Total Questions:50 Total Time: 60 Min
Remaining:
Question:If \(\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,\)then the most general value of \(\theta \) is
\(n\pi + {( - 1)^n}\frac{\pi }{4}\)
\({( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}\)
\(n\pi + \frac{\pi }{4} - \frac{\pi }{3}\)
\(n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}\)
Question:If \({\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,\)then the general value of \(\theta \)is
\(n\pi \pm \frac{\pi }{3}\)
\(2n\pi \pm \frac{\pi }{3}\)
\(2n\pi \pm \frac{\pi }{6}\)
\(n\pi \pm \frac{\pi }{6}\)
Question:If \(4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 \), then the general value of \(\theta \)is
\(2n\pi + \frac{\pi }{4}\)
\(n\pi - \frac{\pi }{3}\)
Question:If \(\cot \theta + \cot \left( {\frac{\pi }{4} + \theta } \right) = 2\), then the general value of \(\theta \) is
Question:The general value of \(\theta \)satisfying the equation \(2{\sin ^2}\theta - 3\sin \theta - 2 = 0\) is
\(n\pi + {( - 1)^n}\frac{\pi }{6}\)
\(n\pi + {( - 1)^n}\frac{\pi }{2}\)
\(n\pi + {( - 1)^n}\frac{{5\pi }}{6}\)
\(n\pi + {( - 1)^n}\frac{{7\pi }}{6}\)
Question:The general solution of the equation \((\sqrt 3 - 1)\sin \theta + (\sqrt 3 + 1)\cos \theta = 2\) is
\(2n\pi \pm \frac{\pi }{4} + \frac{\pi }{{12}}\)
\(n\pi + {( - 1)^n}\frac{\pi }{4} + \frac{\pi }{{12}}\)
\(2n\pi \pm \frac{\pi }{4} - \frac{\pi }{{12}}\)
\(n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{{12}}\)
Question:The solution of the equation \(\left| {\,\begin{array}{*{20}{c}} {\cos \theta } & {\sin \theta } & {\cos \theta } \\ { - \sin \theta } & {\cos \theta } & {\sin \theta } \\ { - \cos \theta } & { - \sin \theta } & {\cos \theta } \\\end{array}\,} \right| = 0\), is
\(\theta = n\pi \)
\(\theta = 2n\pi \pm \frac{\pi }{2}\)
\(\theta = n\pi \pm {( - 1)^n}\frac{\pi }{4}\)
\(\theta = 2n\pi \pm \frac{\pi }{4}\)
Question:The set of values of x for which the expression \(\frac{{\tan 3x - \tan 2x}}{{1 + \tan 3x\tan 2x}} = 1\), is
\(\varphi \)
\(\frac{\pi }{4}\)
\(\left\{ {n\pi + \frac{\pi }{4}:n = 1,\,2,\,3.....} \right\}\)
\(\left\{ {2n\pi + \frac{\pi }{4}:n = 1,\,2,\,3.....} \right\}\)
Question:The number of values of x in the interval [0, 5\(\pi \)] satisfying the equation \(3{\sin ^2}x - 7\sin x + 2 = 0\)is
0
5
6
10
Question:The equation \(\sqrt 3 \sin x + \cos x = 4\)has
Only one solution
Two solutions
Infinitely many solutions
No solution
Question:The equation \(3\cos x + 4\sin x = 6\)has
Finite solution
Infinite solution
One solution
Question:The value of \(\theta \) in between \({0^o}\)and \({360^o}\)and satisfying the equation \(\tan \theta + \frac{1}{{\sqrt 3 }} = 0\)is equal to
\(\theta = {150^o}\)and \({300^o}\)
\(\theta = {120^o}\)and \({300^o}\)
\(\theta = {60^o}\)and \({240^o}\)
\(\theta = {150^o}\)and \({330^o}\)
Question:The solution of equation \({\cos ^2}\theta + \sin \theta + 1 = 0\) lies in the interval
\(\left( { - \frac{\pi }{4},\frac{\pi }{4}} \right)\)
\(\left( {\frac{\pi }{4},\frac{{3\pi }}{4}} \right)\)
\(\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right)\)
\(\left( {\frac{{5\pi }}{4},\frac{{7\pi }}{4}} \right)\)
Question:The number of solution of the equation \(2\cos ({e^x}) = {5^x} + {5^{ - x}}\), are
Question:If \(\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),\)then the value of \(\cos \left( {\theta - \frac{\pi }{4}} \right)\)=
\(\frac{1}{{2\sqrt 2 }}\)
\(\frac{1}{{\sqrt 2 }}\)
\(\frac{1}{{3\sqrt 2 }}\)
\(\frac{1}{{4\sqrt 2 }}\)
Question:If \(\tan (\pi \cos \theta ) = \cot (\pi \sin \theta )\), then \(\sin \left( {\theta + \frac{\pi }{4}} \right)\) equals
\(\frac{1}{2}\)
\(\frac{{\sqrt 3 }}{2}\)
Question:The value of \(\theta \)lying between 0 and \(\pi /2\)and satisfying the equation \(\left| {\,\begin{array}{*{20}{c}} {1 + {{\sin }^2}\theta } & {{{\cos }^2}\theta } & {4\sin 4\theta } \\ {{{\sin }^2}\theta } & {1 + {{\cos }^2}\theta } & {4\sin 4\theta } \\ {{{\sin }^2}\theta } & {{{\cos }^2}\theta } & {1 + 4\sin 4\theta } \\\end{array}\,} \right| = 0\)
\(\frac{{7\pi }}{{24}}\) or \(\frac{{11\pi }}{{24}}\)
\(\frac{{5\pi }}{{24}}\)
\(\frac{\pi }{{24}}\)
None of these
Question:The period of the function \(f(\theta ) = \sin \frac{\theta }{3} + \cos \frac{\theta }{2}\)is
\(3\pi \)
\(6\pi \)
\(9\pi \)
\(12\pi \)
Question:If the period of the function \(f(x) = \sin \left( {\frac{x}{n}} \right)\)is \(4\pi \), then n is equal to
1
4
8
2
Question:Period of \({\sin ^2}x\)is
\(\pi \)
\(2\pi \)
\(\frac{\pi }{2}\)
None of these\(\)
Question:In \(\Delta ABC,\frac{{\sin B}}{{\sin (A + B)}} = \)
\(\frac{b}{{a + b}}\)
\(\frac{b}{c}\)
\(\frac{c}{b}\)
Question:In \(\Delta ABC,\frac{{\sin (A - B)}}{{\sin (A + B)}} = \)
\(\frac{{{a^2} - {b^2}}}{{{c^2}}}\)
\(\frac{{{a^2} + {b^2}}}{{{c^2}}}\)
\(\frac{{{c^2}}}{{{a^2} - {b^2}}}\)
\(\frac{{{c^2}}}{{{a^2} + {b^2}}}\)
Question:If \({\cos ^2}A + {\cos ^2}C = {\sin ^2}B,\)then \(\Delta ABC\)is
Equilateral
Right angled
Isosceles
Question:If the angles of a triangle be in the ratio 1 : 2 : 7, then the ratio of its greatest side to the least side is
\(1:2\)
2:1
\((\sqrt 5 + 1):(\sqrt 5 - 1)\)
\((\sqrt 5 - 1):(\sqrt 5 + 1)\)
Question:In \(\Delta ABC\), \({a^2}({\cos ^2}B - {\cos ^2}C) + \) \({b^2}({\cos ^2}C - {\cos ^2}A) + \)\({c^2}({\cos ^2}A - {\cos ^2}B) = \)
\({a^2} + {b^2} + {c^2}\)
\(2({a^2} + {b^2} + {c^2})\)
Question:In triangle \(ABC,\)\(\frac{{1 + \cos (A - B)\cos C}}{{1 + \cos (A - C)\cos B}} = \)
\(\frac{{a - b}}{{a - c}}\)
\(\frac{{a + b}}{{a + c}}\)
\(\frac{{{a^2} - {b^2}}}{{{a^2} - {c^2}}}\)
\(\frac{{{a^2} + {b^2}}}{{{a^2} + {c^2}}}\)
Question:In a triangle \(ABC\), if \(B = 3C\), then the values of \(\sqrt {\left( {\frac{{b + c}}{{4c}}} \right)} \) and \(\left( {\frac{{b - c}}{{2c}}} \right)\) are
\(\sin C,\sin \frac{A}{2}\)
\(\cos C,\sin \frac{A}{2}\)
\(\sin C,\cos \frac{A}{2}\)
Question:In \(\Delta ABC\), \((b - c)\cot \frac{A}{2} + (c - a)\cot \frac{B}{2} + (a - b)\)\(\cot \frac{C}{2}\) is equal to
\( \pm 1\)
Question:If in a \(\Delta ABC\), \(\cos A + 2\cos B + \cos C = 2\), then\(a,b,c\)are in
A. P.
H. P.
G. P.
Question:If in a \(\Delta ABC\), \(\cos 3A + \cos 3B + \cos 3C = 1\), then one angle must be exactly equal to
\({90^o}\)
\({45^o}\)
\({120^o}\)
Question:If in a \(\Delta ABC,\,\angle A = {45^o},\,\,\angle C = {60^o}\), then \(a + c\sqrt 2 = \)
b
2b
\(\sqrt {2b} \)
\(\sqrt 3 b\)
Question:If the lengths of the sides of a triangle are 3, 5, 7, then the largest angle of the triangle is
\(\pi /2\)
\(5\pi /6\)
\(2\pi /3\)
\(3\pi /4\)
Question:The ratio of the sides of triangle ABC is \(1:\sqrt 3 :2\). The ratio of \(A:B:C\)is
\(3:5:2\)
\(1:\sqrt 3 :2\)
03:02:01
01:02:03
Question:In a triangle \(ABC,\,\,b = \sqrt 3 \), \(c = 1\)and \(\angle A = {30^o}\), then the largest angle of the triangle is
\({135^o}\)
\({60^o}\)
Question:In a triangle \(ABC,\)if \(a\sin A = b\sin B\), then the nature of the triangle
\(a > b\)
\(a < b\)
\(a = b\)
\(a + b = c\)
Question:If in a triangle \(ABC\), \(\cos A + \cos B + \cos C = \frac{3}{2}\), then the triangle is
Question:In triangle ABC and DEF, AB = DE, AC = EF and \(\angle A = 2\angle E\). Two triangles will have the same area, if angle A is equal to
\(\frac{\pi }{3}\)
\(\frac{{2\pi }}{3}\)
\(\frac{{5\pi }}{6}\)
Question:We are given b, c and \(\sin B\) such that B is acute and \(b < c\sin B\). Then
No triangle is possible
One triangle is possible
Two triangles are possible
A right angled triangle is possible
Question:If in a \(\Delta ABC\), the altitudes from the vertices A, B, C on opposite sides are in H.P. then \(\sin A,\,\sin B,\sin C\) are in
A.G.P.
H.P.
G.P.
A.P.
Question:If a, b and c are the sides of a triangle such that \({a^4} + {b^4} + {c^4} = 2{c^2}({a^2} + {b^2})\)then the angles opposite to the side C is
\(45^\circ \) or \(135^\circ \)
\(30^\circ \) or \(100^\circ \)
\(50^\circ \) or \(100^\circ \)
\(60^\circ \) or \(120^\circ \)
Question:In a triangle ABC, \(a:b:c = 4:5:6\). The ratio of the radius of the circumcircle to that of the incircle is
\(\frac{{16}}{9}\)
\(\frac{{16}}{7}\)
\(\frac{{11}}{7}\)
\(\frac{7}{{16}}\)
Question:Which is true in the following [UPSEAT 1999]
\(a\cos A + b\cos B + c\cos C = R\sin A\sin B\sin C\)
\(a\cos A + b\cos B + c\cos C = 2R\sin A\sin B\sin C\)
\(a\cos A + b\cos B + c\cos C = 4R\sin A\sin B\sin C\)
\(a\cos A + b\cos B + c\cos C = 8R\sin A\sin B\sin C\)
Question:The angle of elevation of the top of a tower from a point A due south of the tower is \(\alpha \)and from a point B due east of the tower is \(\beta \). If AB =d, then the height of the tower is
\(\frac{d}{{\sqrt {{{\tan }^2}\alpha - {{\tan }^2}\beta } }}\)
\(\frac{d}{{\sqrt {{{\tan }^2}\alpha + {{\tan }^2}\beta } }}\)
\(\frac{d}{{\sqrt {{{\cot }^2}\alpha + {{\cot }^2}\beta } }}\)
\(\frac{d}{{\sqrt {{{\cot }^2}\alpha - {{\cot }^2}\beta } }}\)
Question:A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \(60^\circ \). When he retires 40 meters from the bank, he finds the angle to be \(30^\circ \). The breadth of the river is
20 m
40 m
30 m
60 m
Question:Two vertical poles of equal heights are 120 m apart. On the line joining their bottoms, A and B are two points. Angle of elevation of the top of one pole from A is \(45^\circ \) and that of the other pole from B is also \(45^\circ \). If AB = 30 m, then the height of each pole is
45 m
50 m
42 m
Question:At a distance 2h from the foot of a tower of height h, the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be
\(\frac{{5h}}{3}\)
\(\frac{{4h}}{3}\)
\(\frac{{7h}}{5}\)
\(\frac{{3h}}{2}\)
Question:From an aeroplane vertically over a straight horizontally road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be a and b, then the height in miles of aeroplane above the road is
\(\frac{{\tan \alpha \,.\,\tan \beta }}{{\cot \alpha + \cot \beta }}\)
\(\frac{{\tan \alpha + \tan \beta }}{{\tan \alpha \,.\,\tan \beta }}\)
\(\frac{{\cot \alpha + \cot \beta }}{{\tan \alpha \,.\,\tan \beta }}\)
\(\frac{{\tan \alpha \,.\,\tan \,\beta }}{{\tan \alpha + \tan \beta }}\)
Question:A balloon is observed simultaneously from three points A, B and C on a straight road directly under it. The angular elevation at B is twice and at C is thrice that of A. If the distance between A and B is 200 metres and the distance between B and C is 100 metres, then the height of balloon is given by
50 metres
\(50\,\sqrt 3 \) metres
\(50\,\sqrt 2 \) Metres
Question:The angles of elevation of the top of a tower from the top and bottom at a building of height a are \({30^0}\) and \({45^0}\) respectively. If the tower and the building stand at the same level, then the height of the tower is [Karnataka CET 2000]
\(a\sqrt 3 \)
\(\frac{{a\sqrt 3 }}{{\sqrt 3 - 1}}\)
\(\frac{{a\,(3 + \sqrt 3 )}}{2}\)
\(a\,(\sqrt 3 - 1)\)
Question:A ladder 5 metre long leans against a vertical wall. The bottom of the ladder is 3 metre from the wall. If the bottom of the ladder is pulled 1 metre farther from the wall, how much does the top of the ladder slide down the wall
1 m
7 m
2 m