If a2 + b2 + c2 = 2 (a - b - c) - 3, then the value of 2a - 3b + 4c is
3
1
2
4
B.
1
a2 + b2 + c2 = 2 (a - b - c) - 3
⟹ (a2 - 2a + 1) + (b2 + 2b + 1) + (c2 + 2c + 1) = 0
⟹ (a - 1)2 + (b + 1)2 + (c + 1)2 = 0
∴ a - 1 = 0, b + 1 = 0, c + 1 = 0
⟹ a = 1, b = -1, c = -1
∴ 2a - 3b + 4c = 2(1) - 3(-1) + 4(-1) = 1
The area of the triangle formed by the lines 5x + 7y = 35, 4x + 3y = 12 and x-axis is
160/13 sq units
150/13 sq units
140/13 sq units
10 sq units
In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocentre. If ∠BOC = 54°, then ∠BAC is
108°
126°
136°
116°
If the ratio of area of two similar triangles is 9 : 16, then the ratio of their corresponding sides is
3 : 5
3 : 4
4 : 5
4 : 3
Let BE and CF be the two medians of a Δ ABC and G be their intersection. Also let EF cut AG at O. Then, AO : OG is
1 : 1
1 : 2
2 : 1
3 : 1
If S is the circumcentre of Δ ABC and ∠A = 50° then the value of ∠BCS is
20°
40°
60°
80°
AC and BC are two equal chords of a circle. BA is produced to any point P and CP, when joined cuts the circle at T. Then,
CT : TP = AB : CA
CT : TP = CA : AB
CT : CB = CA : CP
CT : CB = CP : CA