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- Question
If, a + b + c = 0, the value of ( a 2 + b 2 + c 2 ) is bc ca ab
Options- A. 2
- B. 3
- C. 4
- D. 5
- Correct Answer
- 3
Explanation
- 1. If x = 997, y = 998, z = 999, then the value of x2 + y 2 + z 2 ? xy ? yz ? zx will be
Options- A. 3
- B. 9
- C. 16
- D. 4 Discuss
- 2. If the distance between two points (0,?5) and (x,0) is 13 unit, then x =
Options- A. 10
- B. ± 10
- C. 12
- D. ± 12 Discuss
- 3. Area of the triangle formed by the graph of the line 2x ? 3y + 6 = 0 along with the coordinate axes is:
Options- A. 1 sq. units 2
- B. 3 sq. units 2
- C. 3 sq. units
- D. 6 sq. units Discuss
- 4.
If ?0.03 x 0.3 a = 0.03 x 0.3 x ? b then value of a is b
Options- A. 0.009
- B. 0.9
- C. 0.09
- D. 0.08 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. The equation of this graph is
Options- A. y = ? x
- B. y = ? 3x
- C. y = x
- D. y = 3x Discuss
- 7. 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
- 8. 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
- 9. 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
- 10. If a + b + 1 = 0, then the value of (a 3 + b 3 + 1 ? 3ab) is
Options- A. 3
- B. 0
- C. ?1
- D. 1 Discuss
Elementary Algebra problems
Search Results
Correct Answer: 3
Explanation:
Correct Answer: 12
Explanation:
According to question , we have
?( x - 0 )2 + ( 0 + 5 )2 = 13
? x2 + 25 = 169
? x2 = 169 - 25 = 144
? x = ?144 = 12
Correct Answer: 3 sq. units
Explanation:
Correct Answer: 0.9
Explanation:
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: y = 3x
Explanation:
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: 0
Explanation:
As we know from the formula,
A3 + B3 + C3 = ( A + B + C) (A2 + B2 + C2 ? AB ? BC ? CA) + 3ABC
If A + B + C = 0 then,
A3 + B3 + C3 = 0 x (A2 + B2 + B2 ? AB ? BC ? CA) + 3ABC
A3 + B3 + C3 = 0 + 3ABC
A3 + B3 + C3 - 3ABC= 0
As we know that from given question,
A = a, B = b and C = 1, Put these value in above equation, we will get
a3 + b3 + 13 - 3 x a x b x 1 = 0
a3 + b3 + 1 - 3ab = 0
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