Number System
कुल प्रश्न: 77 | पेज 5
41. 1 न्यूटन (Newton) बल कितने डाइन (Dyne) के बराबर होता है?
सही उत्तर: [C]
हल (Solution):
हल: 1 न्यूटन SI मात्रक है ($1\text{ kg}\cdot\text{m/s}^2$) और डाइन CGS मात्रक है ($1\text{ g}\cdot\text{cm/s}^2$)। विमीय विधि से $M_1L_1T_1^{-2} / M_2L_2T_2^{-2}$ हल करने पर $10^5$ आता
हल: 1 न्यूटन SI मात्रक है ($1\text{ kg}\cdot\text{m/s}^2$) और डाइन CGS मात्रक है ($1\text{ g}\cdot\text{cm/s}^2$)। विमीय विधि से $M_1L_1T_1^{-2} / M_2L_2T_2^{-2}$ हल करने पर $10^5$ आता
42. If an 11-digit number 543247x968y is divisible by 90, then what is the value of (4x + 5y)?
सही उत्तर: [A]
हल (Solution):
For a number to be divisible by 90, it must be divisible by both 10 and 9.
Step 1 (Divisibility by 10): A number is divisible by 10 only if its last digit is 0.
Therefore, y = 0.
The number becomes: 543247x9680.
Step 2 (Divisibility by 9): A number is divisible by 9 if the sum of all its digits is a multiple of 9.
Sum of digits = 5 + 4 + 3 + 2 + 4 + 7 + x + 9 + 6 + 8 + 0 = 48 + x.
The next multiple of 9 after 48 is 54.
So, 48 + x = 54
x = 6.
Step 3 (Calculate final value): * Put the values of x and y in (4x + 5y).
(4 * 6) + (5 * 0) = 24 + 0 = 24.
For a number to be divisible by 90, it must be divisible by both 10 and 9.
Step 1 (Divisibility by 10): A number is divisible by 10 only if its last digit is 0.
Therefore, y = 0.
The number becomes: 543247x9680.
Step 2 (Divisibility by 9): A number is divisible by 9 if the sum of all its digits is a multiple of 9.
Sum of digits = 5 + 4 + 3 + 2 + 4 + 7 + x + 9 + 6 + 8 + 0 = 48 + x.
The next multiple of 9 after 48 is 54.
So, 48 + x = 54
x = 6.
Step 3 (Calculate final value): * Put the values of x and y in (4x + 5y).
(4 * 6) + (5 * 0) = 24 + 0 = 24.
43. If A : B = 2 : 3 and B : C = 4 : 5, then what is the ratio of A : C?
सही उत्तर: [A]
हल (Solution):
A/B = 2/3 and B/C = 4/5
Multiply both: (A/B) * (B/C) = (2/3) * (4/5)
A/C = 8/15. So, A : C = 8 : 15.
A/B = 2/3 and B/C = 4/5
Multiply both: (A/B) * (B/C) = (2/3) * (4/5)
A/C = 8/15. So, A : C = 8 : 15.
44. The average age of 5 numbers is 20. If one number is excluded, the average becomes 18. What is the excluded number?
सही उत्तर: [A]
हल (Solution):
Sum of 5 numbers = 5 * 20 = 100
Sum of 4 numbers = 4 * 18 = 72
Excluded number = 100 - 72 = 28.
Sum of 5 numbers = 5 * 20 = 100
Sum of 4 numbers = 4 * 18 = 72
Excluded number = 100 - 72 = 28.
45. If the cost price of an article is Rs. 500 and the selling price is Rs. 600, what is the profit percentage?
सही उत्तर: [C]
हल (Solution):
Profit = SP - CP = 600 - 500 = 100.
Profit % = (Profit / CP) * 100 = (100 / 500) * 100 = 20%.
Profit = SP - CP = 600 - 500 = 100.
Profit % = (Profit / CP) * 100 = (100 / 500) * 100 = 20%.
46. A can do a work in 10 days and B can do the same work in 15 days. In how many days will they finish the work together?
सही उत्तर: [B]
हल (Solution):
A's 1-day work = 1/10
B's 1-day work = 1/15
Together in 1 day = 1/10 + 1/15 = 5/30 = 1/6
Total days = 6 days.
A's 1-day work = 1/10
B's 1-day work = 1/15
Together in 1 day = 1/10 + 1/15 = 5/30 = 1/6
Total days = 6 days.
47. A car is traveling at a speed of 72 km/hr. What is its speed in m/s?
सही उत्तर: [C]
हल (Solution):
Speed in m/s = Speed in km/hr * (5/18)
72 * (5/18) = 4 * 5 = 20 m/s.
Speed in m/s = Speed in km/hr * (5/18)
72 * (5/18) = 4 * 5 = 20 m/s.
48. Which of the following numbers is completely divisible by 99?
सही उत्तर: [D]
हल (Solution):
A number divisible by 99 must be divisible by both 9 and 11.
Sum of digits of 114345 = 1+1+4+3+4+5 = 18 (Divisible by 9).
Difference of sum of alternate digits = (1+4+4) - (1+3+5) = 9 - 9 = 0 (Divisible by 11).
A number divisible by 99 must be divisible by both 9 and 11.
Sum of digits of 114345 = 1+1+4+3+4+5 = 18 (Divisible by 9).
Difference of sum of alternate digits = (1+4+4) - (1+3+5) = 9 - 9 = 0 (Divisible by 11).
49. What is the unit digit of the product (2467)^153 x (341)^72?
सही उत्तर: [C]
हल (Solution):
Unit digit of (341)^72 is 1 (since 1 to any power is 1).
For (2467)^153, the unit digit depends on 7^153.
The power cycle of 7 is 4. Divide 153 by 4, the remainder is 1.
So, unit digit is 7^1 = 7. Total unit digit = 7 x 1 = 7.
Unit digit of (341)^72 is 1 (since 1 to any power is 1).
For (2467)^153, the unit digit depends on 7^153.
The power cycle of 7 is 4. Divide 153 by 4, the remainder is 1.
So, unit digit is 7^1 = 7. Total unit digit = 7 x 1 = 7.
50. If the number 653xy is completely divisible by 80, then the value of (x + y) is:
सही उत्तर: [D]
हल (Solution):
Divisible by 80 means divisible by 10 and 8.
For divisibility by 10, unit digit 'y' must be 0. Number becomes 653x0.
For divisibility by 8, the last three digits '3x0' must be divisible by 8.
If x=6, 360 is divisible by 8. So x=6, y=0. x+y = 6.
Divisible by 80 means divisible by 10 and 8.
For divisibility by 10, unit digit 'y' must be 0. Number becomes 653x0.
For divisibility by 8, the last three digits '3x0' must be divisible by 8.
If x=6, 360 is divisible by 8. So x=6, y=0. x+y = 6.