JEE Main Mathematics - Trigonometric Functions, Identities and Equation
Exam Duration: 60 Mins Total Questions : 30
If sin3x = 4sinx. sin(y+x). sin(y-x), where \(0
- (a)
10
- (b)
5
- (c)
1
- (d)
0
At how many points the curve \(y={ 81 }^{ { sin }^{ 2 }x }+{ 81 }^{ { cos }^{ 2 }x }-30\) will intersect X-axis in the region \(-\pi \le x\le \pi \) ?
- (a)
4
- (b)
6
- (c)
8
- (d)
None of these
The number of solutions of the equation sin x + 2 sin 2x = 3 + sin 3x in the interval [0, π) is
- (a)
0
- (b)
1
- (c)
2
- (d)
3
The number of solutions of \(\sum _{ r=1 }^{ 5 }{ cos\ r\ x=5 } \) in the interval [0, 2π]
- (a)
0
- (b)
1
- (c)
5
- (d)
10
If 1+sinθ+sin2θ+ ... ∞=4+2-√3, 0<θ<π, \(θ\neq{\pi\over 2}\)then
- (a)
\(\theta={\pi\over 6}\)
- (b)
\(\theta={\pi\over 3}\)
- (c)
\(\theta={\pi\over 6}or{\pi\over 6}\)
- (d)
\(\theta={\pi\over 3}or{2\pi\over 3}\)
If x ∈ [0, 2π), y ∈ [0, 2π) and sin x + sin y = 2, then the value of x + y is
- (a)
π
- (b)
\(π\over 2\)
- (c)
3π
- (d)
none of these
The solution of the equation \(sin^{10}x+cos^{10}x={29\over 16}cos^42x\)is
- (a)
\(x={n\pi\over 4}+{\pi\over 8}, n\epsilon I\)
- (b)
\(x={n\pi}+{\pi\over 4}, n\epsilon I\)
- (c)
\(x=2{n\pi}+{\pi\over 2}, n\epsilon I\)
- (d)
none of these
The general solution of the equation 2cos2x + 1 = 3 . 2- sin 2 x is
- (a)
nπ, n∊I
- (b)
nπ+π, n∊I
- (c)
nπ-π, n∊I
- (d)
none of these
When ever the terms on the two sides of the equation are of different nature, then equations are known as Non standard form, some of them are in the form of an ordinary equation but can not be solved by standard procedures.
Non standard problems require high degree of logic, they also require the use of graphs, inverse properties of functions, in equalities .
The number of real solutions of the equation sin (ex) = 5X + 5-x is
- (a)
0
- (b)
1
- (c)
2
- (d)
infinitely many
When ever the terms on the two sides of the equation are of different nature, then equations are known as Non standard form, some of them are in the form of an ordinary equation but can not be solved by standard procedures.
Non standard problems require high degree of logic, they also require the use of graphs, inverse properties of functions, in equalities .
If \(0\le x\le2\pi\ and\ 2^{cosec^2x}\sqrt{\left({1\over 2}y^2-y+1\right)}\le\sqrt2\) then number of ordered pairs of (x, y) is
- (a)
1
- (b)
2
- (c)
3
- (d)
infinitely many
A wheel rotates making 20 revolutions per second. If the radius of the wheel is 35 cm, what linear distance does a point of rim traverse in three minutes? (take \(\pi\) = 22/7)
- (a)
7.92 km
- (b)
7.70 km
- (c)
7.80 km
- (d)
7.85 km
A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
- (a)
50o
- (b)
210o
- (c)
100o
- (d)
60o
If \(tan\theta={-4\over3}\)then sinθ is
- (a)
\({-4\over5}\)but not \(4\over5\)
- (b)
\({-4\over5}\)or\(4\over5\)
- (c)
\({4\over5}4\)but not -\(4\over5\)
- (d)
\({-3\over4}\)or\(3\over4\)
The value \(sec{2\pi\over 3}+cosec{5\pi\over6}\)is equal
- (a)
2
- (b)
-2
- (c)
4
- (d)
0
Solve the equation
sinx-3sin2x+in3x=cosx-3cos2x+cos3x
- (a)
\({n\pi\over 2}-{\pi\over8}, n∈I\)
- (b)
\({n\pi\over 2}, n∈I\)
- (c)
\({n\pi\over 2}+{\pi\over8}, n∈I\)
- (d)
\({n\pi}, n∈I\)
The value of x in (0, π/2) satisfying the equation sin xcosx=\(1\over 4\)is
- (a)
π/6
- (b)
π/3
- (c)
π/8
- (d)
π/12
One of the principal solutions of √3secx =-2 is equal to
- (a)
2π/3
- (b)
π/6
- (c)
5π/6
- (d)
π/3
If 0 < x < π and cosx+sinx=1/2 then tan x is
- (a)
\((1-\sqrt7)\over4\)
- (b)
\((4-\sqrt7)\over3\)
- (c)
\(-(4-\sqrt7)\over3\)
- (d)
\((1+\sqrt7)\over4\)
Find the maximum and minimum values of 6sinx+cosx+4cos2x
- (a)
5,-5
- (b)
6,-6
- (c)
4,-4
- (d)
2,-2
In a ΔABC if a=2, b=3 and \(sin A=\left(2\over 3\right)\)then find ㄥB
- (a)
900
- (b)
800
- (c)
1100
- (d)
14000
The value of tan 750 - cot750 is equal to
- (a)
2√3
- (b)
2+√3
- (c)
2-√3
- (d)
1
The value of os2 480 - sin2120 is
- (a)
\(\frac { \sqrt { 5 } +1 }{ 8 } \)
- (b)
\(\frac { \sqrt { 5 } -1 }{ 8 } \)
- (c)
\(\frac { \sqrt { 5 } +1 }{ 5 } \)
- (d)
\(\frac { \sqrt { 5 } +1 }{ 2\sqrt { 2 } } \)
Statement - I : if sin2A = sin2Bandcos2A = cos2B, then A = n\(\pi\) + B, n \(\epsilon \)I
Statement - II : If sin A = sin B and cos A = cosB, then A = n\(\pi\) + B, n \(\epsilon \) I
- (a)
If both statement-I and statement -II are trur and statement -II is the correct explantion of statement -I
- (b)
If both statement -I and statement II are true but statment-II is not the correct explanation of statement-I
- (c)
If statement -I is true but statement -II is false
- (d)
if statement -I is false and statement -II is true
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