Mathematics
Assertion (A): 1133 + 153 is divisible by 98.
Reason (R): Factors of a3 + b3 are (a + b) and (a2 - ab + b2).
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Answer
A is false, R is true.
Explanation
a3 + b3 = (a+b)(a2 - ab + b2)
1133 + 153 = (113 + 15)(1132 - 113 x 15 + 152)
= 128(12,769 - 1,695 + 225)
= 128 x 11,299
This means 1133 + 153 is not divisible by 98.
∴ Assertion (A) is false.
a3 + b3 = (a + b)3 - 3ab(a + b)
= (a + b)((a + b)2 - 3ab)
= (a + b)(a2 + b2 + 2ab - 3ab)
= (a + b)(a2 + b2 - ab)
∴ Factors of a3 + b3 are (a + b) and (a2 - ab + b2).
∴ Reason (R) is true.
Hence, Assertion (A) is false, Reason (R) is true.
Related Questions
Assertion (A): 5x5 - 20x3 in the form of factors is 5x3(x2 - 4).
Reason (R):
5x5 - 20x3
= 5x3(x2 - 4)
= 5x3(x + 2)(x - 2).- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Assertion (A): a(2x - 3y) + b(3y - 2x)2 = a(2x - 3y) - b(2x - 3y)2
Reason (R): +b(3y - 2x)2 is not equal to -b(2x - 3y)2.
- A is true, R is false.
- A is false, R is true.
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- Both A and R are false.
Assertion (A): 3x2 - 8x - 15 is not factorisable.
Reason (R): The trinomial ax2 + bx + c is factorisable, if the value of b2 - 4ac, where a = coefficient of x2, b = coefficient of x, c = constant, is perfect square, otherwise not.
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Assertion (A): A moving boat goes downstream at 50 km per hour and upstream at 30 km per hour. The speed of stream is 40 km per hour.
Reason (R): If the speed of boat in still water is x km per hour and speed of stream is y km per hour, then y - x = 50 and y + x = 30 ⇒ y = 40.
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.