Tech Mahindra Equations (Linear & Quadratic) Quiz 1

Ans. B
Solution:
X (X + 2) = 4623
X² + 2X – 4623 = 0
X² + 69X – 67X – 4623 = 0
(X - 67)(X + 69) = 0
X = 67, Greater odd number = X + 2 => 67 + 2 = 69

Ans. A
Solution: (X + 5X)/(Y + 3Y) = 18/17
= > X/Y = 12/17

Ans. B
Solution: 10X + Y – (10Y + X) = 63
9X – 9Y = 63
X – Y = 7
X + Y = 11
Solving these equations, we get
X = 9, Y = 2
Required number = 10X + Y
=> 10 * 9 + 2 = 92

Answer: Both the packets have same value
Solution:
Packet A costs:
100gm = 48 rs
1gm = 48/100
1000gm = (48/100)*1000 = 480 rs

Packet B costs:
150gm = 72 rs
1gm = 72/150
1000gm = (72/150)*1000 = 480 rs

For x= -2
First curve have the value y= 1 (-2,1)
Second curve have the value y = 7 ( -2,7)
For x= -1
First have (-1,5)
Second have ( -1,5)
For x = 0
First have (0,5)
Second have (0,5)
For x= 1
First have (1,7)
Second have (1,7)
So from the points it can be found that curve intersect at 3 points.
Correct Answer : B

x + \frac{1}{x} = 4x^{3}+\frac{1}{x^{3}} = 52

Multiplying both side by x^{2} + \frac{1}{x^{2}}

\left (x^{3} + \frac{1}{x^{3}} \right ) \left(x^{2} + \frac{1}{x^{2}} \right) = 52 \left(x^{2} + \frac{1}{x^{2}} \right)

x^{5}+x+\frac{1}{x^{5}} +\frac{1}{x} = 52 \times 14x^{5}+\frac {1}{x^{5}} +4=728

x^{5} + \frac{1}{x^{5}}=728-4=724

Correct Answer : A

Let the number be x. Then (x – 5)/7 = 10 ⇒ x = 75. When 5 is subtracted from 75, we get 70.
Also when 70 is divided by 8, the remainder is 6.

Answer: 48

Explanation: x = 12 , Y = 4
(x+y)x/y = (12+4)*12/4
= 48

Answer: 7, 5

Explanation: 6x + y = 47 - Equation 1
X + 6y = 37 - Equation 2
From equation 1 and 2 we get
x - y = 2
So, x = 7, y = 5

Discriminant = b² - 4ac

Given that a = 2k, b = 5k, c = 2

b² - 4ac = 0

(5k)² - 4(2k)(2) = 0

25k² - 16k = 0

k(25k - 16) = 0

k = 0 or 25k - 16 = 0

k = 0 or k = 16/25

Answer: k = 0 or k = 16/25

Correct Answer : B