Mock Test Review: 18 MCQs with answers
All 18 multiple-choice questions from this kit, free and with no sign-up.
Warm-up · 9 questions
Q1. In the standard form of a rational number, the common factor of numerator and denominator is always:
BeginnerShow answer & explanation
1
A rational number is in standard form when its denominator is positive and the numerator and denominator have no common factor other than 1.
Q2. Which of the following is not true for rational numbers?
BeginnerShow answer & explanation
Rational numbers are closed under division.
Rational numbers are not closed under division because division by zero is not defined.
Q3. Which of the following numbers does not have a multiplicative inverse?
BeginnerShow answer & explanation
0
0 does not have a multiplicative inverse because there is no rational number which when multiplied by 0 gives 1.
Q4. Which of the following operations is not associative for rational numbers?
BeginnerShow answer & explanation
Both (B) and (C)
Both subtraction and division are not associative for rational numbers. For example, (a - b) - c ≠ a - (b - c).
Q5. By using suitable formula, the value of 102² - 98² is:
BeginnerShow answer & explanation
400
Q6. The numerical expression 3/8 + (-5)/7 = -19/56 shows that:
BeginnerShow answer & explanation
rational numbers are closed under addition.
The sum of two rational numbers is also a rational number, demonstrating closure under addition.
Q7. Zero (0) is:
BeginnerShow answer & explanation
the identity for addition of rational numbers.
0 is the additive identity because adding 0 to any rational number leaves it unchanged.
Q8. Rational numbers are closed under division.
BeginnerShow answer & explanation
False
Rational numbers are not closed under division because division by zero is undefined.
Q9. The value of 102² - 98² is 800.
BeginnerShow answer & explanation
True
102² - 98² = (102-98)(102+98) = 4 × 200 = 800.
Building up · 7 questions
Q10. In a square fractal pattern, the number of smaller squares formed at each step follows a GP with first term 1 and common ratio 8. The number of squares in the 5th step is:
IntermediateShow answer & explanation
4096
The nth term of a GP is ar^(n-1). Here a=1, r=8, and n=5, so the 5th term is 1 × 8^4 = 4096.
Q11. A(-5, 6) and C(9, 1) are the two opposite vertices of a parallelogram ABCD. Its diagonals intersect each other at P(a, b). The relation between a and b is:
IntermediateShow answer & explanation
b = a - 4.5
The diagonals of a parallelogram bisect each other. So P is the midpoint of AC: a = (-5+9)/2 = 2, b = (6+1)/2 = 3.5. Then b = a + 1.5.
Q12. Which term of the AP 5, 15, 25, ..... will be 130 more than its 31st term?
IntermediateShow answer & explanation
44
The AP has first term a=5 and common difference d=10. The 31st term = 5 + 30×10 = 305. We need the term = 305 + 130 = 435. So 5 + (n-1)×10 = 435, giving n = 44.
Q13. 1.272727..... can be expressed in rational form as:
IntermediateShow answer & explanation
14/11
Let x = 1.272727... Then 100x = 127.272727... Subtracting gives 99x = 126, so x = 126/99 = 14/11.
Q14. If b is the multiplicative inverse of a number x, then the multiplicative inverse of a/b is:
IntermediateShow answer & explanation
(xb)/a
The multiplicative inverse of a/b is b/a. Since b = 1/x, we get b/a = (1/x)/a = 1/(ax). But the question asks for the inverse of a/b, which is b/a = (xb)/a when substituting b = 1/x.
Q15. Assertion (A): If x² + 4x + a = (x + 2)² then the value of a is 4. Reason (R): (a + b)² = a² + 2ab + b²
IntermediateShow answer & explanation
Both A and R are true and R is the correct explanation of A.
(x+2)² = x² + 4x + 4, so a = 4. The reason correctly explains why.
Q16. Assertion (A): In a cricket match, a batsman hits a boundary 5 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 8/9. Reason (R): P(E) + P(not E) = 1.
IntermediateShow answer & explanation
Both A and R are true and R is the correct explanation of A.
P(hitting boundary) = 5/45 = 1/9. So P(not hitting) = 1 - 1/9 = 8/9. The reason correctly explains the assertion.
Topper level · 2 questions
Q17. The sum of diameters of two circles is 35 cm and the difference of their circumferences is 22 cm. The area of the smaller circle will be:
AdvancedShow answer & explanation
154 cm²
Let radii be r1 and r2. 2r1 + 2r2 = 35, so r1 + r2 = 17.5. Also 2π(r1 - r2) = 22, so r1 - r2 = 3.5. Solving gives r1 = 10.5 and r2 = 7. Area of smaller circle = π × 7² = 154 cm².
Q18. If the sum of three numbers in GP is 38 and their product is 1728, then the numbers are:
AdvancedShow answer & explanation
8, 12, 18
Let the numbers be a/r, a, ar. Product = a³ = 1728, so a = 12. Sum = 12/r + 12 + 12r = 38. Solving gives r = 2/3 or 3/2. So the numbers are 8, 12, 18.
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