WB JEE 2016 | Trigonometric Functions & Equations Question 47 | Mathematics

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

If z₁, z₂, z₃ are imaginary numbers such that $$|{z_1}|\, = \,|{z_2}|\, = \,|{z_3}|\, = \,\left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right|\, = \,1$$, then $$|{z_1} + {z_2} + {z_3}|$$ is

equal to 1

less than 1

greater than 1

equal to 3

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

$${{7!} \over {2!2!}}$$

$${{7!} \over {2!}}$$

$${{6!} \over {2!}}$$

5! $$ \times $$ 2!

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

$$1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta $$ equals

$${\left( {2\cos {\theta \over 2}} \right)^n}\cos {{n\theta } \over 2}$$

$$2{\cos ^2}{{n\theta } \over 2}$$

$$2{\cos ^{2n}}{\theta \over 2}$$

$${\left( {2{{\cos }^2}{\theta \over 2}} \right)^n}$$

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

Let $$Q = \left[ {\matrix{ {\cos {\pi \over 4}} & { - \sin {\pi \over 4}} \cr {\sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr } } \right]$$ and $$x = \left[ {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{1 \over {\sqrt 2 }}} \cr } } \right]$$, then Q³x is equal to

$$\left( {\matrix{ 0 \cr 1 \cr } } \right)$$

$$\left( {\matrix{ { - {1 \over {\sqrt 2 }}} \cr {{1 \over {\sqrt 2 }}} \cr } } \right)$$

$$\left( {\matrix{ { - 1} \cr 0 \cr } } \right)$$

$$\left( {\matrix{ { - {1 \over {\sqrt 2 }}} \cr { - {1 \over {\sqrt 2 }}} \cr } } \right)$$

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