Correct answer is option - 4

Correct answer is option - 1
Explanation: Squaring the given equation on both sides gives: [√(4x + 9)]² = 3² ==> 4x + 9 = 9.
Solving for ‘x’, subtract 9 on both sides: 4x + 9 - 9 = 9 – 9.
This gives: 4x = 0 ==> x = 0/4 = 0.
But before we confirm it is important to check if it is an extraneous solution.
Plug-in x = 0 in the expression: √ (4*0 + 9) = √(0 + 9) = √9 = 3. The answer is verified!
Hence the value of x = 0.

Correct answer is option - 1
Explanation:According to the ‘Difference of Squares’ formula: a² – b² = (a + b) (a – b).
Similarly, p² – q² = 5 ==> (p + q) (p – q) = 5.
If given (p – q) = 5, then (p + q) * 5 = 5 ==> (p + q) = 5/5 = 1.
Hence the value of (p + q) = 1.

Correct answer is option - 2
Explanation: In a parallelogram, the opposite angles are congruent to each other.
This implies that the measure of angle ABC = angle ADC, and similarly angle BAD = angle BCD.
Therefore we can say that: 3x – 11 = 2x + 13 ==> 3x – 2x = 13 + 11.
This gives: x = 24.
Hence the measure of the angle ABC = 3x – 11 = (3*24 – 11) = 61°
 

Correct answer is option - 3
Explanation: The given polynomial, 3x² – 4x – 7 can be also written as 3x² + 3x – 7x – 7.
Grouping and taking the common factor out from the first two terms and the last two terms, we get: 3x (x + 1) – 7 (x + 1).
This gives: (x + 1) (3x – 7)
Since (x + 1) is not in the options, hence (3x – 7) is the answer!

Correct answer is option - 5
Explanation: According to the trigonometric identity: sin²(θ) + cos²(θ) = 1.
Since sin(θ) = 0.8, using the above identity we get: (0.8)² + cos²(θ) = 1.
This gives: cos²(θ) = 1 – 0.64 = 0.36. This implies cos(θ) = √0.36 = 0.6.
In the first quadrant both sin(θ) and cos(θ) are positive, therefore the above answers verify it.
Hence the value of sin(θ) + cos(θ) = 0.8 + 0.6 = 1.4

Correct answer is option - 4
Explanation: 15² = 225, and hence the given expression can also be written as: √-(225).
This gives: √ [(-1) * (225)] = √-1 * √225 = i * 15.
Hence the answer is 15i.