1. If a, b and c are positive integers, then (a – b – c)3 – a3 + b3 + c3 is always divisible by
2. In the following figure, if ABC and BDC are two triangles, then x + y + z equals
3. If the graph of the linear equation 24x + 7y = 168 cuts the x-axis and y-axis at A and B respectively, then length of AB is equal to
4. If (x 2 – 1) is a factor of ax 198 + bx 195 + cx 192 + dx 187 + e, where a, b, c, d and e are non-zero integers, then
5. In ∆ABC, AD and AE are respectively bisector of ∠A and perpendicular on BC. If ∠EAD = 10° and ∠ABC : ∠ACB = 2 : 1, then ∠ACB equals
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8. A linear equation 7x + 11y = 77 (where x and y are natural numbers) have
9. If a = 62, b = 66 and c = 68, then the value of (a 2 + b 2 + c 2 – ab – bc – ca) is
10. A shopkeeper mixed two varieties of sugar costing ₹45/kg and ₹54/kg so that the mixture costs ₹50/kg. If he mixes 12 kg of sugar costing ₹45/kg, then the quantity of sugar costing ₹54/kg that he mixes is (in kg)
11. In ΔABC, O is the point of intersection of altitudes from vertex A and B and I is the point of intersection of bisectors of ∠A, ∠B and ∠C. If ∠A : ∠B : ∠C = 3 : 4 : 2, then ∠IAO is
12. If (2 a – 4) 3 + (4 a – 2) 3 = (4 a + 2 a – 6) 3, then the greatest value of a (where 2 a + 4a≠ 6) is
13. The sum of the digits of product 22021 52024 is
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15. If P(5, –2) and R(–5, 2) are the coordinates of the opposite vertices of a rectangle PQRS, then the coordinates of the vertex Q and S can be
