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…

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…

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…

The mean of the data x1, x2, x3, …………… x10 is 20 then the mean of (x1 + 4) , (x2 + 4) , (x3 + 4) , …………(x10 + 4) will be a) 20 b) 24 c) 40 d) 10 ( WBBSE – 2019 )

The mean of the data x1, x2, x3, …………… x10 is 20 then the mean of (x1 + 4) , (x2 + 4) , (x3 + 4) , …….(x10 + 4) will be a) 20 b) 24 c) 40 d) 10 Answer : b) 24 Explaination : Mean of the Read more…

Only one circle can be drawn through three non-collinear points. ( WBBSE – 2019 )

Write true or false : Only one circle can be drawn through three non-collinear points. Answer : True Explanatation : Through 3 non-collnear points, only one triangle can be drawn. Hence, only one circumcircle can be drawn. Therefore, the given statement is true.

O is the Centre of a Circle and AB a Diameter. ABCD is a Cyclic Quadrilateral. ∠ABC=65°, ∠DAC=40°, then the Measure of ∠BCD is ______. a)75° b)105° c)115° d)80°

O is te centre of a circle and AB a diameter ABCD is a cyclic quadrilateral. ∠ABC=65°, ∠DAC=40°, then the measure of ∠BCD is ______. a)75° b)105° c)115° d)80° Answer : 115° Explaination: Given: ∠ABC=65° ∠DAC=40° ∠BCD= ?? ∵ ∠ACB is angle in a semicircle. ∴ ∠ACB = 90° ∵ Read more…