JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Medium

1 of 1

Application +4 | -1

If for

x \in \left( {0,\,\frac{\pi }{2}} \right),\,\,{\log _{10}}\sin x + {\log _{10}}\cos x = - 1

and

{\log _{10}}\left( {\sin x + \cos x} \right) = \frac{1}{2}\left( {{{\log }_{10}}n - 1} \right),\,\,n > 0

, then the value of

n

is equal to:

View answer and explanation

Correct option: C

Option C (12) is correct because solving the logarithmic equations and using trigonometric identities leads to n = 12.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}