Correct answer is option - 5
Explanation: Simplifying the given expression we get: 7x – 14 = 4x – 14 + 3x.
This gives: 7x – 14 = 7x – 14.
Subtracting 7x on both sides we get: 7x – 7x – 14 = 7x – 7x – 14.
This implies: -14 = -14.
The above statement is true always for any value of ‘x’ and hence the solution for ‘x’ is all real numbers.

Correct answer is option - 1
Explanation:The expression (a + b)² can be expanded according to its formula as: (a + b)² = a² + 2ab + b² and given a² + b² = 6 and (a + b)² = 36.Hence we get: (a + b)² = a² + 2ab + b² ==> 36 = 6 + 2ab.
This gives: 2ab = 36 – 6 ==> 2ab = 30 ==>ab = 30/2 ==>ab = 15.

Correct answer is option - 1
Explanation: The given expression can also be written as: √(1800/6) = √(300).
300 can be prime factorized as: 300 = 2 * 2 * 3 * 5 * 5
Hence √300 = √(2 * 2 * 3 * 5 * 5) ==> √300 = 10√3.

Correct answer is option - 2
Explanation: We can first simplify the denominator by taking the common denominator between them.
This gives: (1/5 – 1/k) = (k – 5)/ 5k.
Now writing the whole expression together, we get: 3/ [(k – 5)/ 5k].
We should take the reciprocal here, which gives: (3 * 5k)]/ (k – 5) ==> 15k/ (k – 5).
Since given k = 8, we get: (15 * 8)/ (8 – 5) = (15 * 8)/ 3 ==> 40.

Correct answer is option - 1
Explanation: Considering the order of operations, multiplication comes first and then subtraction follows.
Therefore we get: 10 – 6 - |8| + |-4| ==> 4 - |8| + |-4|.
The absolute value of any number is a positive number.
Hence we get: 4 – 8 + 4 = 8 – 8 = 0.
 
 

Correct answer is option - 4
Explanation: Given the length of the rectangle, l = 12cm
Width is one-fourth the length, w = 1/4 * 12cm = 3cm.
Altitude of the triangle = width of the rectangle = 3cm.
From the figure, the base of the triangle is on the length of the rectangle.
Area of the triangle, A = 1/2 * base * height = 1/2 * 12 * 3 = 18 cm².

Correct answer is option - 4
Explanation: In a triangle, the exterior angle is always equal to the sum of interior opposite angles.
This gives the measure of angle ZXM = angle XYZ + angle YZX.
This implies: angle ZXM = 110° + 25° = 135°.
(Or) An alternate method is to consider that the sum of the angles in a triangle is 180° and therefore find the third angle.
Since XY is straight line, subtracting the third angle from 180° gives the exterior angle!