MCQOPTIONS
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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2751. |
If the position vectors of A and B are \[\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] and \[5\mathbf{i}-2\mathbf{j}+4\mathbf{k},\] then the direction cosine of \[\overrightarrow{AB}\] along y-axis is [MNR 1989] |
| A. | \[\frac{4}{\sqrt{162}}\] |
| B. | \[-\frac{5}{\sqrt{162}}\] |
| C. | 5 |
| D. | 11 |
| Answer» C. 5 | |
| 2752. |
If the position vectors of the vertices of a triangle be \[2\mathbf{i}+4\mathbf{j}-\mathbf{k},\] \[4\mathbf{i}+5\mathbf{j}+\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-3\mathbf{k},\] then the triangle is [UPSEAT 2004] |
| A. | Right angled |
| B. | Isosceles |
| C. | Equilateral |
| D. | Right angled isosceles |
| Answer» E. | |
| 2753. |
A force is a |
| A. | Unit vector |
| B. | Localised vector |
| C. | Zero vector |
| D. | Free vector |
| Answer» C. Zero vector | |
| 2754. |
The position vectors of P and Q are \[5\mathbf{i}+4\mathbf{j}+a\mathbf{k}\] and \[-\mathbf{i}+2\mathbf{j}-2\mathbf{k}\] respectively. If the distance between them is 7, then the value of a will be |
| A. | 5, 1 |
| B. | 5, 1 |
| C. | 0, 5 |
| D. | 1, 0 |
| Answer» B. 5, 1 | |
| 2755. |
A unit vector a makes an angle \[\frac{\pi }{4}\] with z-axis. If \[\mathbf{a}+\mathbf{i}+\mathbf{j}\] is a unit vector, then a is equal to [IIT 1988] |
| A. | \[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\] |
| B. | \[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}-\frac{\mathbf{k}}{\sqrt{2}}\] |
| C. | \[-\frac{\mathbf{i}}{2}-\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2756. |
The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are |
| A. | \[\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{6}} \right)\] |
| B. | \[\left( \frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}} \right)\] |
| C. | \[\left( -\frac{1}{\sqrt{6}},\,\,-\frac{1}{\sqrt{6}},\,-\,\frac{1}{\sqrt{6}} \right)\] |
| D. | \[\left( \frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}},\,\frac{1}{\sqrt{3}} \right)\] |
| Answer» E. | |
| 2757. |
The system of vectors \[\mathbf{i},\,\,\mathbf{j},\,\,\mathbf{k}\] is |
| A. | Orthogonal |
| B. | Coplanar |
| C. | Collinear |
| D. | None of these |
| Answer» B. Coplanar | |
| 2758. |
The value of k for which the vectors \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=-2\,\mathbf{i}+k\,\mathbf{j}\] are collinear is [Pb. CET 2004] |
| A. | 2 |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{3}\] |
| D. | 3 |
| Answer» B. \[\frac{1}{2}\] | |
| 2759. |
If a, b, c are three non-coplanar vectors such that \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\alpha \,\mathbf{d}\] and \[\mathbf{b}+\mathbf{c}+\mathbf{d}=\beta \,\mathbf{a},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}\] is equal to |
| A. | 0 |
| B. | \[\alpha \text{ }\mathbf{a}\] |
| C. | \[\beta \text{ }\mathbf{b}\] |
| D. | \[(\alpha +\beta )\,\mathbf{c}\] |
| Answer» B. \[\alpha \text{ }\mathbf{a}\] | |
| 2760. |
The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is [IIT 1984] |
| A. | 12 |
| B. | 15 |
| C. | 9 |
| D. | None |
| Answer» C. 9 | |
| 2761. |
a and b are two non-collinear vectors, then \[x\mathbf{a}+y\mathbf{b}\] (where x and y are scalars) represents a vector which is [MP PET 2003] |
| A. | Parallel to b |
| B. | Parallel to a |
| C. | Coplanar with a and b |
| D. | None of these |
| Answer» D. None of these | |
| 2762. |
If three points A, B and C have position vectors \[(1,\,x,\,3),\,\,(3,\,4,\,7)\] and \[ap+bq+cr=1\] respectively and if they are collinear, then \[(x,\,y)=\] [EAMCET 2002] |
| A. | (2, ? 3) |
| B. | (? 2, 3) |
| C. | (2, 3) |
| D. | (? 2, ? 3) |
| Answer» B. (? 2, 3) | |
| 2763. |
If three points A, B, C are collinear, whose position vectors are \[\mathbf{i}-2\mathbf{j}-8\mathbf{k},\,\,5\mathbf{i}-2\mathbf{k}\] and \[11\,\mathbf{i}+\,3\,\mathbf{j}+7\mathbf{k}\] respectively, then the ratio in which B divides AC is [RPET 1999] |
| A. | 1 : 2 |
| B. | 0.0854166666666667 |
| C. | 2 : 1 |
| D. | 0.0423611111111111 |
| Answer» C. 2 : 1 | |
| 2764. |
The position vectors of four points P, Q, R, S are \[2\mathbf{a}+4\mathbf{c},\,\] \[5\mathbf{a}+3\sqrt{3}\,\mathbf{b}+4\mathbf{c},\] \[-2\sqrt{3}\mathbf{b}+\mathbf{c}\] and \[2\mathbf{a}+\mathbf{c}\] respectively, then [MP PET 1997] |
| A. | \[\overrightarrow{PQ}\] is parallel to \[\overrightarrow{RS}\] |
| B. | \[\overrightarrow{PQ}\] is not parallel to \[\overrightarrow{RS}\] |
| C. | \[\overrightarrow{PQ}\] is equal to \[\overrightarrow{RS}\] |
| D. | \[\overrightarrow{PQ}\] is parallel and equal to \[\overrightarrow{RS}\] |
| Answer» B. \[\overrightarrow{PQ}\] is not parallel to \[\overrightarrow{RS}\] | |
| 2765. |
If \[\mathbf{a}=(1,\,\,-1)\] and \[\mathbf{b}=(-\,2,\,m)\] are two collinear vectors, then m= [MP PET 1998] |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 0 |
| Answer» D. 0 | |
| 2766. |
If a and b are two non-collinear vectors and \[x\,\mathbf{a}+y\,\mathbf{b}=0\] [RPET 2001] |
| A. | \[x=0\], but y is not necessarily zero |
| B. | \[y=0\], but x is not necessarily zero |
| C. | \[x=0\], \[y=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 2767. |
sThe vectors \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\] \[\lambda \mathbf{i}+4\mathbf{j}+7\mathbf{k},\] \[-3\mathbf{i}-2\mathbf{j}-5\mathbf{k}\] are collinear, if l equals [Kurukshetra CEE 1996] |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» B. 4 | |
| 2768. |
If a, b, c are the position vectors of three collinear points, then the existence of x, y, z is such that |
| A. | \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z\ne 0\] |
| B. | \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z=0\] |
| C. | \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z\ne 0\] |
| D. | \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z=0\] |
| Answer» E. | |
| 2769. |
The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by [MP PET 1993] |
| A. | \[15+\sqrt{157}\] |
| B. | \[15-\sqrt{157}\] |
| C. | \[\sqrt{15}-\sqrt{157}\] |
| D. | \[\sqrt{15}+\sqrt{157}\] |
| Answer» B. \[15-\sqrt{157}\] | |
| 2770. |
If \[\mathbf{a}=(2,\,\,5)\] and \[\mathbf{b}=(1,\,\,4),\] then the vector parallel to \[(\mathbf{a}+\mathbf{b})\] is |
| A. | (3, 5) |
| B. | (1, 1) |
| C. | (1, 3) |
| D. | (8, 5) |
| Answer» D. (8, 5) | |
| 2771. |
The vectors a, b and a + b are |
| A. | Collinear |
| B. | Coplanar |
| C. | Non-coplanar |
| D. | None of these |
| Answer» C. Non-coplanar | |
| 2772. |
If the position vectors of A, B, C, D are \[2\,\mathbf{i}+\mathbf{j},\] \[\mathbf{i}-3\,\mathbf{j},\] \[3\,\mathbf{i}+2\,\mathbf{j}\] and \[\mathbf{i}+\lambda \mathbf{j}\] respectively and \[\overrightarrow{AB}||\overrightarrow{CD}\] , then \[\lambda \] will be [RPET 1988] |
| A. | 8 |
| B. | 6 |
| C. | 8 |
| D. | 6 |
| Answer» C. 8 | |
| 2773. |
If \[(x,\,\,y,\,\,z)\ne (0,\,\,0,\,\,0)\] and \[(\mathbf{i}+\mathbf{j}+3\,\mathbf{k})\,x+(3\,\mathbf{i}-3\mathbf{j}+\mathbf{k})\,y\]\[+(-4\mathbf{i}+5\mathbf{j})\,z=\lambda \,(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}),\] then the value of l will be [IIT 1982; RPET 1984] |
| A. | 2, 0 |
| B. | 0, ? 2 |
| C. | 1, 0 |
| D. | 0, ? 1 |
| Answer» E. | |
| 2774. |
If the vectors \[3\,\mathbf{i}+2\,\mathbf{j}-\mathbf{k}\]and \[6\,\mathbf{i}-4x\mathbf{j}+y\mathbf{k}\] are parallel, then the value of x and y will be [RPET 1985, 86] |
| A. | 1, ? 2 |
| B. | 1, ? 2 |
| C. | 1, 2 |
| D. | 1, 2 |
| Answer» B. 1, ? 2 | |
| 2775. |
Three points whose position vectors are \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\mathbf{b}\] will be collinear, if the value of k is [IIT 1984] |
| A. | Zero |
| B. | Only negative real number |
| C. | Only positive real number |
| D. | Every real number |
| Answer» E. | |
| 2776. |
The points with position vectors \[10\,\mathbf{i}+3\,\mathbf{j},\,\,12\,\mathbf{i}-5\,\mathbf{j}\] and \[a\,\mathbf{i}+11\,\mathbf{j}\] are collinear, if \[a=\] [MNR 1992; Kurukshetra CEE 2002] |
| A. | 8 |
| B. | 4 |
| C. | 8 |
| D. | 12 |
| Answer» D. 12 | |
| 2777. |
If O be the origin and the position vector of A be \[4\,\mathbf{i}+5\,\mathbf{j},\] then a unit vector parallel to \[\overrightarrow{OA}\] is |
| A. | \[\frac{4}{\sqrt{41}}\mathbf{i}\] |
| B. | \[\frac{5}{\sqrt{41}}\mathbf{i}\] |
| C. | \[\frac{1}{\sqrt{41}}(4\,\mathbf{i}+5\,\mathbf{j})\] |
| D. | \[\frac{1}{\sqrt{41}}(4\,\mathbf{i}-5\,\mathbf{j})\] |
| Answer» D. \[\frac{1}{\sqrt{41}}(4\,\mathbf{i}-5\,\mathbf{j})\] | |
| 2778. |
The perimeter of a triangle with sides \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\] \[4\mathbf{i}-3\mathbf{j}-5\mathbf{k}\] and \[7\mathbf{i}+\mathbf{j}\] is [MP PET 1991] |
| A. | \[\sqrt{450}\] |
| B. | \[\sqrt{150}\] |
| C. | \[\sqrt{50}\] |
| D. | \[\sqrt{200}\] |
| Answer» B. \[\sqrt{150}\] | |
| 2779. |
If the position vectors of the vertices of a triangle be \[6\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\,\,4\mathbf{i}+5\mathbf{j}+6\mathbf{k}\] and \[5\mathbf{i}+6\mathbf{j}+4\mathbf{k},\] then the triangle is |
| A. | Right angled |
| B. | Isosceles |
| C. | Equilateral |
| D. | None of these |
| Answer» D. None of these | |
| 2780. |
If \[4\hat{i}+7\hat{j}+8\hat{k},\,\,2\hat{i}+3\hat{j}+4\hat{k}\] and \[2\hat{i}+5\hat{j}+7\hat{k}\] are the position vectors of the vertices A, B and C, respectively, of triangle ABC, then the position vector of the point where the bisector of angle A meets BC is |
| A. | \[\frac{2}{3}(-6\hat{i}-8\hat{j}-6\hat{k})\] |
| B. | \[\frac{2}{3}(6\hat{i}+8\hat{j}+6\hat{k})\] |
| C. | \[\frac{1}{3}(6\hat{i}+8\hat{j}\,+18\hat{k})\] |
| D. | \[\frac{1}{3}(5\hat{j}+12\hat{k})\] |
| Answer» D. \[\frac{1}{3}(5\hat{j}+12\hat{k})\] | |
| 2781. |
Find the value of \[\lambda \] so that the points P, Q, R and S on the sides OA, OB, OC and AB, respectively, of a regular tetrahedron OABC are coplanar. It is given that \[\frac{OP}{OA}=\frac{1}{3},\frac{OQ}{OB}=\frac{1}{2},\frac{QR}{OC}=\frac{1}{3}\] and\[\frac{OS}{AB}=\lambda \]. |
| A. | \[\lambda =\frac{1}{2}\] |
| B. | \[\lambda =-1\] |
| C. | \[\lambda =0\] |
| D. | for no value of \[\lambda \] |
| Answer» C. \[\lambda =0\] | |
| 2782. |
If the vectors \[\vec{a}\] and \[\vec{b}\] are linearly independent satisfying\[(\sqrt{3}tan\theta +1)\vec{a}+(\sqrt{3}sec\theta -2)\vec{b}\]=0, then the most general values of \[\theta \] are |
| A. | \[n\pi -\frac{\pi }{6},n\in z\] |
| B. | \[2n\pi \pm \frac{11\pi }{6},n\in z\] |
| C. | \[n\pi \pm \frac{\pi }{6},n\in z\] |
| D. | \[2n\pi +\frac{11\pi }{6},n\in z\] |
| Answer» E. | |
| 2783. |
If \[\vec{a}\] and \[\vec{b}\] are two unit vectors and \[\theta \] is the angle between them, then the unit vector along the angular bisector of \[\vec{a}\] and \[\vec{b}\] will be given by |
| A. | \[\frac{\vec{a}-\vec{b}}{2\cos (\theta /2)}\] |
| B. | \[\frac{\vec{a}+\vec{b}}{2\cos (\theta /2)}\] |
| C. | \[\frac{\vec{a}-\vec{b}}{\cos (\theta /2)}\] |
| D. | none of these |
| Answer» C. \[\frac{\vec{a}-\vec{b}}{\cos (\theta /2)}\] | |
| 2784. |
Given three vectors \[\vec{a}=6\hat{i}-3\hat{j},\hat{b}=2\hat{i}-6\hat{j}\] and \[\vec{c}=-2\hat{i}+21\hat{j}\] such that \[\overrightarrow{\alpha }=\vec{a}+\vec{b}+\vec{c}\]. Then the resolution of the vector \[\overrightarrow{\alpha }\] into components with respect to \[\vec{a}\] and \[\vec{b}\] is given by |
| A. | \[3\vec{a}-2\vec{b}\] |
| B. | \[3\vec{b}\]\[-\]\[2\vec{a}\] |
| C. | \[2\vec{a}-3\vec{b}\] |
| D. | \[\vec{a}-2\vec{b}\] |
| Answer» D. \[\vec{a}-2\vec{b}\] | |
| 2785. |
If \[3\lambda \vec{c}+2\mu (\vec{a}\times \vec{b})=0\], then |
| A. | \[3\lambda +2\mu =0\] |
| B. | \[3\lambda =2\mu \] |
| C. | \[\lambda =\mu \] |
| D. | \[\lambda +\mu =0\] |
| Answer» C. \[\lambda =\mu \] | |
| 2786. |
If vectors \[\overrightarrow{AB}=-3\hat{i}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a \[\Delta \]ABC, then the length of the median through A is |
| A. | \[\sqrt{14}\] |
| B. | \[\sqrt{18}\] |
| C. | \[\sqrt{29}\] |
| D. | 5 |
| Answer» C. \[\sqrt{29}\] | |
| 2787. |
Let the position vectors of the points P and Q be \[4\hat{i}+\hat{j}+\lambda \hat{k}\] and \[2\hat{i}-\hat{j}+\lambda \hat{k}\], respectively. Vector \[\hat{i}-\hat{j}+6\hat{k}\]is perpendicular to the plane containing the origin and the point?s P and Q. then\[\lambda \]equals |
| A. | \[-\,1/2\] |
| B. | 44228 |
| C. | 1 |
| D. | none of these |
| Answer» B. 44228 | |
| 2788. |
Vectors \[3\vec{a}-5\vec{b}\] and \[2\vec{a}+\vec{b}\] are mutually perpendicular. If \[\vec{a}+4\vec{b}\] and \[\vec{b}-\vec{a}\] are also mutually perpendicular, then the cosine of the angle between \[\vec{a}\] and \[\vec{b}\] is |
| A. | \[\frac{19}{5\sqrt{43}}\] |
| B. | \[\frac{19}{3\sqrt{43}}\] |
| C. | \[\frac{19}{2\sqrt{45}}\] |
| D. | \[\frac{19}{6\sqrt{43}}\] |
| Answer» B. \[\frac{19}{3\sqrt{43}}\] | |
| 2789. |
Let \[\vec{a}\cdot \vec{b}=0\] where \[\vec{a}\] and \[\vec{b}\] are unit vectors and the unit vector \[\vec{c}\] is inclined at an angle \[\theta \] to both \[\vec{a}\] and \[\vec{b}\]. If \[\vec{c}=m\vec{a}+n\vec{b}+p(\vec{a}\times \vec{b}),(m,n,p\in R)\], then |
| A. | \[-\frac{\pi }{4}\le \theta \le \frac{\pi }{4}\] |
| B. | \[\frac{\pi }{4}\le \theta \le \frac{3\pi }{4}\] |
| C. | \[0\le \theta \le \frac{\pi }{4}\] |
| D. | \[0\le \theta \le \frac{3\pi }{4}\] |
| Answer» C. \[0\le \theta \le \frac{\pi }{4}\] | |
| 2790. |
Let \[\vec{a}=\hat{i}+\hat{j};\hat{b}=2\hat{i}-\hat{k}\]. Then vector \[\vec{r}\] satisfying the equations \[\vec{r}\times \vec{a}=\vec{b}\times \vec{a}\]and \[\vec{r}\times \vec{b}=\vec{a}\times \vec{b}\] is |
| A. | \[\hat{i}-\hat{j}+\hat{k}\] |
| B. | \[3\hat{i}-\hat{j}+\hat{k}\] |
| C. | \[3\hat{i}+\hat{j}-\hat{k}\] |
| D. | \[\hat{i}-\hat{j}-\hat{k}\] |
| Answer» D. \[\hat{i}-\hat{j}-\hat{k}\] | |
| 2791. |
If \[\hat{a},\] \[\hat{b}\] and \[\hat{c}\] are three unit vectors, such that \[\hat{a}+\hat{b}+\hat{c}\] is also a unit vector and \[{{\theta }_{1}}\], \[{{\theta }_{2}}\] and \[{{\theta }_{3}}\] are angles between the vectors \[\hat{a}\], \[\hat{b}\]; \[\hat{b}\], \[\hat{c}\] and \[\hat{c}\], \[\hat{a}\], respectively, then among \[\theta _{1}^{{}}\],\[\theta _{2}^{{}}\]and \[\theta _{3}^{{}}\] |
| A. | all are acute angles |
| B. | all are right angles |
| C. | at least one is obtuse angle |
| D. | none of these |
| Answer» D. none of these | |
| 2792. |
A uni-modular tangent vector on the curve \[x={{t}^{2}}+2\], \[y=4t-5\], \[z=2{{t}^{2}}-6t\] at t=2 is |
| A. | \[\frac{1}{3}(2\hat{i}+2\hat{j}+\hat{k})\] |
| B. | \[\frac{1}{3}(\hat{i}-\hat{j}-\hat{k})\] |
| C. | \[\frac{1}{6}(2\hat{i}+\hat{j}+\hat{k})\] |
| D. | \[\frac{2}{3}(\hat{i}+\hat{j}+\hat{k})\] |
| Answer» B. \[\frac{1}{3}(\hat{i}-\hat{j}-\hat{k})\] | |
| 2793. |
Let \[\vec{a}\], \[\vec{b}\] and \[\vec{c}\] be the three vectors having magnitudes 1, 5 and 3, respectively, such that the angle between \[\vec{a}\] and \[\vec{b}\] is \[\theta \] and \[\vec{a}\times (\vec{a}\times \vec{b})=\vec{c}\] Then tan \[\theta \] is equal to |
| A. | 0 |
| B. | 44257 |
| C. | 3/5 |
| D. | ¾ |
| Answer» E. | |
| 2794. |
The value of expression \[\frac{2(sin{{1}^{o}}+sin{{2}^{o}}+sin{{3}^{o}}+\cdot \cdot \cdot \cdot +\sin {{89}^{o}})}{2(cos{{1}^{o}}+cos{{2}^{o}}+\cdot \cdot \cdot +cos{{44}^{o}})+1}\]Equals |
| A. | \[\sqrt{2}\] |
| B. | \[1/\sqrt{2}\] |
| C. | \[1/2\] |
| D. | 0 |
| Answer» B. \[1/\sqrt{2}\] | |
| 2795. |
If \[\alpha =\frac{\pi }{14}\],then the value of (\[\tan \alpha \tan 2\alpha +\tan 2\alpha \tan 4\alpha +\tan 4\alpha \tan \alpha \])is |
| A. | 1 |
| B. | 44228 |
| C. | 2 |
| D. | 44256 |
| Answer» B. 44228 | |
| 2796. |
\[\frac{\sqrt{2}-\sin \alpha -\cos \alpha }{\sin \alpha -\cos \alpha }\]is equal to |
| A. | \[\sec \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] |
| B. | \[\cos \left( \frac{\pi }{8}-\frac{\alpha }{2} \right)\] |
| C. | \[\tan \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] |
| D. | \[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] |
| Answer» D. \[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] | |
| 2797. |
If\[\cos \alpha +\cos \beta =0=sin\alpha +sin\beta ,\]then \[\cos 2\alpha +\cos 2\beta \]is equal to |
| A. | \[-2\sin (\alpha +\beta )\] |
| B. | \[-2\cos (\alpha +\beta )\] |
| C. | \[2\sin (\alpha +\beta )\] |
| D. | \[2\cos (\alpha +\beta )\] |
| Answer» C. \[2\sin (\alpha +\beta )\] | |
| 2798. |
If \[y=(1+tan\,A)(1-tan\,B),\]where A-B=\[\frac{\pi }{4}\], then \[{{(y+1)}^{y+1}}\]is equal to |
| A. | 9 |
| B. | 4 |
| C. | 27 |
| D. | 81 |
| Answer» D. 81 | |
| 2799. |
If A, B, C are angles of a triangle, then 2sin \[\frac{A}{2}\cos ec\,\frac{B}{2}\sin \frac{C}{2}-\sin A\cot \frac{B}{2}-\cos A\]is |
| A. | independent of A, B, |
| B. | function of A, B |
| C. | function of C |
| D. | none of these |
| Answer» B. function of A, B | |
| 2800. |
If \[{{\tan }^{2}}\frac{\pi -A}{4}+{{\tan }^{2}}\frac{\pi -B}{4}+{{\tan }^{2}}\frac{\pi -C}{4}=1,then\text{ }\Delta ABC\,\,is\] |
| A. | equilateral |
| B. | isosceles |
| C. | scalene |
| D. | none of these |
| Answer» B. isosceles | |