**Q2. If HCF of (x² + x – 12) and (2x² – kx – 9) is (x – k), then value of k is**

(a) –3

(b) 3

(c) –4

(d) 4

**Q3. If (3x³ – 2x²y – 13xy² + 10y³) is divided by (x – 2y), then what is the remainder?**

(a) 0

(b) y + 5

(c) y + 1

(d) y² + 3

**Q4. Two numbers are such that the sum of twice the first number and thrice the second number is 36 and sum of thrice the first number and twice the second number is 39. Which is the smaller number?**

(a) 9

(b) 5

(c) 7

(d) None of these

**Q5. If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:**

(a) 12

(b) 28

(c) 80

(d) 160

**Q6. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc. Any number of this form is always exactly divisible by:**

(a) 7

(b) 11

(c) 13

(d) Smallest 3-digit prime number

**Q7. A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, then the remainder is:**

(a) 0

(b) 1

(c) 2

(d) 3

**Q8. What is the mode of the following numbers?**

**1, 2, 4, 6, 4, 3, 5, 4**

(a) 1

(b) 2

(c) 3

(d) 4

**Q9. Find the median of the following data. **

**27, 39, 49, 20, 21, 28, 38**

(a) 49

(b) 21

(c) 28

(d) 38

**Q10. The population of a town is increasing at the annual growth rate of 5%. If the present population is 1,60,000 then what will be population 4 years later?**

(a) 1,94,481

(b) 1,78,641

(c) 1,92,000

(d) 1,65,000

**Solutions:**

**S6. Ans.(d)**

**Sol.** By 101 which is the smallest 3-digit prime number.

**S7. Ans.(b)**

**Sol.** The number is 68 × 269 = 18292. 18292, when divided by 67, leaves a remainder of 1.

**S8. Ans.(d)**

**Sol.** The mode is the value which appears the most often in the data. It is possible to have more than one mode if there is more than one value which appears the most.

**S9. Ans.(c)**

**Sol.** To find the median, you need to put the values in order, then find the middle value. If there are two values in the middle, then you find the mean of these two values.

Series = 20, 21, 27, 28, 38, 39, 49

Median = 28

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