Simplification Questions

• If p/q = (x+3)/(x-3), then what is the value of p2+q2p2-q2 ?
• What is the simplified value of (1– sin A cos A)(sin A + cos A)?
• What is the simplified value of 1-sin A1+sin A ?
• What approximate value should come in place of the question mark (?) in the following questions? (You are not expected to calculate the exact value.) 21.003 × 39.998 –209.91 = 126× ?
• What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? [(7.99)2–(13.001)2+(4.01)3]2=?
• In the given questions, two equations numbered I and II are given. Solve both the equation and mark the appropriate answer. I. x2–5x –24 = 0II. 2y2+ 19y + 35 = 0
• For what value of k, the expression x6– 18x3 + k will be a perfect square?
• If 5+x+5-x5+x-5-x = 3 ,then what is the value of x ?
• If x = 4aba+b , then what is the value of x+2ax-2a+x+2bx-2b ?
• In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?
• P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?
• If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ ?
• If tan2θ + cot2θ = 2 , then what is the value of 2sec θ cosec θ ?
• The value of (0.3)2/100= ?
• If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2 ?
• If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3] ?
• If x2+ y2+ z2= xy + yz + zx , then what is the value of (7x + 3y – 5z)/5x?
• If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?
• What is the value of sin (–π/3) + cos(–π/6)?
• If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ ?