10 Questions
What is the breadth of the rectangular ground with an area of 1541 square meters?
28 meters
What is the value of M in the equation 17 × 19 × 4 ÷ M = 161.5?
37
Which of the following is an irrational number?
$0.123456789$
In a proportion P, Q, R, and S, which statement is correct?
$P/R = Q/S$ and $P = RQ$
If Maria's age is X years, what is her age 10 years before?
$-X + 10$
In triangle TPQ, if angle TPQ is a right angle, where is the orthocenter located?
At the vertex containing the right angle
What is the total duration of a trip that started at 6:30 AM on Saturday and ended at 8:50 PM on Sunday?
38 hours
What was the actual duration of a trip that lasted from 6:30 PM Saturday to 6:15 PM Sunday according to the information provided?
37 hours
If a square of side length 8 centimeters is cut into smaller squares of size 1 centimeter at each corner, what is the difference in perimeter between the original square and the one with corners cut?
$0$ centimeters
Which pair of prime numbers has a sum greater than the sum of all prime numbers under 26 and is a difference of two primes?
71 and 73
Study Notes
- The video covers solutions for 8th standard scholarship examination mathematics paper 1, focusing on questions 51-74.
- Question 51: Two rectangular grounds have areas 1541 square meters and 759 square meters. They share the same grid length; find the ground breadth.
- Both grounds have the same breadth and different lengths.
- Find the highest common factor of the two areas to determine the breadth (1541 and 759).
- The highest common factor is 23; therefore, the breadth is 23 meters.
- Question 52: Find the value of M in the equation 17 × 19 × 4 ÷ M = 161.5.
- The equation simplifies to 17 × 19 × 4 × 2 = 323.
- The factors of 323 are 1, 3, 11, 13, 37, 67, and 323.
- Given options, select 23 and 67. Divide 1541 by 23 to get 67; therefore, option 3 is the correct answer.
- Question 55: Find the irrational number from the given options.
- Pi is a rational number, so it is not an irrational number.
- The correct answer is option 3, which is the square root of 2.
- Question 56: Four numbers P, Q, R, and S are in proportion.
- Given statement: P/R = Q/S.
- If this statement is correct, then P = RQ and Q = PS.
- Correct options: P/R = Q/S and P/S = Q/R.
- Question 57: Maria's age is X years. Find her age 10 years before.
- Given equation: Y = X + 10.
- The correct answer is Y - X - 10.
- Question 58: Find the percentage of 31.25.
- 31.25% equals 0.3125.
- Try each option and see which one matches 0.3125.
- Option 1, 0.3125, is the correct answer.
- Question 59: In triangle TPQ, angle TPQ is a right angle.
- The orthocenter of a right angle triangle is located on the vertex containing the right angle.
- Correct options: TP is perpendicular to QR and T is perpendicular to QR.
- Question 61: Find the duration of a school trip.
- The trip started at 6:30 AM on Saturday and ended at 8:50 PM on Sunday.
- Calculate the hours from 6:30 AM Saturday to 6:30 AM Sunday and from 6:30 AM Sunday to 8:50 PM Sunday.
- The total trip duration is 36 hours.- The text discusses various mathematical questions and solutions.
- Question 1: A trip lasted from 6:30 PM Saturday to 6:15 PM Sunday, with an additional 45 minutes. The trip ended up taking 37 whole hours.
- Question 2: A square of side length 8 centimeters is cut into smaller squares of size 1 centimeter at each corner. The difference in perimeter between the original square and the one with corners cut is calculated to be zero.
- Question 3: Two lines intersect at point O. The first statement that lines AB and BA are the same is incorrect. The second statement that lines AB and DC intersect at O is correct.
- Question 4: The correct relation of variation between the areas of two circles with radii R and S is R^2 : S^2 = 2 : 1.
- Question 66: The pair of prime numbers whose sum is more than the sum of all prime numbers under 26 and is a difference of two primes is 71 and 73, with a sum of 144.
- Question 67: The angles of a quadrilateral ABCD, given the ratio of their measures as 7:S:4:2, are found to be 70 degrees, 120 degrees, 60 degrees, and 75 degrees, respectively. The figure is not a rectangle, parallelogram, or rhombus.
- Question 68: The smallest number whose remainder is 1 when divided by every one-digit prime number is 211.
- Question 69: An investor earns different amounts of interest with simple and compound interest over three years with an initial investment of ₹5000. The interest earned with compound interest is ₹16,165.50, while the interest earned with simple interest is ₹5,000.
- Question 71: The value of 4.9^3 + 2.1^3 divided by 4.9^2 is 7.0.
- Question 72: The perimeter of a regular hexagon with each side measuring 14 centimeters is calculated by finding the perimeter of half a circle with a diameter of 14 centimeters, which is 13.2. The total perimeter of the hexagon is 3*13.2 = 39.6 centimeters.
- Question 73: The area of a trapezium with bases PS and QS, height H, and legs PR and QR, is calculated using the formula A = (1/2)(Bh + b*h), where the base B = PS = QS, and the height H = 4. The area of the trapezium is 32 square units.
- Instead of investing ₹3000 with simple interest for 2.5 years, investing ₹4000 with simple interest for 2 years would result in earning ₹25 more interest. The rate of interest is 5%.
This quiz provides solutions for questions 51 to 74 from the 8th standard scholarship examination mathematics paper 1. It covers topics like geometry, algebra, proportions, number systems, time and percentage calculations, prime numbers, interest calculation, and area and perimeter formulas.
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