The average of the runs made by Raju, Shyam and Hari is 7 less than that made by Shyam, Hari and Kishore. If the number of Kishore's run is 35, what is Raju's run?
21
35
7
14
A starts business with ₹ 7000 and after 5 months, B joined as a partner. After a year the profit is divided in the ratios 2 : 3. The capital of B is
₹ 10000
₹ 6500
₹ 18000
₹ 9000
A grain dealer cheats to the extent of 10% while buying as well as selling by using false weights. His total profit percentage is
21
23
25
20
If x sin3θ + y cos3θ = sin θ cos θ ≠ 0
and x sin θ - y cos θ = 0, then the value of (x2 + y2) is
sin θ - cos θ
sin θ + cos θ
0
1
D.
1
Given, x sin3θ + y cos3θ = sinθ cos θ ...(i)
and x sin θ - y cos θ = 0
or x sin θ = y cos θ ...(ii)
Put the value of eq (ii) in eq (i),
y cos θ . sin2θ + y cos3θ = sin θ cos θ
y cos θ (sin2 θ + cos2θ) = sin θ cos θ
⟹ y = sin θ
Put the value of y = sin θ in eq (ii), we get
x = cos θ
∴ x2 + y2 = sin2 θ + cos2 θ = 1
The radius of a circle is 13 cm and xy is a chord which is at a distance of 12 cm from the centre. The length of the chord is
12 cm
10 cm
20 cm
15 cm