?. 2x ² + 11x + 14 = 0
?. 4y ² + 12y + 9 = 0

According to question ,we have
From equation ?. x² = 729
? x = ± ?729 = ± 27
From equation ?. y = ?729
? y = 27
Hence , x ? y is required answer .

According to question ,we have
From equation ?. x² ? 4 = 0
? x = ± 2,
From equation ?. y² + 6y + 9 = 0
? ( y + 3 )² = 0
? ( y + 3 )( y + 3 ) = 0
? y + 3 = 0 ? y = -3 , -3
Clearly , x > y is required answer .

Let, the two natural consecutive odd numbers be n and (n + 2)
Now, according to the question,
? n² + ( n + 2 )² = 394
? n² + n² + 4 + 4n = 394
? 2n² + 4n - 390= 0
? n² + 2n - 195 = 0
? n² + 15n - 13n - 195 = 0
? n( n + 15 ) - 13( n + 15 ) = 0
? ( n + 15 ) ( n - 13 ) = 0
? n = 13 and n ? - 15
? The two natural consecutive odd numbers be 13 and (13 + 2) = 15 .
? the sum of the numbers = 13 + 15 = 28
Quicker Approach:
By mental operation, 13² + 15² = 169 + 225 = 394
? Required sum = 13 + 15 = 28

According to question ,we can say that
Let , x = ?30 + ?30 + ?30 +........
On squaring both sides, we have
x² = 30 + ?30 + ?30 + ?30 +........
? x² = 30 + x ? x² - x - 30 = 0
? x² - 6x + 5x - 30 = 0
? x( x - 6 ) + 5( x - 6 ) = 0
? ( x - 6 ) ( x + 5 ) = 0
? x = 6 because x ? - 5
Hence , required answer is 6 .

As per the given above equations , we have
From equation ?. x² - 7x + 12 = 0
? x² - 4x - 3x + 12 = 0
? x( x - 4) - 3( x - 4) = 0
? ( x - 4) ( x - 3) = 0
? x = 4 or, 3
?. y² - 12y + 32 = 0
? y² - 8y - 4y + 32 = 0
? y( y - 8) - 4( y - 8) = 0
? ( y - 8) ( y - 4) = 0
? y = 4 or, 8
Thus , x ? y is required answer .

Given that :- Given that :- ?. 5x + 2y = 31 .....( 1 )
?. 3x + 7y = 36 .....( 2 )
Solving these two linear equations, we get x = 5, y = 3 .
? x > y is correct answer .

According to question , we can say that
The equation x² ? px + q = 0, p, q ? R has no real root
On comparing with quadratic eq. Ax² + Bx + C = 0 , we get
? A =1, B= - p, C = q
Now ,we have B² < 4AC
? ( - P )² < 4 x 1 x q
? p² < 4q.
Hence , option B is correct answer .

The given quadratic equation 3x² + (k ? 1)x + 9 = 0
Putting x = 3 in above given eq. , we get
27 + 3(k ? 1) + 9 = 0
? 27 + 3k - 3 + 9 = 0
? 3k = ?33 ? k = ?11.
Hence , the value of k is ?11.