The value of   $${cosθ+sin^6θ+3sin^2θ \ cos^2θ}\over cosecθsecθ(sinθ+cosθ-1)(sinθ+cosθ+1) $$

A person has to cover a distance of 160 km in 15 hours. If he covers $${4\over 5}$$ of the distance in $${2\over 3}$$  of the time, then what should be his speed (in km/h) to cover the remaining distance in the remaining time?

If the 5-digit number 535ab is divisible by 3, 7 and 11, then what is the value of (a² - b² + ab)?

A person divided a certain sum between his three sons in the ratio 3:4: 5. Had he divided the sum in $${1\over 3}:{1\over 4}:{1\over 5}$$ the ratio: the son, who got the least share earlier, would have got ₹1,188 more. The sum (in) was:

In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at the point C on it. If ∠BPT = 36°, then what is the measure of ∠BCP?

If 15x² – 26x + 8 = (Ax + B) (Cx + D), where A and C are positive integers, then what is the value of (2A + B – C – 2D) ?

P = 12xy – 10y² – 18x²,

Q = 14x² + 12y² + 9xy, and

R = 5y² – x² + xy

then (P + Q) – R =

If a + b + c = 6, a³ + b³+c³-3abc=342, then what is the value of ab + bc + ca?