The rationalising factor of sqrt(5) + sqrt(3) is:

1. The rationalising factor of sqrt(5) + sqrt(3) is: Step 1: Identify the expression to be rationalized. The expression is sqrt(5) + sqrt(3). Step 2: Determine the rationalizing factor. For an expression of the form sqrt(a) + sqrt(b), its rationalizing factor is sqrt(a) - sqrt(b). Therefore, the rationalizing factor of sqrt(5) + sqrt(3) is sqrt(5) - sqrt(3). The correct option is A. A) sqrt(5) - sqrt(3) 2. In a cricket match two batsmen together scored 181 runs. The linear equation form for the statement is: Step 1: Define variables for the runs scored by each batsman. Let x be the runs scored by the first batsman. Let y be the runs scored by the second batsman. Step 2: Formulate the equation based on the given information. "Two batsmen together scored 181 runs" means the sum of their runs is 181. So, x + y = 181. The correct option is C. C) x + y = 181 3. In a parallelogram, if the adjacent angles are in the ratio 2:3, then the measure of these adjacent angles are: Step 1: Recall the property of adjacent angles in a parallelogram. Adjacent angles in a parallelogram are supplementary, meaning their sum is 180^. Step 2: Set up an equation based on the given ratio. Let the adjacent angles be 2k and 3k. 2k + 3k = 180^ Step 3: Solve for k. 5k = 180^ k = (180^)/(5) k = 36^ Step 4: Calculate the measure of each angle. First angle: 2k = 2 × 36^ = 72^ Second angle: 3k = 3 × 36^ = 108^ The correct option is B. B) 72^ and 108^ 4. If the radius of a sphere is 2r, then its volume will be: Step 1: Write down the formula for the volume of a sphere. The volume V of a sphere with radius R is given by: V = (4)/(3) R^3 Step 2: Substitute the given radius into the formula. Given radius R = 2r. V = (4)/(3) (2r)^3 Step 3: Simplify the expression. V = (4)/(3) (2^3 r^3) V = (4)/(3) (8 r^3) V = (4 × 8)/(3) r^3 V = (32)/(3) r^3 The correct option is D. D) (32)/(3) r^3