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- Question
The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?
Options- A. 0.04
- B. 0.043
- C. 0.047
- D. 0.05
- Correct Answer
- 0.043
ExplanationVowels are A I A I O,
C A S T I G A T I O N
(O) (E) (O) (E) (O) (E) (O) (E) (O) (E) (O)
So there are 5 even places in which five vowels can be arranged and in rest of 6 places 6 constants can be arranged as follows :
- 1. 445, 221, 109, 46, 25, 11, 4
Options- A. 221
- B. 109
- C. 46
- D. 25
- E. 11 Discuss
- 2. A boat cover a distance of 30 km downstream in 2 h while it takes 6 h to cover the same distance distance upstream. What is the speed of the boat (in km/h)?
Options- A. 5
- B. 7.5
- C. 13
- D. 10 Discuss
- 3. A 220 m long train passes a signal post in 12 s. Find the speed f the train.?
Options- A. 72 km/h
- B. 60 km/h
- C. 66 km/h
- D. 69 km/h Discuss
- 4. The banker's gain on a bill due 2 years hence at 5% is Rs. 8, find the present worth of the bill?
Options- A. Rs. 800
- B. Rs. 650
- C. Rs. 750
- D. Rs. 850 Discuss
- 5. The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is?
Options- A. 0
- B. 1
- C. a
- D. ab Discuss
- 6.
If x = 2 + ?3, then the value of ?x + 1 is : ?x
Options- A. ?3
- B. ?6
- C. 2 ?6
- D. 6 Discuss
- 7. A shopkeeper marked 50% more price than cost price of the article . If he allows 30% discount to his customers, then his profit per cent is
Options- A. 5%
- B. 10%
- C. 12%
- D. 15% Discuss
- 8. Find 2 consecutive positive odd integers whose squares have the sum 290.
Options- A. 11, 13
- B. 13, 15
- C. 9, 11
- D. None of these Discuss
- 9. ?. 18x 2 + 18x + 4 = 0
?. 12y 2 + 29y + l4 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. One root of the quadratic equation x2 - 5 x + 6 = 0 is 3. Find the other root.
Options- A. 2
- B. ?2
- C. 1
- D. ?1 Discuss
More questions
Correct Answer: 46
Explanation:
Clearly, 46 is wrong.
Correct Answer: 10
Explanation:
Speed of boat downstream = Distance covered / Time taken
= 30/2 = 15 km/h
Now, speed of boat upstream = Distance covered / Time taken
= 30/6 = 5 km/h
Now, speed of boat = (Speed download + Speed upstream) / 2
= (15 + 5) / 2 = 10 km/h
Correct Answer: 66 km/h
Explanation:
We know that,
Speed = Distance/ Time
Speed of the train = 220/12 x (18/5) km/h
Correct Answer: Rs. 800
Explanation:
P.W. = [8 x 100 x 100] / [10 x 10]
= Rs. 800
Correct Answer: 1
Explanation:
? loga x = ( logabx) / (logaba)
? The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1
Correct Answer: ?6
Explanation:
Correct Answer: 5%
Explanation:
Here, r = 50% and r1 = 30%
? Gain per cent = [r(100 - r1)/100] - r1
= [50 x (100 - 30)/100] - 30
= 35 - 30 = 5%
Correct Answer: 11, 13
Explanation:
According to question ,
Let, the two consecutive odd positive integers be 2x + 1 and 2x + 3 where x is a whole number.
Now, ( 2x + 1 )2 + ( 2x + 3 )2 = 290
? 4x2 + 4x + 1 + 4x2 + 12x + 9 = 290
? 8x2 + 16x - 280 = 0
? x2 + 2x - 35 = 0
? ( x + 7 ) ( x - 5 ) = 0
? x = 7, - 5
But, x = ?7 is not possible, since ?7 is not a whole number .
? x = 5.
We get , 2x + 1 = 2 x 5 + 1 = 11 and 2x + 3 = 2 x 5 + 3 = 13
Thus , two consecutive positive odd integers are 11 and 13 .
Correct Answer: 4
Explanation:
Correct Answer: 2
Explanation:
The given equation is
x2 - 5x + 6 = 0 ? x 2 - 2x - 3x+ 6 = 0
? x( x - 2 ) - 3( x - 2 ) = 0
? ( x - 2 ) ( x - 3 ) = 0
? x - 2 = 0 or x - 3 = 0
? x = 2 or x = 3
Thus, the other root of the given quadratic equation is 2.
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