Solution - Career Point

5. If A and B are two invertible matrices of the same order,then adj (AB) is equal to -(A) adj (B) adj (A) (B) |B| |A| B –1 A –1(C) |B| |A| A –1 B –1 (D) |A| |B| (AB) –1⎡ cosα6. If A (α , β) =⎢⎢− sin α⎢⎣0sin αcosα00 ⎤0⎥⎥, then⎥⎦βe(A) A (α, β)′ = A (– α, β)(B) A (α, β) –1 = A (–α, –β)(C) Adj (A (α, β)) = e –β A (–α, –β)(D) A (α, β)′ = A (α, – β)7. For a positive integer n, if the expansion ofn⎛ 5 4 ⎞⎜ + x ⎟ has a term independent of x, then n can2⎝ x ⎠be(A) 18 (B) 21(C) 27 (D) 998. If k is odd then k C r is maximum for r equal to(A) 21 (k – 1) (B) 21 (k + 1)(C)k – 19. Let a n = ( 111...1) , then14243n times(A) a 912 is not prime(C) a 480 is not prime(D) k(B) a 951 is not prime(D) a 91 is not primeSECTION – IIIMatrix - Match TypeThis section contains 2 questions. Each questioncontains statements given in two columns, which haveto be matched. The statements in Column I are labeledA, B, C and D, while the statements in Column II arelabeled p, q, r, s and t. any given statement in Column Ican have correct matching with ONE OR MOREstatements (s) in column II. The appropriate bubbledcorresponding to the answers to these questions have tobe darkened as illustrated in the following example :If the correct matches are A – p, s and t; B – q and r;C – p and q; and D – s and t; then the correctdarkening of bubbles will look like the following.p q r s tABCDppqqrrrsstt10. Match the followingColumn-1Column-IIEquationGeneral Solutions(A) 2 sin θ – 3 = 0 (p) nπ + (–1) n π3(B) 2 sin 2θ + 3π(q) 2nπ – 3= 2 sin θ + 2 3 cos θπ(C) sin 2θ + cos 2θ + 4 sin θ (r) 2nπ + 3= 1 + 4 cos θ(D) cos 2 θ = 41(s) nπ – 4π(t) nπ + 4π11. Match the following :Column- I(A) If three unequal numbers a, b, care in A.P. and b – c,c – b, a are in G.P., then3 3 3a + b + cis equal to3abc(B) Let x be the arithmetic meanand y,z be two geometricmeans between any twopositive numbers, theny3 3+ zis equal toxyz(C) If a, b, c be three positivenumber which form threesuccessive terms of a G.P. andc> 4b –3a, then the commonratio of the G.P. can be equal to(D)⎪⎧lim tan ⎨n→∞⎪⎩⎪is equal ton∑r=1tan−1⎛ 1⎜⎝ 2r2⎞⎪⎫⎟ ⎬⎠ ⎭SECTION – IVInteger answer typeColumn- II(p) 1/3(q) 1(r) 2(s) 3(t) 1/2This section contains 8 questions. The answer to each ofthe questions is a single-digit integer, ranging from 0 to9. The appropriate bubbles below the respectivequestion numbers in the ORS have to be darkened. Forexample, if the correct answers to question numbers X,Y, Z and W (say) are 6, 0, 9 and 2, respectively, thenthe correct darkening of bubbles will look like thefollowing :XtraEdge for IIT-JEE 65APRIL 2010