Directions (1-5): What should come in place of question mark (?) in the following questions?
Q1. √225÷ ∛125× 40% of 550 =?
Q2. 150% of 220+120% of 140+?=850
Q3. 30% of 340 - 70% of 110 = 65 - ?
Q4. [7 × (4.4 + 8.6)] - 8² = ?
= 27
Q5. (5555 ÷ 55) + (625 ÷ 25) + (120 ÷ 24) = ?
= 131
Q6. In a class, there are 15 girls and 10 boys. Three students are selected at random. The probability that only girls or only boys get selected is:
Q7. Two letters are chosen out of the alphabets of the English language. Find the probability that both the letters are vowels.
Q8. How many three digits number can be formed by using the digits 0, 2, 4, 6, 7 if repetition of digits is allowed.
First place can be filled up by using only one of 4 digits (except 0, since 0 at the first place is meaning less).
Second place can be filled up by using any one of out of 5 digits (because repetition is allowed).
Similarly, third place can be filled up by using any one of out of all the five digits.
Thus,
Places: 0 0 0
Digit: 4 5 5
Total numbers = 4 × 5 × 5 = 100
Q9. Find the numbers between 100 and 1000 in which all digits are distinct.
Total digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 which are 10.
First place can be filled up by using any one of 9 digits (except 0, since 0 at the first place is meaningless).
Second place can be filled up by using any one of 9 digits (as one digit has been used at first place)
Third place can be filled up by using only one of 8 digits.
Thus,
Places: 0 0 0
Digits: 9 9 8
Total number = 9 × 9 × 8 = 648
Q10. The letters of the word ‘PROMISE’ are to be arranged so that all the vowels should not come together. Find the number of arrangements.
Directions (11-15): Solve the following equations and mark the correct option given below.
Q11. I. x² – 27x + 180 = 0
II. y² – 7y = 60
x² – 12x – 15x + 180 = 0
x (x – 12) –15(x – 12) = 0
(x – 15) (x – 12) = 0
x = 15, 12
II. y² – 7y – 60 = 0
y² – 12y + 5y – 60 = 0
y (y – 12) +5 (y – 12) = 0
(y + 5) (y – 12) = 0
y= -5, 12
⇒ x ≥ y
Q12. I. x² – 59x + 868 = 0
II. y² – 53y + 702 = 0
x² – 28x – 31x + 868 = 0
x (x – 28) – 31 (x – 28) = 0
(x – 31) (x – 28) = 0
x = 28, 31
II. y² – 53y + 702 = 0
y² – 27y – 26y + 702 = 0
y (y – 27) – 26(y – 27) = 0
(y– 27) (y – 26) = 0
y = 26, 27
⇒ x > y
Q13. I. 100x² – 120x + 32 = 0
II. 10y² – 17y + 6 = 0
100x² – 40x – 80x + 32 = 0
20x (5x – 2) – 16(5x – 2) = 0
(20x – 16) (5x – 2) = 0
x=4/5, 2/5
II. 10y² – 17y + 6 = 0
10y² – 12y – 5y + 6 = 0
2y (5y – 6) – 1 (5y – 6) = 0
(2y – 1) (5y – 6) = 0
y=1/2, 6/5
⇒ No relation
Q14. I. 15x² – 22x + 8 = 0
II. 12y² – 5y – 2 = 0
15x² – 12x – 10x + 8 = 0
3x (5x – 4) –2 (5x – 4) = 0
(5x – 4) (3x– 2) = 0
x=4/5, 2/3
II. 12y² – 5y – 2 = 0
12y² – 8y + 3y – 2 = 0
4y (3y – 2) + 1 (3y – 2) = 0
(4y + 1) (3y – 2) = 0
y= -1/4, 2/3
⇒ x ≥ y
Q15. I. x² + 8x + 15 = 0
II. y² – 2y – 8 = 0
x² + 5x + 3x + 15 = 0
x (x + 5) + 3 (x+ 5) = 0
(x + 5) (x + 3) = 0
x = –5, –3
II. y² – 2y – 8 = 0
y² – 4y + 2y – 8 = 0
y (y – 4) + 2(y – 4) = 0
(y – 4) (y + 2) = 0
y= –2, 4
⇒ x < y