Elementary Algebra problems
- 1. The sum of the squares of two numbers is 234 and the square of their difference is 144. Find the product of the two numbers?
Options- A. 28
- B. 52
- C. 36
- D. 45 Discuss
Correct Answer: 45
Explanation:
Let the two numbers be x and y.
Then, x2 + y2 = 234 ...(i)
and (x - y)2 = 144 ...(ii)
Now, (x - y)2 = 144
? x2 + y2 - 2xy = 144
? 234 - 2xy = 144 [using Eq.(i)]
On substituting the value of x2 + y2 from Eq.(i) in Eq.(ii),
we get
2xy = 90
? xy = 45
So, the product of the two numbers is 45.
- 2. The degree of polynomial p(x) = x 3 + 1 + 2x = 6x + 1/x is?
Options- A. 2
- B. 4
- C. 3
- D. 5 Discuss
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.
- 3. 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
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
- 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
Correct Answer: 0.9
Explanation:
- 5. 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
Correct Answer: 3 sq. units
Explanation:
- 6. 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
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
- 7. 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
Correct Answer: 3
Explanation:
- 8.
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 Discuss
Correct Answer: 3
Explanation:
- 9. The equation of this graph is
Options- A. y = ? x
- B. y = ? 3x
- C. y = x
- D. y = 3x Discuss
Correct Answer: y = 3x
Explanation:
- 10. 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
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
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