In the given figure AD : DC = 3 : 4 then find the value of ∠ABC :
-
Solution
∴
So BD is angle bisector of ∠ABC
∴ ∠ABC = 2 × [180 – 140 – 20] = 40°
If = 727 then find the value of :
-
Solution
x4 + = 727 + 2
⇒
⇒
⇒ x –
∴
⇒ x3 –
If (a + b + c) = 0 then find the value of :
-
Solution
a + b + c = 0
⇒ a + b = – c
⇒ b + c = – a
⇒ a + c = – b
∴
If sin θ + sin2θ = 1 then find the value of cos2θ + cos4θ = ?
-
Solution
sin θ + sin2 θ = 1
sin θ = 1 – sin2 θ = cos2 θ
∴ cos2θ + cos4θ = cos2θ + sin2θ = 1
If , then find the value of x3 +
-
Solution
⇒ x +
Taking cube
⇒
⇒ x3 +
⇒ x3 + = 322
If the marked price of a article is 40% more than the cost price and a discount of 20% is gives on it, then the percentage profit is-
-
Solution
Let the cost price is Rs. 100
∴ Marked price = Rs. 140
Discount = = Rs. 28
∴ Selling Price = 140 – 28 = Rs. 112
∴ % profit = 112 – 100 = 12%
Each interior angle of a regular polygon is 156°. Find the value of its each exterior angle-
-
Solution
Let number of sides in polygon is n.
∴
n = 15
∴ Exterior Angle =
When a wire is bent in the form of a square, the area so enclosed in is 484 sq. m. what will be the area enclosed by wire when it is bent in the form of a circle?
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Solution
Side of square = = 22 m
∴ Perimeter of square or length of wire = 4 × 22 = 88 m
∴ radius of circle = m
∴ area of circle = m2
A borrowed Rs. 1720 for 4 years at the rate of simple interest 5% per annum. What will be the annual payment to discharge the debt?
-
Solution
Installment = = Rs. 400
If = 3. then the value of (sin4 θ – cos4 θ) is-
-
Solution
sin4θ – cos4 θ = (sin2θ – cos2θ) (sin2θ + cos2θ)
sin4θ – cos4 θ = (sin2θ – cos2θ)
Now
⇒ sin θ + cos θ = 3 sin θ – 3 cos θ
⇒ tan θ = 2
∴ sin θ = , cos θ =
∴ sin4 θ – cos4 θ =