Mathematics - Trigonometric Functions, Identities and Equation
Exam Duration: 45 Mins Total Questions : 30
The maximum and minimum values of cos2x - 6sinxcosx + 3sin2x + 2 are
- (a)
\(4-\sqrt { 10 } ,4+\sqrt { 10 } \)
- (b)
\(2-\sqrt { 10 } ,2+\sqrt { 10 } \)
- (c)
\(3-\sqrt { 5 } ,4+\sqrt { 5 } \)
- (d)
\(None\quad of\quad the\quad above\)
If A = sin2x + cos4x, then for all real x
- (a)
\(\frac { 13 }{ 16 } \le A\le 1\)
- (b)
\(1\le A\le 2\)
- (c)
\(\frac { 3 }{ 4 } \le A\le \frac { 13 }{ 16 } \)
- (d)
\(\frac { 3 }{ 4 } \le A\le 1\)
| tan x + see x| = |tan x| + Isee x|, x ∈ [0, 2π], if and only if x belongs to the interval
- (a)
[0, π]
- (b)
\([0,{\pi\over 2})\cup({\pi\over 2}, \pi]\)
- (c)
\([0,{3\pi\over 2})\cup({3\pi\over 2}, 2\pi]\)
- (d)
(π, 2π]
If sin4x+cos4y+2=4sinxcosy and 0 < x, y <\(\pi\over 2\) then sin x + cos y is equal to
- (a)
-2
- (b)
0
- (c)
2
- (d)
\(3\over 2\)
The number of solutions of the equation tan x + see x = 2 cos x lying in the interval [0, 2π] is
- (a)
0
- (b)
1
- (c)
2
- (d)
3
2 sin x cos 2x = sin x, if
- (a)
\(x=n\pi+{\pi\over 6}(n\epsilon I)\)
- (b)
\(x=n\pi-{\pi\over 6}(n\epsilon I)\)
- (c)
\(x=n\pi(n\epsilon I)\)
- (d)
\(x=n\pi+{\pi\over 2}(n\epsilon I)\)
The equation sin x = [1 + sin xl + [1 - cos xl has (where [xl is the greatest integer less than or equal to x)
- (a)
no solution in \(\left[-{\pi\over 2},{\pi\over 2}\right]\)
- (b)
no solution in \(\left[{\pi\over 2},\pi\right]\)
- (c)
no solution in \(\left[\pi,{3\pi\over 2}\right]\)
- (d)
no solution in for x ∈ R
solution (x, y) of the system of equations \(x-y={1\over 3}\)and \(cos^2(\pi\ x)-sin^2(\pi\ y)={1\over 2} \)is given by
- (a)
\(\left\{{7\over 6},{5\over 6}\right\}\)
- (b)
\(\left\{{2\over 3},{1\over 3}\right\}\)
- (c)
\(\left\{-{5\over 6},-{7\over 6}\right\}\)
- (d)
\(\left\{{13\over 3},{11\over 3}\right\}\)
\(2sin^2\left({\pi\over 2}cos^2 x\right)=1-cos(\pi\ sin\ 2x)\) if
- (a)
\(x=(2n+1){\pi\over4}n\epsilon I\)
- (b)
\(tan\ x={1\over 2}, n\epsilon I\)
- (c)
\(tan\ x=-{1\over 2}, n\epsilon I\)
- (d)
\(x={n\pi\over 2},n\epsilon I\)
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 equation \(2cos^2\left(x\over 2\right)sin^2\ x=x^2+x^{-2},0<x\le{\pi\over 2}\) has
- (a)
one real solutions
- (b)
more than one real solutions
- (c)
no real solution
- (d)
none of the above
A circular wire of radius 3cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48cm. Find the angle in degrees which is subtended at the centre of hoop
- (a)
21.50
- (b)
23.50
- (c)
22.50
- (d)
24.50
Find the circular measure of the following angle 3300
- (a)
\(\pi\over 6\)
- (b)
\(5\pi\over 12\)
- (c)
\(11\pi\over 6\)
- (d)
\(\pi\over 8\)
Find the radian measure of 250 and -470 30' respetively
- (a)
5π/36, -19π/72
- (b)
7π/36,17π/72
- (c)
5π/36, π/72
- (d)
7π36,π/72
Find x from the equation
cosec(900 +θ)+xcosθcot(900+θ)=sin(900+θ)
- (a)
cotθ
- (b)
tanθ
- (c)
-tanθ
- (d)
-cotθ
If sinθ=3sin(θ+2α), then the value of tan(θ+α)+2tanα is
- (a)
3
- (b)
2
- (c)
-1
- (d)
0
If 8cos2θ+8sec2θ=65, 0<θ <π/2 then the value of 4cos4θ is equal
- (a)
- 33/2
- (b)
-31/32
- (c)
-31/32
- (d)
-33/32
The solution of tanx+secx=2cosx in[0, 2π)
- (a)
\({3π\over2},{π\over6}\)
- (b)
\({\pi\over6},{5π\over6}\)
- (c)
\({π\over2},π\)
- (d)
\({π\over4},{π\over 3}\)
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
If sinθ+cosecθ=2 then sin2θ+cosec2θ is equal to
- (a)
1
- (b)
- (c)
2
- (d)
None of these
If f(x)=cos2x+sec2x then
- (a)
f(x)<1
- (b)
f(x)=1
- (c)
2<f(x)<1
- (d)
f(x) > 2
The value of cos10cos20 cos 30...cos1790 is
- (a)
\(1\over\sqrt2\)
- (b)
0
- (c)
1
- (d)
-1
The value of tan 750 - cot750 is equal to
- (a)
2√3
- (b)
2+√3
- (c)
2-√3
- (d)
1
The value of tan3A-tan2A-tanA is equal to
- (a)
tan3A tna2A tanA
- (b)
-tan3A tan2A tanA
- (c)
ranA tan2A - tan2Atan3A - tan3A tanA
- (d)
None of these
The value of \(\frac { \pi }{ 10 } sin\frac { 13\pi }{ 10 } \) is
- (a)
\(\frac { 1 }{ 2 } \)
- (b)
-\(\frac { 1 }{ 2 } \)
- (c)
-\(\frac { 1 }{ 4 } \)
- (d)
1
let \(\alpha\) be a real number lying between 0 and \(\frac { \pi }{ 2 } \) and n be a positive integer.
Statement -I: tana + 2tan2\(\alpha\) + 22tan22\(\alpha\) + .... + 2n-1 tan2n-1 \(\alpha\) + 2n cot 2n\(\alpha\) = cot \(\alpha\)
Statement-II : cot\(\alpha\) - tan\(\alpha\) =2cot2\(\alpha\)
- (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
Statement I : The solution of the equation
6sec2\(\theta\) - 5sec\(\theta\) + 1 = 0 is sec\(\theta\) = \(\frac { 1 }{ 3 } ,\frac { 1 }{ 2 } \)
Statement - II : sec2\(\theta\) \(\ge\) 1
- (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
Which of the following statements is/are true?
Statement-I: If cotθ + tanθ = 2cosecθ, then the general value of θ is \(n\pi\pm {\pi\over 3}, n\in Z\)
Statement-II: If secx cos5x + 1 = 0, where 0 < x ≤ \({\pi\over 2}\) then the value of x is \({\pi\over 3}\)
- (a)
Only Statement-I
- (b)
Only Staternent-Il
- (c)
Both Statement-I and Staternent-II
- (d)
Neither Statement-I nor Statement-II