Mock Test Review: 18 flashcards
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1. In the standard form of a rational number, what is the common factor of numerator and denominator always?
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1 (they are co-prime)
2. If 2x, (x + 10), and (3x + 2) are three consecutive terms of an AP, find the value of x.
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x = 6 (since 2(x+10) = 2x + 3x + 2 ⇒ 2x + 20 = 5x + 2 ⇒ 18 = 3x ⇒ x = 6)
3. Which operation is not closed for rational numbers?
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Division (division by zero is undefined)
4. Which rational number does not have a multiplicative inverse?
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0
5. Which operations are not associative for rational numbers?
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Subtraction and division
6. In a square fractal pattern, the number of smaller squares follows a GP with first term 1 and common ratio 8. How many squares are in the 5th step?
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4096 (1 × 8^4 = 4096)
7. The sum of diameters of two circles is 35 cm and the difference of their circumferences is 22 cm. What is the area of the smaller circle?
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154 cm²
8. Evaluate 102² - 98² using a suitable formula.
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800 (using a² - b² = (a+b)(a-b) = 200 × 4 = 800)
9. A(-5, 6) and C(9, 1) are opposite vertices of a parallelogram. Diagonals intersect at P(a, b). What is the relation between a and b?
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b = a + 1.5 (midpoint of AC is (2, 3.5), so a=2, b=3.5, thus b = a + 1.5)
10. The expression 3/8 + (-5)/7 = -19/56 shows that rational numbers are closed under which operation?
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Addition
11. Which term of the AP 5, 15, 25, ... is 130 more than its 31st term?
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44th term (31st term = 5 + 30×10 = 305; 305+130=435; 5+(n-1)10=435 ⇒ n=44)
12. Express 1.272727... as a rational number.
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14/11
13. If b is the multiplicative inverse of x, what is the multiplicative inverse of a/b?
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b/a (since a/b × b/a = 1)
14. Zero (0) is the identity for which operation on rational numbers?
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Addition
15. If the sum of three numbers in GP is 38 and their product is 1728, what are the numbers?
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8, 12, 18
16. Assertion: If x² + 4x + a = (x+2)², then a = 4. Reason: (a+b)² = a² + 2ab + b². Which option is correct?
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Both A and R are true and R is the correct explanation of A.
17. In a cricket match, a batsman hits a boundary 5 times out of 45 balls. What is the probability he does not hit a boundary?
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8/9 (P(not boundary) = 1 - 5/45 = 40/45 = 8/9)
18. Find x such that the distance between A(x, 2) and B(9, 8) is 10 units.
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x = 1 or x = 17
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