Total Questions:50 Total Time: 60 Min
Remaining:
Question:If \(2\sin \theta + \tan \theta = 0\), then the general values of \(\theta \) are
\(2n\pi \pm \frac{\pi }{3}\)
\(n\pi ,2n\pi \pm \frac{{2\pi }}{3}\)
\(n\pi ,2n\pi \pm \frac{\pi }{3}\)
\(n\pi ,\,\,n\pi + \frac{{2\pi }}{3}\)
Question:If \(\sqrt 3 \tan 2\theta + \sqrt 3 \tan 3\theta + \tan 2\theta \tan 3\theta = 1\), then the general value of\(\theta \)is
\(n\pi + \frac{\pi }{5}\)
\(\left( {n + \frac{1}{6}} \right)\frac{\pi }{5}\)
\(\left( {2n \pm \frac{1}{6}} \right)\frac{\pi }{5}\)
\(\left( {n + \frac{1}{3}} \right)\frac{\pi }{5}\)
Question:If \(\tan \theta - \sqrt 2 \sec \theta = \sqrt 3 \), then the general value of \(\theta \) is
\(n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}\)
\(n\pi + {( - 1)^n}\frac{\pi }{3} - \frac{\pi }{4}\)
\(n\pi + {( - 1)^n}\frac{\pi }{3} + \frac{\pi }{4}\)
\(n\pi + {( - 1)^n}\frac{\pi }{4} + \frac{\pi }{3}\)
Question:If \(\sin \theta + \cos \theta = \sqrt 2 \cos \alpha \), then the general value of \(\theta \) is
\(2n\pi - \frac{\pi }{4} \pm \,\,\alpha \)
\(2n\pi + \frac{\pi }{4} \pm \alpha \)
\(n\pi - \frac{\pi }{4} \pm \alpha \)
\(n\pi + \frac{\pi }{4} \pm \alpha \)
Question:General value of \(\theta \) satisfying the equation \({\tan ^2}\theta + \sec 2\theta - = 1\) is
\(m\pi ,n\pi + \frac{\pi }{3}\)
\(m\pi ,n\pi \pm \frac{\pi }{3}\)
\(m\pi ,n\pi \pm \frac{\pi }{6}\)
None of these
Question:The general value \(\theta \) is obtained from the equation \(\cos 2\theta = \sin \alpha ,\) is
\(2\theta = \frac{\pi }{2} - \alpha \)
\(\theta = 2n\pi \pm \left( {\frac{\pi }{2} - \alpha } \right)\)
\(\theta = \frac{{n\pi + {{( - 1)}^n}\alpha }}{2}\)
\(\theta = n\pi \pm \left( {\frac{\pi }{4} - \frac{\alpha }{2}} \right)\)
Question:If \(\frac{{\tan 3\theta - 1}}{{\tan 3\theta + 1}} = \sqrt 3 \), then the general value of \(\theta \)is
\(\frac{{n\pi }}{3} + \frac{\pi }{{12}}\)
\(\frac{{n\pi }}{3} + \frac{{7\pi }}{{36}}\)
\(n\pi + \frac{{7\pi }}{{12}}\)
\(n\pi + \frac{\pi }{{12}}\)
Question:If \(2{\cos ^2}x + 3\sin x - 3 = 0,\,\,0 \le x \le {180^o}\), then x =
\({30^o},{90^o},{150^o}\)
\({60^o},{120^o},{180^o}\)
\({0^o},{30^o},{150^o}\)
\({45^o},{90^o},{135^o}\)
Question:If \(2{\sin ^2}\theta = 3\cos \theta ,\)where \(0 \le \theta \le 2\pi \), then \(\theta = \)
\(\frac{\pi }{6},\frac{{7\pi }}{6}\)
\(\frac{\pi }{3},\frac{{5\pi }}{3}\)
\(\frac{\pi }{3},\frac{{7\pi }}{3}\)
Question:If\(\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0\), where \(0 < \theta < {180^o}\), then \(\theta \) =
\({30^o},{45^o}\)
\({45^o},{90^o}\)
\({135^o},{150^o}\)
\({30^o},{45^o},{90^o},{135^o},{150^o}\)
Question:Common roots of the equations \(2{\sin ^2}x + {\sin ^2}2x = 2\) and \(\sin 2x + \cos 2x = \tan x,\) are
\(x = (2n - 1)\frac{\pi }{2}\)
\(x = (2n + 1)\frac{\pi }{4}\)
\(x = (2n + 1)\frac{\pi }{3}\)
Question:If \(r\,\sin \theta = 3,r = 4(1 + \sin \theta ),\,\,0 \le \theta \le 2\pi ,\)then \(\theta = \)
\(\frac{\pi }{6},\frac{\pi }{3}\)
\(\frac{\pi }{6},\frac{{5\pi }}{6}\)
\(\frac{\pi }{3},\frac{\pi }{4}\)
\(\frac{\pi }{2},\pi \)
Question:The general solution of \(\sin x - \cos x = \sqrt 2 \), for any integer n is
\(n\pi \)
\(2n\pi + \frac{{3\pi }}{4}\)
\(2n\pi \)
\((2n + 1)\,\pi \)
Question:If \(12{\cot ^2}\theta - 31\,{\rm{cosec }}\theta + {\rm{32}} = {\rm{0}}\), then the value of \(\sin \theta \) is
\(\frac{3}{5}\) or 1
\( - \sin (B + 2C) = \frac{1}{2}\) or \(\frac{{ - 2}}{3}\)
\(\frac{4}{5}\) or \(\frac{3}{4}\)
\( \pm \frac{1}{2}\)
Question:The period of the function \(\sin \left( {\frac{{2x}}{3}} \right) + \sin \left( {\frac{{3x}}{2}} \right)\)is
\(2\pi \)
\(10\pi \)
\(6\pi \)
\(12\pi \)
Question:Let \(f(x) = \cos px + \sin x\) be periodic, then p must be
Irrational
Positive real number
Rational
Question:In \(\Delta ABC,\)if \({\sin ^2}\frac{A}{2},{\sin ^2}\frac{B}{2},{\sin ^2}\frac{C}{2}\) be in H. P. then a, b, c will be in
A. P.
G. P.
H. P.
Question:In \(\Delta ABC,{(a - b)^2}{\cos ^2}\frac{C}{2} + {(a + b)^2}{\sin ^2}\frac{C}{2} = \)
\({a^2}\)
\({b^2}\)
\({c^2}\)
Question:If \(\tan \frac{{B - C}}{2} = x\cot \frac{A}{2},\)then \(x = \)
\(\frac{{c - a}}{{c + a}}\)
\(\frac{{a - b}}{{a + b}}\)
\(\frac{{b - c}}{{b + c}}\)
Question:In \(\Delta ABC\), if \(a = 3,b = 4,c = 5\), then \(\sin 2B = \)
05/Apr
20/Mar
24/25
01/50
Question:If the sides of a triangle are in A. P., then the cotangent of its half the angles will be in [MP PET 1993]
G . P.
No particular order
Question:If the angles of a triangle are in the ratio 1: 2: 3, then their corresponding sides are in the ratio
01:02:03
\(1:\sqrt 3 :2\)
\(\sqrt 2 :\sqrt 3 :3\)
\(1:\sqrt 3 :3\)
Question:The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is \({60^o}\). If the third side is 3, the remaining fourth side is
2
3
4
5
Question:In a triangle \(ABC,\)\(a = 4,b = 3\), \(\angle A = {60^o}\). Then c is the root of the equation
\({c^2} - 3c - 7 = 0\)
\({c^2} + 3c + 7 = 0\)
\({c^2} - 3c + 7 = 0\)
\({c^2} + 3c - 7 = 0\)
Question:In a triangle \(ABC\), if \(a = 2,B = {60^o}\)and \(C = {75^o}\), then b =
\(\sqrt 3 \)
\(\sqrt 6 \)
\(\sqrt 9 \)
\(1 + \sqrt 2 \)
Question:In triangle ABC, \(A = {30^o},b = 8,a = 6\), then \(B = {\sin ^{ - 1}}x\), where x =
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{2}{3}\)
1
Question:In a \(\Delta ABC\), \(b = 2,C = {60^o},c = \sqrt 6 \), then a =
\(\sqrt 3 - 1\)
\(\sqrt 3 + 1\)
Question:In a \(\Delta ABC,\)\(2a\sin \,\,\left( {\frac{{A - B + C}}{2}} \right)\) is equal to
\({a^2} + {b^2} - {c^2}\)
\({c^2} + {a^2} - {b^2}\)
\({b^2} - {c^2} - {a^2}\)
\({c^2} - {a^2} - {b^2}\)
Question:In a triangle \(ABC\), right angled at C, the value of \(\tan A + \tan B\) is
\(a + b\)
\(\frac{{{a^2}}}{{bc}}\)
\(\frac{{{b^2}}}{{ac}}\)
\(\frac{{{c^2}}}{{ab}}\)
Question:In a \(\Delta ABC,\) \(A:B:C\). Then \([a + b + c\sqrt 2 ]\) is equal to
2b
2c
3b
3a
Question:If \(\alpha ,\beta ,\gamma \) are angles of a triangle, then \({\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma - 2\cos \alpha \cos \beta \cos \gamma \)is
0
Question:If in \(\Delta ABC,\)\(a = 6,b = 3\)and \(\cos (A - B) = \frac{4}{5}\), then its area will be
7 square unit
8 square unit
9 square unit
Question:In \(\Delta ABC\), if \(2s = a + b + c\), then the value of \(\frac{{s(s - a)}}{{bc}} - \frac{{(s - b)(s - c)}}{{bc}} = \)
\(\sin A\)
\(\cos A\)
\(\tan A\)
Question:If the area of a triangle ABC is D, then \({a^2}\sin 2B + {b^2}\sin 2A\) is equal to
\(3\Delta \)
\(2\Delta \)
\(4\Delta \)
\( - 4\Delta \)
Question:In a right triangle \(AC = BC\) and D is the mid point of AC cotangent of angle \(DBC\) is equal to
1/2
1/3
Question:If a, b, c are the sides and A, B, C are the angles of a triangle \(ABC\), then \(\tan \left( {\frac{A}{2}} \right)\)is equal to
\(\sqrt {\frac{{(s - c)(s - a)}}{{s(s - b)}}} \)
\(\sqrt {\frac{{(s - b)(s - c)}}{{s(s - a)}}} \)
\(\sqrt {\frac{{(s - a)(s - b)}}{{s(s - c)}}} \)
\(\sqrt {\frac{{(s - a)s}}{{(s - b)(s - c)}}} \)
Question:In a \(\Delta ABC\), \(a,\;b,\;A\)are given and \({c_1},\;{c_2}\)are two values of the third side c. The sum of the areas of two triangles with sides \(a,\;b,\;{c_1}\) and \(a,b,\;{c_2}\) is
\(\frac{1}{2}{b^2}\sin 2A\)
\(\frac{1}{2}{a^2}\sin 2A\)
\({b^2}\sin 2A\)
Question:If in a triangle \(ABC\), \(2\cos A = \sin B\,{\rm{cosec}}\,C,\) then
\(a = b\)
\(b = c\)
\(c = a\)
\(2a = bc\)
Question:If the line segment joining the points \(A(a,\,b)\) and \(B(c,\,d)\) subtends an angle \(\theta \) at the origin, then \(\cos \theta \) is equal to
\(\frac{{ab + cd}}{{\sqrt {({a^2} + {b^2})\,({c^2} + {d^2})} }}\)
\(\frac{{ac + bd}}{{\sqrt {({a^2} + {b^2})\,({c^2} + {d^2})} }}\)
\(\frac{{ac - bd}}{{\sqrt {({a^2} + {b^2})\,({c^2} + {d^2})} }}\)
Question:\(ABC\) is a right angled isosceles triangle with \(\angle B = {90^o}\). If D is a point on \(AB\) so that \(\angle DCB = {15^o}\) and if \(AD = 35cm\), then \(CD = \)
\(35\sqrt 2 \)cm\(70\sqrt 2 cm\)
\(\frac{{35\sqrt 3 }}{2}cm\)
\(35\sqrt 6 \)cm
\(\frac{{35\sqrt 2 }}{2}cm\)
Question:If R is the radius of the circumcircle of the \(\Delta ABC\)and \(\Delta \)is its area, then
\(R = \frac{{a + b + c}}{\Delta }\)
\(R = \frac{{a + b + c}}{{4\Delta }}\)
\(R = \frac{{abc}}{{4\Delta }}\)
\(R = \frac{{abc}}{\Delta }\)
Question:The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is
\(a\cot \left( {\frac{\pi }{n}} \right)\)
\(\frac{a}{2}\cot \left( {\frac{\pi }{{2n}}} \right)\)
\(a\cot \left( {\frac{\pi }{{2n}}} \right)\)
Question:An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be \(30^\circ \)o. After 3 minutes this angle becomes 60o. After how much more time, the car will reach the tree
4 min.
4.5 min.
1.5 min.
2 min.
Question:A house of height 100 metres subtends a right angle at the window of an opposite house. If the height of the window be 64 metres, then the distance between the two houses is
48 m
36 m
54 m
72 m
Question:A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of \({60^0}\) with the horizontal and height of the house be \(6\sqrt 3 \) meters, then the length of the ladder is
\(12\sqrt 3 \)
12 m
\(12/\sqrt 3 \,\,m\)
Question:If the angles of elevation of two towers from the middle point of the line joining their feet be \(60^\circ \) and \(30^\circ \) respectively, then the ratio of their heights is
02:01
\(1\,\,:\,\,\sqrt 2 \)
03:01
\(1\,\,:\,\,\sqrt 3 \)
Question:A balloon is coming down at the rate of 4 m/min. and its angle of elevation is \({45^0}\) from a point on the ground which has been reduced to 30o after 10 minutes. Balloon will be on the ground at a distance of how many meters from the observer
\(20\,\sqrt 3 \,m\)
\(20\,(3 + \sqrt 3 )\,m\)
\(10\,(3 + \sqrt 3 )\,m\)
Question:A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45o. Then which of the following statements is correct
Breadth of the river is twice the height of the tower
Breadth of the river and the height of the tower are the same
Breadth of the river is half of the height of the tower
None of the above
Question:The shadow of a tower standing on a level ground is found to be 60 m longer when the sun's altitude is \({30^0}\) than when it is \({45^0}\). The height of the tower is
60 m
30 m
\(60\sqrt 3 m\)
\(30(\sqrt 3 + 1)m\)
Question:If the angle of elevation of the top of tower at a distance 500 m from its foot is \({30^0}\), then height of the tower is
\(\frac{1}{{\sqrt 3 }}\)
\(\frac{{500}}{{\sqrt 3 }}\)
\(\frac{1}{{500}}\)