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Vector Algebra question

2011 · Shift 2 · Q30
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  5. /2011 · Shift 2 · Q30

Vector Algebra question

2011 · Shift 2 · Q30

JEE AdvancedMathematicsVector AlgebraMCQ+4 / −1
Match the statements given in Column -III with the values given in Column-II.            II.\,\,\,\,\,\,\,\,\,\,\,\,II. Column-III(A)     \,\,\,\, If a→=j^+3k^,b→=−j^+3k^\overrightarrow a = \widehat j + \sqrt 3 \widehat k,\overrightarrow b = - \widehat j + \sqrt 3 \widehat ka=j​+3​k,b=−j​+3​k and c→=23k^\overrightarrow c = 2\sqrt 3 \widehat kc=23​k form a triangle, then the internal angle of the triangle between a→\overrightarrow aa and b→\overrightarrow bb is (B)     \,\,\,\, If ∫ab(f(x)−3x)dx=a2−b2,\int\limits_a^b {\left( {f\left( x \right) - 3x} \right)dx = {a^2} - {b^2},}a∫b​(f(x)−3x)dx=a2−b2, then the value of fff(π6)\left( {{\pi \over 6}} \right)(6π​) is (C)     \,\,\,\, The value of π2ℓn3∫7/65/6sec⁡(πx)dx{{{\pi ^2}} \over {\ell n3}}\int\limits_{7/6}^{5/6} {\sec \left( {\pi x} \right)dx}ℓn3π2​7/6∫5/6​sec(πx)dx is (D)     \,\,\,\, The maximum value of ∣Arg(11−z)∣\left| {Arg\left( {{1 \over {1 - z}}} \right)} \right|​Arg(1−z1​)​ for ∣z∣=1, ze1\left| z \right| = 1,\,z e 1∣z∣=1,ze1 is given by             \,\,\,\,\,\,\,\,\,\,\,\, Column-IIIIII (p)     π6\,\,\,\,{{\pi \over 6}}6π​ (q)     2π3\,\,\,\,{{2\pi \over 3}}32π​ (r)     π3\,\,\,\,{{\pi \over 3}}3π​ (s)     π\,\,\,\,\piπ(t)     π2\,\,\,\,{{\pi \over 2}}2π​
  1. A
    (A)→q;  (B)→p;  (C)→s;  (D)→t\left( A \right) \to q;\,\,\left( B \right) \to p;\,\,\left( C \right) \to s;\,\,\left( D \right) \to t(A)→q;(B)→p;(C)→s;(D)→t
  2. B
    (A)→q;  (B)→p;  (C)→t;  (D)→s\left( A \right) \to q;\,\,\left( B \right) \to p;\,\,\left( C \right) \to t;\,\,\left( D \right) \to s(A)→q;(B)→p;(C)→t;(D)→s
  3. C
    (A)→p;  (B)→q;  (C)→s;  (D)→t\left( A \right) \to p;\,\,\left( B \right) \to q;\,\,\left( C \right) \to s;\,\,\left( D \right) \to t(A)→p;(B)→q;(C)→s;(D)→t
  4. D
    (A)→q;  (B)→s;  (C)→p;  (D)→t\left( A \right) \to q;\,\,\left( B \right) \to s;\,\,\left( C \right) \to p;\,\,\left( D \right) \to t(A)→q;(B)→s;(C)→p;(D)→t
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