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- Question
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Options- A. 120960
- B. 120000
- C. 146700
- D. None of these
- Correct Answer
- 120960
ExplanationIn the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2! x 2!)= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4!/2!= 12.
Required number of words = (10080 x 12) = 120960
- 1. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Options- A. 2 times
- B.
2 1 times 2 - C.
2 3 times 4 - D. 3 times Discuss
- 2. A flagstaff 17.5 meters high casts a shadow of length 40.25 meters. What will be the height of a building, which casts a shadow of length 28.75 meters under similar conditions?
Options- A. 12.5 m
- B. 11.5 m
- C. 14.8
- D. 12.9 Discuss
- 3. A person covers 9 km with a speed of 3 km/h, 25 km with a speed of 5 km/h and 30 km with a speed of 10 km/h. Find out the average speed of person.
Options- A. 59/11 km/h
- B. 115/9 km/h
- C. 95/11 km/h
- D. 55/11 km/h Discuss
- 4. The ratio of two numbers is 3 : 4 and their HCF is 4. What will be their LCM?
Options- A. 12
- B. 16
- C. 24
- D. 48 Discuss
- 5. If ? 3 =1.732 and ? 2 = 1.414, the value of 1/(? 3 + ? 2) is?
Options- A. 0.064
- B. 0.308
- C. 0.318
- D. 2.146 Discuss
- 6. A sum of the ? 300 is divided among P, Q and R in such a way that Q gets ? 30 more than P and R gets ? 60 more then Q. Then, ratio of their shares is?
Options- A. 2 : 3 : 5
- B. 3 : 2 : 5
- C. 2 : 5 : 3
- D. 5 : 3 : 2 Discuss
- 7. A dealer buys an article marked at ? 40000 with 20% and 10% off. He spends ? 1200 on its repairs and sells it for ? 30000. What is his gain or loss per cent?
Options- A. 10% gain
- B. 10% loss
- C. No gain no loss
- D. None of these Discuss
- 8. The sum which amount to ? 364.80 in 8 yr at 3.5% simple interest per annum is
Options- A. ? 285
- B. ? 280
- C. ? 275
- D. ? 270 Discuss
- 9. A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it catches the deer?
Options- A. 600 m
- B. 700 m
- C. 800 m
- D. 1000 m Discuss
- 10. Rakesh lent out ? 8750 at 7% annual interest, Find the simple interest in 3 yr.
Options- A. ? 1870
- B. ? 1837.50
- C. ? 1560
- D. ? 2200 Discuss
More questions
Correct Answer: 2 times
Explanation:
| ∴ | (4x + 8) = | 5 | (x + 8) |
| 2 |
⟹ 8x + 16 = 5x + 40
⟹ 3x = 24
⟹ x = 8.
| Hence, required ratio = | (4x + 16) | = | 48 | = 2. |
| (x + 16) | 24 |
Correct Answer: 12.5 m
Explanation:
According to question,
A shadow of length 40.25 meters is build for a height of 17.5 meters.
A shadow of length 1 meters is build for a height of 17.5 /40.25 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 28.75 /40.25 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 2875 /4025 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 575 /805 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 115/161 meters.
A shadow of length 28.75 meters is build for a height of 12.5 meters.
Correct Answer: 59/11 km/h
Explanation:
Here, P = 9 km/h, Q = 25 km/h, R = 30 km
x = 3 km/h, y = 5 km/h and z = 10 km/h
? Required average speed
= [P + Q + R] / [(P/x) + (Q/y) + (R/z)] = [9+25 + 30] / [(9/3) + (25/5) + (30/10)]
= 64/(3 + 5 + 3)
= 64/11
= 59/11 km/h
Correct Answer: 48
Explanation:
According to the question,
1st number = 3M, 2nd number = 4M
where, M = HCF
But given, M = 4
We know that,
LCM = Product of two numbers / HCF
= (3M x 4M) / M
LCM = 12M = 12 x 4 = 48
Correct Answer: 0.318
Explanation:
1/ (?3 + ?2)
= (?3 - ?2) / [ 1/ (?3 - ?2) x (?3 + ?2)]
= (?3 - ?2) / (3 - 2)
= (1.7732 - 1.414) = 0.318
Correct Answer: 2 : 3 : 5
Explanation:
Let the share of P = x
Then, Q's share = x + 30 and
R's share = (x + 30) + 60 = x + 90
Sum of money with P, Q and R = 300
? x + (x + 30) + (x + 90) = 300
? 3x + 120 = 300
? x = (300 - 120)/3 = 60
? Required ratio = 60 : (60 + 30) : (60 + 90) = 2 : 3 : 5
Correct Answer: No gain no loss
Explanation:
CP. = (80% of 90% of ?40000) + ?(1200)
= [(80/100) x (90/100) x 40000] + 1200
= (28800 + 1200)
= ?30000
? CP = ?30000
So, no gain no loss in the transaction.
Correct Answer: ? 285
Explanation:
Given, t = 8 yr, r = 3.5%, A = ? 364.80
Let amount = ? P
Since, A =P [1 + (RT/100)]
? 364.80 = P[1 + (3.5 x 8)/100]
? 364.80 = P[ 1+ (35 x 8)/100]
? 3648/10 = P x (128/100)
? P = 3648/128
= ? 285
Correct Answer: 800 m
Explanation:
Speed of tiger = 40 m/min
Speed of dear = 20 m/min
Relative speed = 40 - 20 = 20 m/min
Difference in distance = 50 x 8 = 400 m
? Time taken in overtaking (or catching) = 400/20 = 20min
? Distance travelled in 20 min = 20 x 40 = 800 m
Correct Answer: ? 1837.50
Explanation:
Given, P = ? 8750., R = 7% T = 3 yr
According to the formula.
SI = (P x R x T)/100 = (8750 x 7 x 3)/100
= ? 1837.50
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