## The length, breadth and height of a cuboid of a room be a unit, b unit and c unit respectively and a + b + c = 25, ab + bc + bc = 240.5 then find the length of the longest rod to be kept inside the room. ( WBBSE – 2019 )

The length, breadth and height of a cuboid room be a unit, b unit and c unit respectively and a + b + c = 25, ab + bc + bc = 240.5 then find the length of the longest rod to be kept inside the room. Solution : The Read more…

## If sin 10θ = cos8θ and 10θ is a positive acute angle, then find the value of tan9θ. ( WBBSE – 2019 )

If sin 10θ = cos8θ and 10θ is a positive acute angle, then find the value of tan9θ. Solution : sin 10θ = cos8θ [ ∵ sin ( 90 – θ ) = cos = θ ] ⇒ sin 10θ = sin ( 90 – 8θ ) ⇒ 10θ = Read more…

## Find the values of (0° ≤ θ ≤ 90° ) for which 2 sinθ cosθ = cosθ. ( WBBSE – 2019 )

Find the values of (0° ≤ θ ≤ 90° ) for which 2 sinθ cosθ = cosθ. Solution : 2 sinθ cosθ = cosθ ⇒ 2 sinθ cosθ – cosθ = 0 ⇒ cosθ ( 2 sinθ – 1 ) = 0Either cosθ = 0 ⇒ cosθ = cos90° ( Read more…

## If ( a / 2 ) = ( b / 3 ) = ( c / 4 ) = ( 2a – 3b + 4c ) / ( p ), then find p. ( WBBSE – 2019 )

If ( a / 2 ) = ( b / 3 ) = ( c / 4 ) = ( 2a – 3b + 4c ) / ( p ), then find p. Given : ( a / 2 ) = ( b / 3 ) = ( c / Read more…

## In a partnership business the ratio of capitals of three men is 3 : 5 : 8 . The share of profit of the first member is Rs. 60 less then that of the third member, then what is the total profit in the business ? ( WBBSE – 2019 )

In a partnership business the ratio of capitals of three men is 3 : 5 : 8 . The share of profit of the first member is Rs. 60 less then that of the third member, then what is the total profit in the business ? solution : ∵ Capital Read more…

## Find the capital which gives Rs. 1 as interest per month at 5 % rate of interest per annum.

Question : Find the capital which gives ₹ 1 as interest per month at 5 % rate of interest per annum. solution : Interest ( I ) = ₹ 1 Time ( T ) = 1 month = 1 / 12 years Rate ( R ) = 5 % Principal Read more…

## The difference between the simple interest the compound interest of Rs.100 in 1 year at the rate of 10% p.a is Rs.1.

The different between the simple interest the compound interest of ₹100 in 1 year at the rate of 10% p.a is Rs.1. Answer : False Explanation : Principle (P) = ₹ 100 Rate of interest (R) = 10% Time (T) = 1 year Simple interest ( S.I ) = PRT/100 Read more…

## The compound ratio of ab :c2, bc : a2 and ca : b2 is 1:1.

The compound ratio of ab :c2, bc : a2 and ca : b2 is 1:1. Answer : True Explanation : The given ratios are ab :c2 bc : a2 ca : b2 Compound Ratio of the given ratios = ( ab × bc × ca ) : ( c2 × Read more…

## If the product and sum of two quadratic surds is a rational number then surds are _______ surd. ( WBBSE – 2019 )

If the product and sum of two quadratic surds is a rational number then surds are _______ surd. Answer : Complementary or conjugate . Explanation : Let us consider that { √a + b) } and { -√a + b) } are two quadratic surds, where ‘a’ and ‘b’ are Read more…

## A person deposited Rs. 100 in a bank and gets the amount Rs. 121 after two years . The rate of the compound interest is _______ % . ( WBBSE – 2019 )

A person deposited ₹ 100 in a bank and gets the amount ₹ 121 after two years . The rate of the compound interest is ______% . Answer : 10% Explatation : Principal (P) = ₹ 100 Amount (A) = ₹ 121 Time (T) = ?? According to problem, A = P Read more…