The length of the base of an isosceles triangle is 2x - 2y + 4z, and its perimeter is 4x - 2y + 6z. Then the length of each of the equal sides is:
x + y
x + y + z
2(x + y)
x + z
Visitors to a show were charged â¹ 15 each on the first day, â¹ 7.50 on the second day, â¹ 2.50 on the third day and total attendance on three days were in the ratio 2 : 5 : 13 respectively. The average charge per person for the entire three day is
â¹ 5
â¹ 5.50
â¹ 6
â¹ 7
If and xyz = -1, then x3 + y3 + z3 is equal to:
-1
1
-2
2
B.
1
x + y + z = 1
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
1 = x2 + y2 + z2 + 2(-1)
x2 + y2 + z2 = 1 + 2 = 3
x3 + y3 + z3 - 3xyz = (x + y + z) [x2 + y2 + z2 - (xy + yz + zx)]
x3 + y3 + z3 - 3(-1) = 1[3 -(-1)]
x3 + y3 + z3 + 3 = 3 + 1
∴ x3 + y3 + z3 = 4 - 3 = 1
In Δ PQR, L and M are two points on the sides PQ and PR respectively such that LM || QR. If PL = 2 cm, LQ = 6 cm and PM = 1.5 cm, then MR in cm is
0.5
4.5
9
8
The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is
2 cm
3 cm
4 cm
15 cm
The upper part of a tree broke at a certain height makes an angle of 60° with the ground at a distance of 10 m from its feet. The original height of the tree was
20√3 m
10√3 m
10(2 + √3) m
10(2 - √3) m
What would be the compound interest of â¹ 25,000/- for 2 years at 5% per annum?
â¹ 2,500
â¹ 2,562.5
â¹ 2,425.25
â¹ 5,512.5