Question
In a ∆ABC, points P, Q and R are taken on AB, BC and
CA, respectively, such that BQ = PQ and QC = QR. If ∠ BAC = 75°, what is the measure of ∠ PQR (in degrees)?Solution
∠BAC = 75º ∠ABC + ∠ACB + ∠BAC = 180° ∠ABC + ∠ACB + 75° = 180° ∠ABC + ∠ACB = 180° - 75° = 105° Let, ∠ABC = ∠PBQ = 70° and ∠ACB = ∠RCQ = 35° So, ∠PQR = 180° - (∠PQB + ∠RQC) = 180° - [(180° - 2∠PBQ) + (180° - 2∠RQC) [∵ BQ = PQ; QC = QR] = 180° - [(180° - 2 × 70°) + (180° - 2 × 35°)] = 180° - (40° + 110°) = 180° - 150° = 30°
I. 8x² + 2x – 3 = 0
II. 6y² + 11y + 4 = 0
Quantity I: The price of rice is decreased by 30%, by how much % the consumption is increase so that the expenditure will decreased by 10%?
Quant...
I. 4 x ² - 4 x + 1 = 0
II. 4 y ² + 4 y + 1 = 0
...I. 27(p + 2) = 2p(24 – p)
II. 2q2 – 25q + 78 = 0
I. 35x² + 83x + 36 = 0
II. 42y² + 53y + 15 = 0
What are the coordinates of the point which divides the line joining (-1, 7) and (4, 3) in the ratio 2:3?
I. 49y2 + 35y + 6 = 0
II. 12x2 + 17 x + 6 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 42x + 392 = 0
Equation 2: y² - 46y + 480 = 0
I. 4x2 + 25x + 36 =0
II. 2y2 + 5y + 3 = 0
I. (x13/5 ÷7) = 5488 ÷ x7/5
II. (y2/3 × y2/3 ) ÷ √4 = (343y)1/3...
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