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.
| 6551. |
The coefficients of three successive terms in the expansion of \[{{(1+x)}^{n}}\] are 165, 330 and 462 respectively, then the value of n will be [UPSEAT 1999] |
| A. | 11 |
| B. | 10 |
| C. | 12 |
| D. | 8 |
| Answer» B. 10 | |
| 6552. |
The equation \[2{{\cos }^{-1}}x+{{\sin }^{-1}}x=\frac{11\pi }{6}\]has [AMU 1999] |
| A. | No solution |
| B. | Only one solution |
| C. | Two solutions |
| D. | Three solutions |
| Answer» B. Only one solution | |
| 6553. |
If \[{{x}_{1}},{{x}_{2}},{{x}_{3}},\,\,\text{and }\,{{y}_{1}},{{y}_{2}},{{y}_{3}}\] are both in G.P. with the same common ratio, then the points \[({{x}_{1}},{{y}_{1}}),\] \[({{x}_{2}},\,{{y}_{2}})\] and \[({{x}_{3}},\,{{y}_{3}})\][AIEEE 2003] |
| A. | Lie on a straight line |
| B. | Lie on an ellipse |
| C. | Lie on a circle |
| D. | Are vertices of a triangle |
| Answer» B. Lie on an ellipse | |
| 6554. |
The angle between the pair of straight lines \[{{y}^{2}}{{\sin }^{2}}\theta -xy{{\sin }^{2}}\theta +{{x}^{2}}({{\cos }^{2}}\theta -1)=1,\]is [MNR 1985; UPSEAT 2000; Kerala (Engg.) 2005] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{2\pi }{3}\] |
| D. | None of these |
| Answer» E. | |
| 6555. |
The solution of the differential equation \[x\frac{dy}{dx}=y(\log y-\log x+1)\]is [IIT 1986; AIEEE 2005] |
| A. | \[y=x{{e}^{cx}}\] |
| B. | \[y+x{{e}^{cx}}=0\] |
| C. | \[y+{{e}^{x}}=0\] |
| D. | None of these |
| Answer» B. \[y+x{{e}^{cx}}=0\] | |
| 6556. |
\[\int_{{}}^{{}}{\sin \sqrt{x}}\ dx=\] [Roorkee 1977] |
| A. | \[2[\sin \sqrt{x}-\cos \sqrt{x}]+c\] |
| B. | \[2[\sin \sqrt{x}-\sqrt{x}\cos \sqrt{x}]+c\] |
| C. | \[2[\sin \sqrt{x}+\cos \sqrt{x}]+c\] |
| D. | \[2[\sin \sqrt{x}+\sqrt{x}\cos \sqrt{x}]+c\] |
| Answer» C. \[2[\sin \sqrt{x}+\cos \sqrt{x}]+c\] | |
| 6557. |
Let \[2{{\sin }^{2}}x+3\sin x-2>0\] and \[{{x}^{2}}-x-2 |
| A. | \[\left( \frac{\pi }{6},\ \frac{5\pi }{6} \right)\] |
| B. | \[\left( -1,\ \frac{5\pi }{6} \right)\] |
| C. | \[(-1,\ 2)\] |
| D. | \[\left( \frac{\pi }{6},\ 2 \right)\] |
| Answer» E. | |
| 6558. |
The points \[O,\,A,\,B,\,C,\,D\] are such that \[\overrightarrow{OA}=\mathbf{a},\] \[\overrightarrow{OB}=\mathbf{b},\,\] \[\overrightarrow{OC}=2\mathbf{a}+3\mathbf{b}\] and \[\overrightarrow{OD}=\mathbf{a}-2\mathbf{b}.\] If \[|\mathbf{a}|\,=3\,|\mathbf{b}|,\] then the angle between \[\overrightarrow{BD}\] and \[\overrightarrow{AC}\] is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | None of these |
| Answer» E. | |
| 6559. |
With reference to a universal set, the inclusion of a subset in another, is relation, which is [Karnataka CET 1995] |
| A. | Symmetric only |
| B. | Equivalence relation |
| C. | Reflexive only |
| D. | None of these |
| Answer» E. | |
| 6560. |
Let R be the relation on the set R of all real numbers defined by a R b iff \[|a-b|\le 1\]. Then R is [Roorkee 1998] |
| A. | Reflexive and Symmetric |
| B. | Symmetric only |
| C. | Transitive only |
| D. | Anti-symmetric only |
| Answer» B. Symmetric only | |
| 6561. |
Let A = {1, 2, 3}, B = {1, 3, 5}. A relation \[R:A\to B\] is defined by R = {(1, 3), (1, 5), (2, 1)}. Then \[{{R}^{-1}}\] is defined by |
| A. | {(1,2), (3,1), (1,3), (1,5)} |
| B. | {(1, 2), (3, 1), (2, 1)} |
| C. | {(1, 2), (5, 1), (3, 1)} |
| D. | None of these |
| Answer» D. None of these | |
| 6562. |
If the coefficient of x in the expansion of \[{{\left( {{x}^{2}}+\frac{k}{x} \right)}^{5}}\] is 270, then k = [EAMCET 2002] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 6563. |
If the solution for \[\theta \]of \[\cos p\theta +\cos q\theta =0,\ p>0,\ q>0\]are in A.P., then the numerically smallest common difference of A.P. is [Kerala (Engg.) 2001] |
| A. | \[\frac{\pi }{p+q}\] |
| B. | \[\frac{2\pi }{p+q}\] |
| C. | \[\frac{\pi }{2(p+q)}\] |
| D. | \[\frac{1}{p+q}\] |
| Answer» C. \[\frac{\pi }{2(p+q)}\] | |
| 6564. |
The solution set of \[(5+4\cos \theta )(2\cos \theta +1)=0\]in the interval \[[0,\,\,2\pi ]\] is [EAMCET 2003] |
| A. | \[\left\{ \frac{\pi }{3},\,\frac{2\pi }{3} \right\}\] |
| B. | \[\left\{ \frac{\pi }{3},\,\pi \right\}\] |
| C. | \[\left\{ \frac{2\pi }{3},\frac{4\pi }{3} \right\}\] |
| D. | \[\left\{ \frac{2\pi }{3},\frac{5\pi }{3} \right\}\] |
| Answer» D. \[\left\{ \frac{2\pi }{3},\frac{5\pi }{3} \right\}\] | |
| 6565. |
If \[1+\sin x+{{\sin }^{2}}x+.....\]to \[\infty =4+2\sqrt{3},\,0 |
| A. | \[x=\frac{\pi }{6}\] |
| B. | \[x=\frac{\pi }{3}\] |
| C. | \[x=\frac{\pi }{3}\]or \[\frac{\pi }{6}\] |
| D. | \[x=\frac{\pi }{3}\]or \[\frac{2\pi }{3}\] |
| Answer» E. | |
| 6566. |
The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (-2, 6). The third vertex is [Kerala (Engg.) 2002] |
| A. | (0, 0) |
| B. | (4, 7) |
| C. | (7, 4) |
| D. | (7, 7) |
| Answer» C. (7, 4) | |
| 6567. |
If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5), then the centroid of the triangle is |
| A. | (5/3, 2) |
| B. | (5/6, 1) |
| C. | (2, 5/3) |
| D. | (1, 5/6) |
| Answer» D. (1, 5/6) | |
| 6568. |
The number of real solutions of \[{{\tan }^{-1}}\sqrt{x(x+1)}+{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}=\frac{\pi }{2}\]is [IIT 1999] |
| A. | Zero |
| B. | One |
| C. | Two |
| D. | Infinite |
| Answer» D. Infinite | |
| 6569. |
If the equation of base of an equilateral triangle is \[2x-y=1\] and the vertex is (?1, 2), then the length of the side of the triangle is [Kerala (Engg.) 2005] |
| A. | \[\sqrt{\frac{20}{3}}\] |
| B. | \[\frac{2}{\sqrt{15}}\] |
| C. | \[\sqrt{\frac{8}{15}}\] |
| D. | \[\sqrt{\frac{15}{2}}\] |
| Answer» B. \[\frac{2}{\sqrt{15}}\] | |
| 6570. |
The graph of the function \[\cos x\ \cos (x+2)-{{\cos }^{2}}(x+1)\] is [IIT 1997 Re-Exam] |
| A. | A straight line passing through \[(0,\,\,-{{\sin }^{2}}1)\]with slope 2 |
| B. | A straight line passing through (0, 0) |
| C. | A parabola with vertex \[{{75}^{o}}\] |
| D. | A straight line passing through the point \[\left( \frac{\pi }{2},-{{\sin }^{2}}1 \right)\] and parallel to the x?axis |
| Answer» E. | |
| 6571. |
The equations of two equal sides of an isosceles triangle are \[7x-y+3=0\] and \[x+y-3=0\] and the third side passes through the point (1, ? 10). The equation of the third side is [IIT 1984] |
| A. | \[y=\sqrt{3}x+9\] but not \[{{x}^{2}}-9{{y}^{2}}=0\] |
| B. | \[3x+y+7=0\] but not \[{{60}^{o}}\] |
| C. | \[3x+y+7=0\] or \[x-3y-31=0\] |
| D. | Neither \[3x+y+7\] nor \[x-3y-31=0\] |
| Answer» D. Neither \[3x+y+7\] nor \[x-3y-31=0\] | |
| 6572. |
If the bisectors of the lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\] be \[{{x}^{2}}-2qxy-{{y}^{2}}=0,\] then [MP PET 1993; DCE 1999; RPET 2003; AIEEE 2003; Kerala (Engg.) 2005] |
| A. | \[pq+1=0\] |
| B. | \[pq-1=0\] |
| C. | \[p+q=0\] |
| D. | \[p-q=0\] |
| Answer» B. \[pq-1=0\] | |
| 6573. |
The equation of the pair of straight lines, each of which makes an angle \[\alpha \]with the line \[y=x\], is [MP PET 1990] |
| A. | \[{{x}^{2}}+2xy\sec 2\alpha +{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| C. | \[{{x}^{2}}-2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}-2xy\sec 2\alpha +{{y}^{2}}=0\] |
| Answer» E. | |
| 6574. |
Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}\,{{x}_{ij}}}\] Subject to : \[\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}\] \[\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}\] is a (L.P.P.) with number of constraints [MP PET 1999] |
| A. | \[m+n\] |
| B. | \[m-n\] |
| C. | mn |
| D. | \[\frac{m}{n}\] |
| Answer» B. \[m-n\] | |
| 6575. |
The maximum value of \[z=4x+3y\] subject to the constraints \[3x+2y\ge 160,\ 5x+2y\ge 200\], \[x+2y\ge 80\]; \[x,\ y\ge 0\] is [MP PET 1998] |
| A. | 320 |
| B. | 300 |
| C. | 230 |
| D. | None of these |
| Answer» E. | |
| 6576. |
The S.D. of a variate x is s. The S.D. of the variate \[\frac{ax+b}{c}\] where a, b, c are constant, is [Pb. CET 1996] |
| A. | \[\left( \frac{a}{c} \right)\,\sigma \] |
| B. | \[\left| \frac{a}{c} \right|\,\sigma \] |
| C. | \[\left( \frac{{{a}^{2}}}{{{c}^{2}}} \right)\,\sigma \] |
| D. | None of these |
| Answer» C. \[\left( \frac{{{a}^{2}}}{{{c}^{2}}} \right)\,\sigma \] | |
| 6577. |
In a series of 2n observations, half of them equal to a and remaining half equal to ?a. If the standard deviation of the observations is 2, then |a| equals [AIEEE 2004] |
| A. | \[\frac{\sqrt{2}}{n}\] |
| B. | \[\sqrt{2}\] |
| C. | 2 |
| D. | \[\frac{1}{n}\] |
| Answer» D. \[\frac{1}{n}\] | |
| 6578. |
The solution of the differential equation \[\sqrt{a+x}\frac{dy}{dx}+xy=0\]is [MP PET 1998] |
| A. | \[y=A{{e}^{2/3(2a-x)\sqrt{x+a}}}\] |
| B. | \[y=A{{e}^{-2/3(a-x)\sqrt{x+a}}}\] |
| C. | \[y=A{{e}^{2/3(2a+x)\sqrt{x+a}}}\] |
| D. | \[y=A{{e}^{-2/3(2a-x)\sqrt{x+a}}}\] (Where A is an arbitrary constant.) |
| Answer» B. \[y=A{{e}^{-2/3(a-x)\sqrt{x+a}}}\] | |
| 6579. |
\[\int_{{}}^{{}}{\frac{a\ dx}{b+c{{e}^{x}}}}=\] [MP PET 1988; BIT Ranchi 1979] |
| A. | \[\frac{a}{b}\log \left( \frac{{{e}^{x}}}{b+c{{e}^{x}}} \right)+c\] |
| B. | \[\frac{a}{b}\log \left( \frac{b+c{{e}^{x}}}{{{e}^{x}}} \right)+c\] |
| C. | \[\frac{b}{a}\log \left( \frac{{{e}^{x}}}{b+c{{e}^{x}}} \right)+c\] |
| D. | \[\frac{b}{a}\log \left( \frac{b+c{{e}^{x}}}{{{e}^{x}}} \right)+c\] |
| Answer» B. \[\frac{a}{b}\log \left( \frac{b+c{{e}^{x}}}{{{e}^{x}}} \right)+c\] | |
| 6580. |
\[\int{\frac{dx}{\sin x-\cos x+\sqrt{2}}}\] equals [MP PET 2002] |
| A. | \[-\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+c\] |
| B. | \[\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+c\] |
| C. | \[\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+c\] |
| D. | \[-\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+c\] |
| Answer» E. | |
| 6581. |
\[\int_{{}}^{{}}{\frac{{{x}^{5}}}{\sqrt{1+{{x}^{3}}}}dx=}\] [IIT 1985] |
| A. | \[\frac{2}{9}{{(1+{{x}^{3}})}^{3/2}}+c\] |
| B. | \[\frac{2}{9}{{(1+{{x}^{3}})}^{3/2}}+\frac{2}{3}{{(1+{{x}^{3}})}^{1/2}}+c\] |
| C. | \[\frac{2}{9}{{(1+{{x}^{3}})}^{3/2}}-\frac{2}{3}{{(1+{{x}^{3}})}^{1/2}}+c\] |
| D. | None of these |
| Answer» D. None of these | |
| 6582. |
\[\frac{d}{dx}\left[ {{\tan }^{-1}}\frac{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}} \right]=\] [Roorkee 1980; Karnataka CET 2005] |
| A. | \[\frac{-x}{\sqrt{1-{{x}^{4}}}}\] |
| B. | \[\frac{x}{\sqrt{1-{{x}^{4}}}}\] |
| C. | \[\frac{-1}{2\sqrt{1-{{x}^{4}}}}\] |
| D. | \[\frac{1}{2\sqrt{1-{{x}^{4}}}}\] |
| Answer» B. \[\frac{x}{\sqrt{1-{{x}^{4}}}}\] | |
| 6583. |
If \[y={{(x\log x)}^{\log \,\log x}}\], then \[\frac{dy}{dx}=\] [Roorkee 1981] |
| A. | \[{{(x\log x)}^{\log \log x}}\left\{ \frac{1}{x\log x}(\log x+\log \log x)+(\log \,\,\log x)\text{ }\left( \frac{1}{x}+\frac{1}{x\log x} \right)\text{ } \right\}\] |
| B. | \[{{(x\log x)}^{x\log x}}\log \log x\left[ \frac{2}{\log x}+\frac{1}{x} \right]\] |
| C. | \[{{(x\log x)}^{x\log x}}\log \log x\left[ \frac{2}{\log x}+\frac{1}{x} \right]\] |
| D. | None of these |
| Answer» B. \[{{(x\log x)}^{x\log x}}\log \log x\left[ \frac{2}{\log x}+\frac{1}{x} \right]\] | |
| 6584. |
Let \[f(x)=(1+{{b}^{2}}){{x}^{2}}+2bx+1\] and \[m(b)\] the minimum value of \[f(x)\]for a given b. As b varies, the range of m is [IIT Screening 2001] |
| A. | [0, 1] |
| B. | \[\left( 0,\ \frac{1}{2} \right]\] |
| C. | \[\left[ \frac{1}{2},\ 1 \right]\] |
| D. | \[(0,\ 1]\] |
| Answer» E. | |
| 6585. |
The range of the function \[f(x){{=}^{7-x}}{{P}_{x-3}}\] is [AIEEE 2004] |
| A. | {1, 2, 3, 4, 5} |
| B. | (1, 2, 3, 4, 5, 6) |
| C. | {1, 2, 3, 4} |
| D. | {1, 2, 3} |
| Answer» E. | |
| 6586. |
The vector \[\mathbf{a}+\mathbf{b}\] bisects the angle between the vectors a and b, if |
| A. | \[|\mathbf{a}|\,=\,|\mathbf{b}|\] |
| B. | \[|\mathbf{a}|\,=\,|\mathbf{b}|\] or angle between a and b is zero |
| C. | \[|\mathbf{a}|\,\,=m\,|\mathbf{b}|\] |
| D. | None of these |
| Answer» C. \[|\mathbf{a}|\,\,=m\,|\mathbf{b}|\] | |
| 6587. |
Let the unit vectors a and b be perpendicular and the unit vector c be inclined at an angle q to both a and b. If \[\mathbf{c}=\alpha \,\mathbf{a}+\beta \,\mathbf{b}+\gamma \,(\mathbf{a}\times \mathbf{b}),\] then [Orissa JEE 2003] |
| A. | \[\alpha =\beta =\cos \theta ,\,\,{{\gamma }^{2}}=\cos \,\,2\theta \] |
| B. | \[\alpha =\beta =\cos \theta ,\,\,{{\gamma }^{2}}=-\cos \,\,2\theta \] |
| C. | \[\alpha =\cos \theta ,\,\,\beta =\sin \theta ,\,\,{{\gamma }^{2}}=\cos \,\,2\theta \] |
| D. | None of these |
| Answer» C. \[\alpha =\cos \theta ,\,\,\beta =\sin \theta ,\,\,{{\gamma }^{2}}=\cos \,\,2\theta \] | |
| 6588. |
If three non-zero vectors are \[\mathbf{a}={{a}_{1}}\mathbf{i}+{{a}_{2}}\mathbf{j}+{{a}_{3}}\mathbf{k},\] \[\mathbf{b}={{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k}\] and \[\mathbf{c}={{c}_{1}}\mathbf{i}+{{c}_{2}}\mathbf{j}+{{c}_{3}}\mathbf{k}.\] If c is the unit vector perpendicular to the vectors a and b and the angle between a and b is \[\frac{\pi }{6},\] then \[{{\left| \,\begin{matrix} {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ \end{matrix}\, \right|}^{2}}\] is equal to [IIT 1986] |
| A. | 0 |
| B. | \[\frac{3\,(\Sigma a_{1}^{2})\,(\Sigma b_{1}^{2})\,(\Sigma c_{1}^{2})}{4}\] |
| C. | 1 |
| D. | \[\frac{(\Sigma a_{1}^{2})\,(\Sigma b_{1}^{2})}{4}\] |
| Answer» E. | |
| 6589. |
If \[{{N}_{a}}=\{an:n\in N\},\] then \[{{N}_{3}}\cap {{N}_{4}}=\] |
| A. | \[{{N}_{7}}\] |
| B. | \[{{N}_{12}}\] |
| C. | \[{{N}_{3}}\] |
| D. | \[{{N}_{4}}\] |
| Answer» C. \[{{N}_{3}}\] | |
| 6590. |
If \[X=\{{{8}^{n}}-7n-1:n\in N\}\] and \[Y=\{49(n-1):n\in N\},\] then |
| A. | \[X\subseteq Y\] |
| B. | \[Y\subseteq X\] |
| C. | \[X=Y\] |
| D. | None of these |
| Answer» B. \[Y\subseteq X\] | |
| 6591. |
If \[{{(1+ax)}^{n}}=1+8x+24{{x}^{2}}+....,\]then the value of a and n is [IIT 1983; Pb. CET 1994, 99] |
| A. | 2, 4 |
| B. | 2, 3 |
| C. | 3, 6 |
| D. | 1, 2 |
| Answer» B. 2, 3 | |
| 6592. |
The value of \[{{(\sqrt{2}+1)}^{6}}+{{(\sqrt{2}-1)}^{6}}\] will be [RPET 1997] |
| A. | - 198 |
| B. | 198 |
| C. | 99 |
| D. | -99 |
| Answer» C. 99 | |
| 6593. |
If \[5{{\cos }^{2}}\theta +7{{\sin }^{2}}\theta -6=0\], then the general value of \[\theta \]is |
| A. | \[2n\pi \pm \frac{\pi }{4}\] |
| B. | \[n\pi \pm \frac{\pi }{4}\] |
| C. | \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] |
| D. | None of these |
| Answer» C. \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] | |
| 6594. |
The general solution of \[\sin x-3\sin 2x+\sin 3x=\] \[\cos x-3\cos 2x+\cos 3x\] is [IIT 1989] |
| A. | \[n\pi +\frac{\pi }{8}\] |
| B. | \[\frac{n\pi }{2}+\frac{\pi }{8}\] |
| C. | \[{{(-1)}^{n}}\frac{n\pi }{2}+\frac{\pi }{8}\] |
| D. | \[2n\pi +{{\cos }^{-1}}\frac{3}{2}\] |
| Answer» C. \[{{(-1)}^{n}}\frac{n\pi }{2}+\frac{\pi }{8}\] | |
| 6595. |
The principal value of \[{{\sin }^{-1}}\left[ \sin \left( \frac{2\pi }{3} \right) \right]\]is [IIT 1986] |
| A. | \[-\frac{2\pi }{3}\] |
| B. | \[\frac{2\pi }{3}\] |
| C. | \[\frac{4\pi }{3}\] |
| D. | None of these |
| Answer» E. | |
| 6596. |
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are [Orissa JEE 2003] |
| A. | \[\left( 13/5,\ 0 \right)\] |
| B. | \[\left( 5/13,\ 0 \right)\] |
| C. | (- 7, 0) |
| D. | None of these |
| Answer» B. \[\left( 5/13,\ 0 \right)\] | |
| 6597. |
\[{{\cot }^{-1}}\left[ \frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}} \right]=\] [MNR 1986] |
| A. | \[\pi -x\] |
| B. | \[2\pi -x\] |
| C. | \[\frac{x}{2}\] |
| D. | \[\pi -\frac{x}{2}\] |
| Answer» E. | |
| 6598. |
The orthocentre of the triangle formed by the lines \[xy=0\]and \[x+y=1\]is [IIT 1995] |
| A. | \[(0,0)\] |
| B. | \[\left( \frac{1}{2},\frac{1}{2} \right)\] |
| C. | \[\left( \frac{1}{3},\frac{1}{3} \right)\] |
| D. | \[\left( \frac{1}{4},\frac{1}{4} \right)\] |
| Answer» B. \[\left( \frac{1}{2},\frac{1}{2} \right)\] | |
| 6599. |
The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is |
| A. | \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2ax-2by=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] | |
| 6600. |
In equations \[3x-y\ge 3\] and \[4x-y>4\] [MP PET 2001] |
| A. | Have solution for positive x and y |
| B. | Have no solution for positive x and y |
| C. | Have solution for all x |
| D. | Have solution for all y |
| Answer» B. Have no solution for positive x and y | |