Math

A01-A-11(English Version) Part- I1. If the co-ordinate of the orthocenter and the co-ordinate of the centroid of a triangle are (భఱర,భఱర) and (ఴయ,ఴయ) respectively then co-ordinate of circumcentre isA) (భళర,భళర) B) (భళఴ,భళఴ) C) (భళభల,భళభల) D) (భళయమ,భళయమ)2. The number of common tangent of the circles ݔݕ + ଶଶ − 6ݔ − 2ݕ + 9 = 0 and ݔݕ + ଶଶ − 14ݔ − 8ݕ + 61 =0 will be A) 2 B) 3 C) 1 D) 43. The focus of the parabola ݕ = 2ݔଶ + ݔ will beA) (0,0) B) (−భర,଴) C) (భమ,భర) D) (−భర,భఴ)= ߚ + ߙ If. 4గଶ= ߙ tan then ߙ = ߜ + ߚ andA) 2(tanߚ + tan ߜ (B) (tan ߚ + tan ߜ(C) (tan ߚ + 2 tan ߜ (D) (2 tan ߚ + tan ߜ(5. In triangle ABC, 2ܽܿ sin(ಲషಳశ಴మ) =A) ܽଶ + ܾଶ − ܿଶ B) ܿଶ + ܽଶ − ܾଶ C) ܾଶ − ܿଶ − ܽଶ D) ܿଶ − ܽଶ − ܾଶ6. If arg(ݖ > (0 then arg(−ݖ − (arg (ݖ (will beA) −గଶB) గଶߨ− (D ߨ (C7. The number of irrational terms in the expansion of (5భల + 2భఴ)ହ଴ isA) 49 B) 47 C) 48 D) 508. If logଷଶ, logଷ(2௫ − 5) and logଷ(2௫ −ళమ) are in AP then the value of ݔ isA) 2 B) 4 C) 3 D) 59. If the letters of the word ‘SACHIN’ is rearranged in every possible way and arranged according to the rule of dictionary. Then what would be the rank of the word ‘SACHIN’A) 602 B) 603 C) 600 D) 60110. If two dices are tossed once then the probability of even number in the first dice or sum of both dices is 8 isA) భయలB) యయలC) ଵଵଷ଺D) ఱవ11. If ݕ = tanିଵ రೣభశఱೣమ + tanିଵ మశయೣయషమೣthen ௗ௬ௗ௫=A) భభశೣమ B) యభశవೣమ C) ହଵାଶହ௫మ D) None of the these12. If A={ݔ :ݔis even natural numbers and less than 8} and B={ݕ :ݕ is a prime numbers less than 7} then the numbers of relation ܣ → ܤ isA) 2ଽ B) 9ଶ C) 3ଶ D) 2ଽ − 113. ∫ |1 − ݔଶ|݀ݔ ଷିଶ=A) ଶ଼ଷB) భయC) ଵସଷD) ଻ଷ14. The greatest value of the function ݂(ݔ = (3 cos ݔ − 4 sin ݔ + 1 isA) 3 B) 4 C) 5 D) 6