Test Details

Trigonometric Functions-3

JEE and CET exam questions ACP Classes

Feb 12, 8:35 PM

40 minutes

Feb 12, 9:15 PM

50.0 marks

MCQ

23 questions

Sarjerao Tupe

Class Details

Biology

Chemistry

ACP 12th Bio,Chem

Biology

Chemistry

Professional learning of biology and chemistry. all concepts are simply learned. basic concepts are invoked. enhanced doubt clearance session. problem solution.

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Question Text

Question 3 :
value of $ \displaystyle (\cos \Theta +\sin \Theta )^{2}+(\cos \Theta -\sin \Theta )^{2} $ is

Question 4 :
If $3\left( \sec ^{ 2 }{ \theta } +\tan ^{ 2 }{ \theta } \right) =5$, then the general value of $\theta $ is -

Question 5 :
If $\sin x - \cos x = 0$, then what is the value of $\sin^{4}x + \cos^{4}x$?

Question 6 :
If $sin2x-2cosx=0$ .Then the number of values of $\theta$ lying in $[0, \pi]$ is?

Question 7 :
IF $ \displaystyle \Theta $ is any angle, then $ \displaystyle \sec ^{4}\Theta -\sec ^{2}\Theta $ is equal to

Question 10 :
The value of $ \displaystyle \cos ^{4}\frac{\pi }{4}-\cos ^{4}\frac{\pi }{6}+\sin ^{4}\frac{\pi }{6}+\sin ^{4}\frac{4\pi }{3} $ is

Question 12 :
If $\displaystyle 0\leq a\leq 3, 0\leq b\leq 3$ and the equation $\displaystyle x^{2}+4+3 cos\left ( ax+b \right )=2x$ has at least one solution then the value of $\displaystyle a+b$ is

Question 13 :
The interval for which $2\tan ^{ -1 }{ x } +\sin ^{ -1 }{ \dfrac { 2 }{ 1+x } } $ is independent of $x$ is

Question 15 :
Assertion (A): lf $\tan\alpha, \tan\beta$ are the roots of $x^{2}+px+q=0$, then $\tan(\alpha+\beta)=\dfrac{p}{1-q}$ Reason (R) : lf $\alpha, \beta$ the roots $ax^{2}+bx+c=0$, then $\displaystyle \alpha+\beta=\frac{-b}{a}$ and $\alpha\beta= \dfrac{c}{a}$

Question 17 :
If $\tan x - \tan^{2} x = 1$, then the value of $\tan^{4} x - 2 \tan^{3} x - \tan^{2} x+2\tan x +1$ is:

Question 18 :
If $\cos { \alpha } +\cos { \beta } +\cos { \gamma } =\sin { \alpha } +\sin { \beta } +\sin { \gamma } =0$, then the value of $\cos { 3\alpha } +\cos { 3\beta } +\cos { 3\gamma } $ is

Question 19 :
If $\displaystyle \sum_{n = 1}^{2013} \tan \left (\dfrac {\theta}{2^{n}}\right )\sec \left (\dfrac {\theta}{2^{n - 1}}\right ) = \tan \left (\dfrac {\theta}{2^{a}}\right ) - \tan \left (\dfrac {\theta}{2^{b}}\right )$ then $(b + a)$ equals

Question 20 :
Simplify: $\tan5\tan { 30 } \times 4\tan { 85=\_ \_ \_ } $

Question 21 :
If $\sin^{2}x-2\sin x - 1=0$has exactly four different solution in $x\in [0, n\pi]$, then value / values of n is / are $(n \in N)$

Question 23 :
In a $\Delta ABC,\angle A\lt \angle B$. If $\sin A$ and $\sin B$ satisfy the equation $3 \sin x - 4 \sin ^{3}x - k =0$, where $0<K<1$, then find measure of $\angle C$.

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