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Approximate Value Of 1 0002 3000 Is

1) 1.2 2) 1.4 3) 1.6 4) 1.8 Solution: (3) 1.6 Let y = f (x) = x3000 x = 1 and δ(x) = 0.0002 x + δx = 1.0002 (dy / dx) = 3000... View Article

1) Even function 2) Odd function 3) Not define 4) Increasing Function Solution: (2) Odd function It is an odd function.... View Article

1) 3, |x| < 1 2) 3, |x| ≤ 1 / 2 and -3, 1 / 2 < |x| < 1 3) -3, |x| < 1 4) 3, |x| ≤ 1 / 2 and 3, 1 / 2 < |x| < 1... View Article

1) 0 2) 1 3) –1 4) 2 Solution: (2) 1 (dy / dx)x=0 = f (f (f (x))), dy / dx x sec2 (x / 2) (1 / 2) tan (x / 2) = f’ (f (f (x)). F’... View Article

1) 5 2) 10 3) 0 4) 15 Solution: g (x) = f ‘ (x) --- (i) g’ (x) = f’’ (x) = - f (x) ---- (ii) F (x) = [f (x / 2)]2 + [g (x /... View Article

1) 2n 2) 2n-1 3) 0 4) 1 Solution: (3) 0 f (x) = xn f’ (x) = nxn-1 f’’ (x) = n (n - 1)x2 fn (x) = n (n - 1) (n - 2) ….. 2... View Article

1) 1 2) 0 3) 9 4) 18 Solution: (1) 1 g (x) = f (f (x)) = |f (x) - 2| = ||(x - 2) - 2| = ||x - 2| - 2| = |x - 2 - 2| = |x - 4|... View Article

1) 2xey-x + 2y (x + 1) 2) 2xex-y - 3y (x + 1) 3) [2xey-x - 2y (x + 1)] / [x (xey-x + 2)] 4) [2xey-x - y (x + 1)] Solution: (3)... View Article

1) 4 2) 2 3) 1 4) –4 Solution: (1) 4 f (x) = Ax + B f' (x) = A as f'(x) = 2 A = 2 and f (0) = B f (0) = 2 B = 2 f (x) = 2x +... View Article

1) (n - 1) x 2) (n + 1) x 3) nx 4) (1 - n) x Solution: (2) (n + 1) x y = cosn x . sinnx (dy / dx) = n ∙cosn–1 x ∙ (– sinx) ∙ sin... View Article

(1) AP (2) GP (3) HP (4) None of these Solution: We know (x+y)n = nC0xn + nC1xn-1y + nC2xn-2y2 + …..nCnyn where a = nC0 , b =... View Article

(1) 3 (2) 5 (3) 9 (4) 8 Solution: AM of a and 2 = (a+2)/2 GM of a and 2 = √(2a) Given AM exceeds GM by 1 So (a+2)/2 - √(2a) = 1... View Article

(1) 2,4,8 (2) 4,8,16 (3) 3,6,12 (4) None of these Solution: Let a/r, a, ar be the terms in GP. Then product = (a/r)a(ar) = 512... View Article

(1) an + cn < 2bn (2) an + cn > 2bn (3) an + cn = 2bn (4) None of these Solution: Given a,b,c are in HP. Then HM, b =... View Article

(1) AP (2) GP (3) HP (4) None of these Solution: Given 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0 Rearranging the terms [(1/a) + 1/(c-b)]... View Article

(1) AP (2) GP (3) HP (4) None of these Solution: Given (a+bx)/(a-bx) = (b+cx)/(b-cx) = (c+dx)/(c-dx) (a+bx)/(a-bx) =... View Article

(1) AP (2) GP (3) HP (4) None of these Solution: Given (x+y)/2, y, (y+z)/2 are in HP. So 2/(x+y), 1/y, 2/(y+z) are in AP. (1/y)... View Article

(1) 1 (2) 3 (3) 5 (4) 6 Solution: Let A1,A2 ...A9 are the AM’s and H1, H2, ...H9 are the HM’s between a and b. 9 AM’s and HM’s... View Article

(1) (a+b)/ab (2) (a+b)/2ab (3) 2ab/(a+b) (4) ab/(a+b) Solution: Let a, A1, A2, b are in AP. Then (a+b)/2 = (A1+A2)/2 (A1+A2) =... View Article

(1) 2√(ab) > (a+b) (2) 2√(ab) < (a+b) (3) 2√(ab) = (a+b) (4) none of these Solution: We know AM ≥ GM (a+b)/2 ≥ √(ab) (a+b)... View Article