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  1. \frac{x}{\sqrt{1+x^{2}}}
  2. \frac{1}{\sqrt{1+x^{2}}}
  3. \frac{\sqrt{1+x^{2}}}{x}
  4. \sqrt{1+x^{2}}
Let  Using Pythagoras theorem,  Option (2) is correct
Engineering
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Let f_{k}\left ( x \right )= \frac{1}{k}\left ( \sin ^{k}x+\cos ^{k}x \right )where x\epsilon R\: \: and\: \: k\geqslant 1      Then f_{4}(x)-f_{6}(x)  equals :

  • Option 1)

    \frac{1}{4}

  • Option 2)

    \frac{1}{12}

  • Option 3)

    \frac{1}{6}

  • Option 4)

    \frac{1}{3}

 

Option 2

Engineering
114 Views   |  

Which of the following is correct?

  • Option 1)

    tan1>tan^{-1}1

  • Option 2)

    tan1<tan^{-1}1

  • Option 3)

    tan1=tan^{-1}1

  • Option 4)

    None of the above

 
  Important Results of Inverse Trigonometric Functions - - wherein if      By Graph So x=1 Option 1) Option is Correct Option 2) Option is incorrect Option 3) Option is incorrect Option 4) None of the above Option is incorrect
Engineering
107 Views   |  

The value of  tan^{-1}\left ( 1 \right )+tan^{-1}\left ( 0 \right )+tan^{-1}\left ( 2 \right )+tan^{-1}\left ( 3 \right )  is equal to

  • Option 1)

    \pi

  • Option 2)

    \frac{5\pi}{4}

  • Option 3)

    \frac{\pi}{2}

  • Option 4)

    None of these

 
As we learnt in Formulae of Inverse Trigonometric Functions - - wherein      or   Formulae of Inverse Trigonometric Functions - - wherein         Option 1) Correct option Option 2) Incorrect option Option 3) Incorrect option Option 4) None of these Incorrect option
Engineering
84 Views   |  

The value of Cot^{-1}\frac{3}{4}+Sin^{-1}\frac{5}{13}     is

  • Option 1)

    Sin^{-1}\, \, \frac{12}{13}

  • Option 2)

    Sin^{-1}\, \, \frac{63}{65}

  • Option 3)

    Sin^{-1}\, \, \frac{5}{12}

  • Option 4)

    Sin^{-1}\, \, \frac{65}{68}

 
As we learnt in Formulae of Inverse Trigonometric Functions - - wherein      or    Formulae of Inverse Trigonometric Functions - - wherein         Option 1) Incorrect option Option 2) correct option Option 3) Incorrect option Option 4) Incorrect option
Engineering
102 Views   |  

The number of solutions of \cos x+ \sqrt{3}\sin x=50\leq x\leq 5\pi is

 

  • Option 1)

    4

  • Option 2)

    0

  • Option 3)

    5

  • Option 4)

    None of these

 
As we learnt Maximum and minimum values - Max. value  Min. value  - wherein The maximum and minimum value of      min value of  & max value is 2 So     Option 1) 4 Incorrect option  Option 2) 0 correct option  Option 3) 5 Incorrect option  Option 4) None of these Incorrect option 
Engineering
88 Views   |  

The number of solutions of the equation \tan A+ \sec A = 2 \cos A lying in the interval [0, 2\pi ]

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    3

 
As we learnt in General Solution of Trigonometric Ratios - - wherein  is the given angle         Option 1) 0 Incorrect option  Option 2) 1 Incorrect option  Option 3) 2 correct option  Option 4) 3 Incorrect option 
Engineering
166 Views   |  

The number of real solution of \sin e^{x}.\cos e^{x}=2^{x-2}+2^{-x-2} is 

  • Option 1)

    Zero

  • Option 2)

    One

  • Option 3)

    Two 

  • Option 4)

    Infinite

 
As learnt in Trigonometric Ratios of Functions - - wherein                                    which is impossible because  and  minvalue    Option 1) Zero This option is correct Option 2) One This option is incorrect Option 3) Two  This option is incorrect Option 4) Infinite This option is incorrect
Engineering
89 Views   |  

The equation a\cos x-3\sin x = a+1 is solvable only if a belongs to the interval

  • Option 1)

    \left [a, +\infty \right ]

  • Option 2)

    \left [ -4, 4 \right ]

  • Option 3)

    (-\infty, 4)

  • Option 4)

    None of these

 
As learnt in Results from Submultiples of an angle - -     for real    Option 1) Incorrect option Option 2) Incorrect option Option 3) Correct option Option 4) None of these Incorrect option
Engineering
83 Views   |  

The equation 2cos^{^{-1}}x+sin^{-1}x=\frac{11\pi}{6}\, \, has

  • Option 1)

    No solution

  • Option 2)

    Only one solution

  • Option 3)

    two solutions

  • Option 4)

    three solutions

 
  Important Results of Inverse Trigonometric Functions - - wherein When       but  and    Option 1) No solution Correct option Option 2) Only one solution Incorrect option Option 3) two solutions Incorrect option Option 4) three solutions Incorrect option
Engineering
127 Views   |  

The degree and radian measure of the angle between the hour-hand and the minute-hand of a clock at tweny minutes past seven is

  • Option 1)

    \frac{5\pi }{4}

  • Option 2)

    \frac{5\pi }{8}

  • Option 3)

    \frac{5\pi }{7}

  • Option 4)

    \frac{5\pi^c }{9}

 
  Sexagesimal System - In this system, an angle is measured in degrees, minutes and seconds. - wherein    Angle made by hour hand and minute hand is approx  degrees for past seven and two minute total length will be approx 16.6{ because there are 60 gaps and each gap having   measurement  total angle 16.6 X 6 = 99.6  [ the hour hand rotates through an angle of  in one hour or  in one...
Engineering
217 Views   |  

Rohit was moving towards the hill to have a sight scene from its top. At a certain point in his way, he found that the angle of depression to top of the hill was45^{\circ}. After travelling 30m towards the hill, he found that the angle of depression to the top of the hill now became 60^{\circ}. Find the height of the hill.

  • Option 1)

    69.80m

  • Option 2)

    70.98m

  • Option 3)

    68.47m

  • Option 4)

    None

 
  Angle of Depression - If an object is below the horizontal line from the eye, we have to lower our head to view the object. - wherein    from fig Now in                                                                                                                                             Option 1) 69.80m This solution is incorrect. Option 2) 70.98m This solution is...
Engineering
100 Views   |  

If x=2\sin^{2}\alpha - \cos2\alpha, then \:\: x \:\: lies \:\: in\:\: the \:\: interval

  • Option 1)

    \left [-1, 3 \right ]

  • Option 2)

    \left [1, 2 \right ]

  • Option 3)

    \left [-2, 4 \right ]

  • Option 4)

    None of these

 
  Results from General Solution -  If            then  - wherein  is the given angle                                                            Option 1) This solution is correct. Option 2) This solution is incorrect. Option 3) This solution is incorrect. Option 4) None of these This solution is incorrect.
Engineering
635 Views   |  

If f(x) = 3 \left [ \sin^{4} \left (\frac{3\pi}{2} -x\right )+\sin^{4}(3\pi+x)\right ] - 2 \left [\sin^{6} \left (\frac{\pi}{2}+x\right ) + \sin^{6}( 5\pi-x \right ) ], then for all permissible values of x, f(x) is 

  • Option 1)

    -1

  • Option 2)

    0

  • Option 3)

    1

  • Option 4)

    Not a constant function

 
  Allied Angles - - wherein The trigonometric ratios for angles in all the four quadrants.     Option 1) -1 This is incorrect option Option 2) 0 This is incorrect option Option 3) 1 This is correct option Option 4) Not a constant function This is incorrect option
Engineering
100 Views   |  

if 4\sin ^{2}\alpha =1, then the values of \alpha are

  • Option 1)

    2n\pi \pm \frac{\pi}{3}, n\epsilon Z

  • Option 2)

    n\pi \pm \frac{\pi}{3}, n\epsilon Z

  • Option 3)

    n\pi \pm \frac{\pi}{6}, n\epsilon Z

  • Option 4)

    2n\pi\pm\frac{\pi}{6}, n\epsilon Z

 
As we learnt in Results from General Solution -  If            then  - wherein  is the given angle              Option 1) This option is incorrect. Option 2) This option is incorrect. Option 3) This option is correct. Option 4) This option is incorrect.
Engineering
175 Views   |  

If \tan x.\tan y = p and x+y = \frac{\pi}{6}, then \tan x and \tan y satisfy the equation

  • Option 1)

    x^{2}-\sqrt{3}(1-p)x+a=0

  • Option 2)

    \sqrt3x^{2}-(1-p)x+p\sqrt3=0

  • Option 3)

    x^{2}+\sqrt{3}(1+p)x-p=0

  • Option 4)

    \sqrt{3}x^{2}+(1+p)x-p\sqrt{3}=0

 
  Subtraction Formulae - - wherein A and B are two angles.       Option 1) This option is incorrect. Option 2) This option is correct. Option 3) This option is incorrect. Option 4) This option is incorrect.
Engineering
92 Views   |  

If \sin\theta+\sin^{2}\theta=1 , then the value of \cos^{12}\theta+3\cos^{10}\theta+3\cos^{8}\theta+\cos^{6}\theta-1 is equal to

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    -1

  • Option 4)

    2

 
  Trigonometric Identities - - wherein They are true for all real values of      Option 1) 0 This option is correct. Option 2) 1 This option is incorrect. Option 3) -1 This option is incorrect. Option 4) 2 This option is incorrect.
Engineering
353 Views   |  

If \sin A + \sin B = p and \cos A - \cos B = q then \tan \frac{A-B}{2} is equal to

 

  • Option 1)

    \frac{-p}{q}

  • Option 2)

    \frac{-q}{p}

  • Option 3)

    \sqrt{p^{2}+q^{2}}

  • Option 4)

    None of these

 
  Transformation Formulae - - wherein These formula are also called C-D formulae.   Option 1) This solution is incorrect. Option 2) This solution is correct. Option 3) This solution is incorrect. Option 4) None of these This solution is incorrect.
Engineering
90 Views   |  

If    2 tan^{-1}\left ( cosx \right )=tan^{-1}\left ( 2cosec\, \, x \right )   then the value of x is

  • Option 1)

    \frac{3\pi}{4}

  • Option 2)

    \frac{\pi}{4}

  • Option 3)

    \frac{\pi}{3}

  • Option 4)

    None of these

 
As we discussed in concept Relation between all the Inverse Trigonometric Functions - - wherein This happens with domain of functions, x0     => =>                             Option 1) This option is incorrect. Option 2) This option is correct. Option 3) This option is incorrect. Option 4) None of these This option is incorrect.
Engineering
118 Views   |  

If in a triangle, ABC

p \cos ^{2}(\frac{C}{2})+r \cos ^{2}(\frac{A}{2})=\frac{3q}{2}, then the sides p, q and r

  • Option 1)

    are in AP

  • Option 2)

    are in GP

  • Option 3)

    are in HP

  • Option 4)

    satisfy p+q=r

 
As we discussed in concept Double Angle Formula - - wherein These are formulae for double angles.     =>                                                                                                                                                            Option 1) are in AP This option is correct. Option 2) are in GP This option is incorrect. Option 3) are in HP This option is...
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