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- Question
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options- A. 209
- B. 290
- C. 200
- D. 208
- Correct Answer
- 209
ExplanationWe may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways =
= = 209.
- 1. A person has only ? 1 and ? 2 coins with him. If the total number of coins that he has is 50 and the amount of money with him is 75, then the number of coins ? 1 and ? 2, respectively are?
Options- A. 15 and 35
- B. 35 and 15
- C. 30 and 20
- D. 25 and 25 Discuss
- 2. In a rare coins collection, there is one gold coins for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:2. Based on the information, the total number of coins in the collection now becomes?
Options- A. 90
- B. 80
- C. 60
- D. 50 Discuss
- 3. If the price of a book when reduced by Rs. 5,a person can buy 2 more books for Rs. 200. Find the original price of the book?
Options- A. Rs. 25
- B. Rs. 30
- C. Rs. 20
- D. Rs. 15 Discuss
- 4. The degree of polynomial p(x) = x 3 + 1 + 2x = 6x + 1/x is?
Options- A. 2
- B. 4
- C. 3
- D. 5 Discuss
- 5. A piece of cloth cost ? 120. If the piece, then was 2 m longer and each metre of cloth costs ? 2 less than cost of the piece of cloth would have remained unchanged. What is the original rate per metre of the cloth?
Options- A. ? 12
- B. ? 15
- C. ? 10
- D. ? 8 Discuss
- 6. Angry Arjun carried some arrows for fighting with Bheshhm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the rath driver of Bheeshm. with one arrows each he Knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrow he laid Bheeshm unconscious on an arrow bed. What is the total number of arrows Arjun had?
Options- A. 90
- B. 101
- C. 100
- D. 104 Discuss
- 7. If the cost of 2 apples, 3 oranges and a pear is Rs.62 and the cost of 5 apples, 6 oranges and 4 pears is Rs. 120, then find the cost of 3 apples, 3 oranges and 3 pears?
Options- A. Rs. 39
- B. Rs. 46
- C. Rs. 58
- D. Rs. 24 Discuss
- 8. Two candidates attempt to solved a quadratic equation of from x 2 + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. Other starts with a wrong value of q and find the root to be 2 and -9. Find the correct roots and equation?
Options- A. -3, -2 and x x2 + 9x + 18
- B. 3, 4 and x2 + 8x + 15
- C. -3, -4 and x2 + 7x + 12
- D. 2, 6 and x2+ 7x + 12 Discuss
- 9. What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?
Options- A. 30
- B. 31
- C. 32
- D. 35 Discuss
- 10. If (x+2) is the HCF of x 2 + ax + b and x 2 + cx + d , then which one of the following is correct?
Options- A. a + c = b + d
- B. 2a + b = 2c + d
- C. b + 2c = 2a + d
- D. b - 2c = 2a - d Discuss
More questions
Correct Answer: 25 and 25
Explanation:
Total number of coins = 50
Let ? 1 coins = x and ? 2 coins = y
Now,according to the question,
x + y = 50 ... (i)
and x + 2y = 75 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 25 and y = 25
Correct Answer: 90
Explanation:
Let the number of gold coins initially be x and the number of non-gold coins be y.
According to the question, 3x = y .....(i)
When 10 more gold coins are added, then total number of gold coins becomes x + 10 and the number of non-gold coins remain the same as y.
Now,we have 2(10 + x) = y ....(ii)
On solving these two equations, we get x = 20 and y = 60
? Total number of coins in the collection at the end is equal to x + 10 + y = 20 + 10 + 60 = 90.
Correct Answer: Rs. 25
Explanation:
Let the original price of the book be Rs. x.
? Number of books bought for Rs.200 = 200/x
and reduced price of the book=Rs.(x - 5)
? Number of books bought for Rs.200 = 200/(x - 5)
Now, according to the condition,
200/(x - 5) - 200/x = 2
? (200x - 200x + 1000)/(x - 5)x = 2
? (200x - 200x + 1000)/x(x - 5) = 2
? 1000/x(x - 5) = 2
? 1000/x(x - 5) = 1
? 1000/x(x - 5) = 2
? 500/x(x - 5) = 1
? 500 = x(x-5)
? x2 -5x - 50 = 0
? x2- 25 + 20x - 500 = 0
? x(x - 25) + 20(x - 25) = 0
? (x - 25)(x + 20) = 0
? x - 25 = 0 or x + 20 = 0
? x = 25 0r -20
? x = 25 (since,x cannot be negatives)
So, the original price of the bok is Rs.25.
Correct Answer: 4
Explanation:
x3 + 1 + 2x = 6x + 1/x
x3 + 1 + 2x = (6x2 + 1) / x
(x3 + 1 + 2x)x = 6x22 + 1
x4 + x + 2x2 - 6x2 - 1 = 0
x4 - 4x2 + x - 1 = 0
Degree of polynomial is highest exponent degree term i. e., 4.
Correct Answer: ? 12
Explanation:
Let the length of the piece be L m.
Then,rate per metre = ? 120/L
New length = (L + 2) m
Since, the cost remains same.
? New rate per metre =Rs.120/(L + 2)
According to the given condition, 120/L - 120/(L + 2) = 2
? [120(L + 2) - 120L]/L(L + 2) = 2
? [120L + 240 - 120L] / L(L + 2) = 2
? [120L + 240 -120L] / L(L + 2) = 2
? 240/L(L + 2) = 2
? 240 = 2L(L + 2)
? 120 = L(L + 2) = L2 + 2L
? L2 + 2L - 120 = 0
? L2 + 12L - 10L - 120 = 0
? L(L + 12) - 10 x (L + 12) = 0
? (L + 12)(L - 10) = 0
? L + 12 = 0 or L - 10 = 0
? L = -12 or 10
? L = 10(since, L cannot be negative)
? Original rate per metre of cloth = 120/L = 120/10 = ? 12
Correct Answer: 100
Explanation:
Let Arjun had x arrows.
? x/2 + 6 + 3 + 4?x + 1 = x
? x = 20 + 8?x
? x - 20 =8?x
On squaring both sides and by solving the formed quadratics equation, we get x = 100
Correct Answer: Rs. 58
Explanation:
Let the cost of each apple,orange nd pear be Rs.x,y and z, respectively.Then,
2x + 3y + z = 62 ...(i)
5x + 6y + 4z = 20 ...(ii)
On subtracting Eq.(i)from Eq.(ii), we get
3x + 3y + 3z = 58
So, the cost of 3 apple,3 oranges and 3 pears is Rs. 58.
Correct Answer: -3, -4 and x2 + 7x + 12
Explanation:
When p is wrong i.e., -b/a = (? + ?) is wrong but c/a =(??) is correct.
Then ?? = c/a = 2 x 6 = 12 ....(i)
Again, when q is wrong i.e.,c/a = (?.? ) is wrong but -b/a = ?+? is correct.
Then, -b/a = ?+?= 2 + (-9) = -7
So, the required correct quadratic equations is
x2 -(? + ?)x + ?.?=0
? x2 - (-7)x + 12 = 0
? x2 + 7x + 12 = 0
and correct roots this equations are -3, -4.
Correct Answer: 32
Explanation:
The required greatest number is the HCF of 263-7, 935-7, 1383-7
i.e. 256, 928 and 1376 HCF = 32
Correct Answer: b + 2c = 2a + d
Explanation:
If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d
b + 2c = 2a + d
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