Discussion
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- Question
- If ax + by = 6, bx ? ay = 2 and x 2 + y 2 = 4, then the value of ( a 2 + b 2) would be :
Options- A. 10
- B. 2
- C. 4
- D. 5
- Correct Answer
- 10
ExplanationAs we know that given in question,
ax + by = 6 ........................ (i)
bx ? ay = 2 ........................ (ii)
On squaring the both equation and adding,
a2 x2 + b2 y2 + 2abxy + b2 x2 + a2 y2 ? 2abxy = 36 + 4
? x2 (a2 + b2) + y2 (a2 + b2) = 40
? (a2 + b2) (x2 + y2) = 40
As per given question, x2 + y2 = 40 , Put this value in above equation, we will get
? (a2 + b2) × 4 = 40
? a2 + b2 = 10 - 1.
If a + 1 = 1, then the value of a3 is : a
Options- A. ? 2
- B. 2
- C. ? 1
- D. 4 Discuss
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. In xy?plane, P and Q are two points having co? ordinates (2, 0) and (5, 4) respectively. Then the numerical value of the area of the circle with radius PQ is
Options- A. 16 ?
- B. 32 ?
- C. 14 ?
- D. 25 ? Discuss
- 7. In the xy?coordinate system, if ( a, b) and ( a + 3, b + k) are two points on the line defined by the equation x = 3y ? 7, then k =?
Options- A. 7 3
- B. 1
- C. 9
- D. 3 Discuss
- 8.
If a = ? 3 - ? 2 , b = ? 3 + ? 2 , then the value of ?3 + ?2 ?3 - ?2 a 2 + b 2 is : b a
Options- A. 900
- B. 970
- C. 1030
- D. 930 Discuss
- 9. Area of the trapezium formed by x-axis; y-axis and the lines 3x + 4y = 12 and 6x + 8y = 60 is:
Options- A. 37.5 sq. unit
- B. 31.5 sq. unit
- C. 48 sq. unit
- D. 36.5 sq. unit Discuss
- 10. If x = 1 + ?2 + ?3, then the value of ( 2x4 ? 8x3 ? 5x2 + 26x ? 28) is
Options- A. 6 ?6
- B. 0
- C. 3 ?6
- D. 2 ?6 Discuss
Elementary Algebra problems
Search Results
Correct Answer: ? 1
Explanation:
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
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: 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: 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: 25 ?
Explanation:
According to question ,
PQ = ?( 5 - 2 )2 + ( 4 - 0 )2
PQ = ?9 + 16 = 5
? Area of circle = ?r2
Area of circle = 25 ? sq. units
Correct Answer: 1
Explanation:
Given in the question,
Points (a, b) and [(a + 3), (b + k)] will satisfy the equation x ? 3y + 7 = 0.
Points (a, b) in the equation x ? 3y + 7 = 0, We will get
? a ? 3b + 7 = 0 ...................... (i)
Points (a + 3), (b + k) in the equation x ? 3y + 7 = 0, We will get
a + 3 ? 3 (b + k) + 7 = 0
? a + 3 ? 3b ? 3 k + 7 = 0 (Rearrange the equation)
? a ? 3b + 7 + 3 ? 3 k = 0 (a ? 3b + 7 = 0 , Put the value from Equation (1) ), We will get
? 0 + 3 ? 3k = 0
? 3k = 3
? k = 1
Correct Answer: 970
Explanation:
Correct Answer: 31.5 sq. unit
Explanation:
Correct Answer: 6 ?6
Explanation:
Given in the question ,
x - 1 = ?2 + ?3
On squaring both sides ,
x 2 ? 2x + 1 = 2 + 3 + 2?6
? x 2 - 2x - 4 = 2 ?6
On squaring again,
? x4 + 4x2 + 16 ? 4x3 ? 8x2 + 16x = 24
? x4 ? 4x3 ? 4x2 + 16x ? 8 = 0
? 2x4 ? 8x3 ? 8x2 + 32x ? 16 = 0
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 ? 3x2 + 6x + 12 = 0
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3x2 ? 6x ? 12
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3 (x2 ? 2x ? 4)
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3 x 2?6 = 6 ?6
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