle is 2*70 - 30 = 110 degrees.
- 4. 2
  - A number is divisible by 3 if the sum of its digits is divisible by 3.
  - The sum of digits in 467x8 is 25 + x. So, x = 2 makes the sum divisible by 3.
- 5. 840
  - Let the number be x. 5% of x is 42. So, 0.05x = 42
  - Solving for x, we get x = 840.
- 6. {0, 4, 6, 8}
  - B-A means all elements in B that are not in A.
  - B is the set of even numbers. A is the set of prime numbers. So, B - A includes all even numbers except for 2, since 2 is a prime number.
- 7. C
  - A convex polygon has all its interior angles less than 180 degrees.
- 8. 0.3
  - the square root of 0.09 is 0.3.
Question 2
- A. selling price = ₹ 803
  - Discount = 6% of ₹ 850 = (6/100)*850 = ₹ 51.
  - Selling Price = Marked Price – Discount = ₹ 850 - ₹ 51 = ₹ 803.
- B. x = 1
  - (4)^(3x+2) = (4)^(4-3x)
  - Since the bases are the same, the exponents must be equal. So, 3x+2 = 4-3x. Solving for x, we get x = 1.
- C. A = 8, B = 3
  - From the rightmost column, we need 8 + B to give a units digit of 1. Therefore, B = 3.
  - Moving to the tens column, we have 6 + 8 + 5 = 19 + B (carry-over from previous column). Since we need the units digit to be 6, the carry-over from the hundreds column must be 7. This means A must be 8.
Question 3
- A. Construct a quadrilateral ABCD
  - Draw a line segment AB of length 3.5 cm.
  - At point B, construct an angle of 120 degrees.
  - Mark point C on the angle ray such that BC is 2.5 cm.
  - From point C, draw a perpendicular line segment (CD) of length 4.1 cm.
  - Join D to A. ABCD is the required quadrilateral.
- B. X = 10
  - √900 = 30, and the equation states that √900 X = 30. Therefore, X = 1. Simplifying: 30X = 30. Therefore X = 1.
- C. Segment AB
  - The shaded region is the line segment that connects points A and B, which is a part of the circle's circumference.
- D. ∠x = 110 degrees
  - The angles on the straight line sum up to 180 degrees. Therefore, ∠x = 180 - 70 = 110 degrees.

Section B

Question 4
- A. 200 students are left out
  - The number of students in each row is equal to the number of rows, so the number of rows is √4500.
  - Since the square root of 4500 is not a whole number, we find the nearest integer that is less than √4500.
  - √4500 is approximately 67. So, 67 rows can be formed with 67*67 = 4489 students.
  - This leaves 4500 - 4489 = 200 students out.
- B. ∠x = 90 degrees and ∠y = 55 degrees
  - Since PT is a tangent to the circle, angle OPT is 90 degrees.
  - The sum of angles in a triangle is 180 degrees. So, ∠x = 180 - 90 - 25 = 65 degrees.
  - Angle y and ∠x form a linear pair. Therefore, ∠y = 180 - ∠x = 115 degrees.
Question 5
- A. Five rational numbers between -3/4 and -4/5:
  - Find a common denominator for the fractions: -3/4 = -15/20 and -4/5 = -16/20.
  - Rational numbers between -15/20 and -16/20 could be: -14/20, -13/20, -12/20, -11/20, -10/20.
- B. -1/8
  - Simplifying the expression inside the first brackets: (1/4) - (1/3) = -1/12.
  - Simplifying the expression in the second bracket: (1/2) - (1/3) = 1/6.
  - The final expression simplifies to: (-1/12) ÷ (1/6) = -1/2.
Question 6
- A. Find n(X∪Y), n(X∩Y), n(X’)
  - 𝜉 = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.
  - X = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.
  - Y = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}.
  - X∪Y = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}. So, n(X∪Y) = 16.
  - X∩Y = {10, 11, 12, 13, 14}. So, n(X∩Y) = 5.
  - X’ = {5, 6, 7, 8, 9}. So, n(X’) = 5.
- B. 10; cube root of product is 52
  - Find the prime factorization of 10584: 2 x 2 x 2 x 1323= 2³ x 7 x 11 x 11 = 2³ x 7 x 11².
  - To make it a perfect cube, we need one more 7 and one more 11. So, multiply by 7 x 11 = 77.
  - The cube root of product is 2 x 7 x 11 = 154, which is the cube root of 10584 x 77.
Question 7
- A. Multiplicative inverse of 4/5 and 2^-4
  - The multiplicative inverse of a number is its reciprocal. The reciprocal of 4/5 is 5/4.
  - The multiplicative inverse of 2^-4 is 2^4 = 16. (Recall that the multiplicative inverse of x^n is x^-n).
- B. The numbers are 43 and 34
  - Let the ten's digit be x and the unit's digit be y. The number is 10x + y.
  - The sum of digits is 7 means x+y = 7.
  - The number obtained by reversing the digits is 10y + x, and their difference is 9: 10x + y - (10y + x) = 9.
  - Simplify the equations, and solve for x and y. We get x = 4 and y = 3. So, the numbers are 43 and 34.
Question 8
- A. Breadth of rectangular field is 3/4 m
  - Area of rectangle = length x breadth.
  - Given that area = 10 3/12 m² = 123/12m² and length = 2m. Substitute these values and solve for breadth: 123/12 = 2 x breadth.
  - Therefore, breadth = 123/24 = 3/4 m.
- B. Price before GST is 5000
  - Let the original price be x.
  - The price including 8% GST is 1.08x, which is equal to ₹5400: 1.08x = 5400.
  - Solving for x: x = 5400 / 1.08 = ₹ 5000.
Question 9
- A. Incomplete question
  - The question is incomplete and requires additional information to be solved.

Algebra Class 10 - Section A Quiz

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Questions and Answers

In a school with 4500 students, how many students are left out when arranging them in rows where the number of students equals the number of rows?

What is the measure of angle ∠x if PT is tangent to the circle at point T and O is the center of the circle?

What are the first two rational numbers between -3 and -4?

What is the result of simplifying the expression {(1/4) - (1/3)} ÷ (1/2)?

How many elements are in set A ∪ B if A = {x : x Є N, 5 ≤ x ≤ 20} and B = {x : x Є N, 10 ≤ x ≤ 20}?

If 10584 must be multiplied by what smallest number to make it a perfect cube?

What is the multiplicative inverse of 4/5?

If a two-digit number has digits summing to 7 and the difference between the number and its reverse is 9, what is the number?

Which two integers does $-2.5$ lie between?

How many sides does a regular polygon have if each interior angle measures $140^{ ext{o}}$?

What is the measure of the larger angle in a parallelogram if it is $30^{ ext{o}}$ less than twice the measure of the smaller angle?

What is the value of $x$ if $467x8$ is divisible by 3?

If 5% of a number is $42$, what is the original number?

What does the set $B - A$ contain where $A$ is the set of prime numbers and $B$ is the set of even digits?

What is the square root of $0.09$?

What is the selling price of an article marked at ₹850 after a 6% discount?

Study Notes

Section A

Section B

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