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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.
| 7601. |
If a line in the space makes angle \[\alpha ,\beta \] and \[\gamma \] with the coordinate axes, then \[cos\text{ }2\alpha +cos2\beta \] \[+cos\,2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \]equals. test- The two given expressions on both the sides of the \['='\] sign will have the same value if two numbers from either side or both sides are interchanged. Select the correct numbers to be interchanged from the given options. \['='\] चिन्ह के दोनों ओर दिए गए व्यंजकों का मान तब बराबर होगा जब उनमें किसी एक ओर या दोनों ओर की संख्याओं को आपस में बदला जाएगा। दिए गए विकल्पों में से आपस में बदली जाने वाली सही संख्याओं का चयन करें। \[3+5\times 4-24\div 3=7\times 4-3+36\div 6\] |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 7602. |
What is the angle between the planes\[2x-y+z=6\] and\[x+y+2z=3\]? |
| A. | \[\pi /2\] |
| B. | \[\pi /3\] |
| C. | \[\pi /4\] |
| D. | \[\pi /6\] |
| Answer» C. \[\pi /4\] | |
| 7603. |
The plane \[x+3y+13=0\] passes through the line of intersection of the planes \[2x-8y+4z=p\]and\[3x-5y+4z+10=0\]. If the plane is perpendicular to the plane\[3x-y-2z-4=0\], then the value of p is equal to |
| A. | 2 |
| B. | 5 |
| C. | 9 |
| D. | 3 |
| Answer» E. | |
| 7604. |
The direction ratios of the normal to the plane passing through the points (1, -2, 3), (-1, 2, -1) and parallel to \[\frac{x-2}{2}=\frac{y+1}{3}=\frac{z}{4}\] is |
| A. | (2, 3, 4) |
| B. | (14, 0, 7) |
| C. | (-2, 0, -1) |
| D. | (2, 0, -1) |
| Answer» E. | |
| 7605. |
ABC is a triangle and AD is the median. If the coordinates of A are (4, 7, -8) and the coordinates of centroid of the triangle ABC are (1, 1, 1), what are the coordinates of D? |
| A. | \[\left( -\frac{1}{2},\,\,2,\,\,11 \right)\] |
| B. | \[\left( -\frac{1}{2},-2,\frac{11}{2} \right)\] |
| C. | \[(-1,2,11)\] |
| D. | \[(-5,-11,19)\] |
| Answer» C. \[(-1,2,11)\] | |
| 7606. |
Find the equation of set points P such that \[P{{A}^{2}}+P{{B}^{2}}=2{{K}^{2}},\] where A and B are the points (3, 4, 5) and (-1, 3, -7), respectively: |
| A. | \[{{K}^{2}}-109\] |
| B. | \[2{{K}^{2}}-109\] |
| C. | \[3{{K}^{2}}-109\] |
| D. | \[4{{K}^{2}}-10\] |
| Answer» C. \[3{{K}^{2}}-109\] | |
| 7607. |
The xy-plane divides the line joining the points (-1, 3, 4) (2, -5, 6) |
| A. | Internally in the ratio 2:3 |
| B. | Externally in the ratio 2:3 |
| C. | Internally in the ratio 3:2 |
| D. | Externally in the ratio 3:2 |
| Answer» E. | |
| 7608. |
What are coordinates of the point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0)? |
| A. | \[\left( \frac{a}{3},\frac{a}{3},\frac{a}{3} \right)\] |
| B. | \[\left( \frac{a}{2},\frac{a}{2},\frac{a}{2} \right)\] |
| C. | \[(a,a,a)\] |
| D. | \[(2a,2a,2a)\] |
| Answer» C. \[(a,a,a)\] | |
| 7609. |
The points (5, 2, 4), (6, -1, 2) and (8, -7, k) are collinear if k is equal to |
| A. | -2 |
| B. | 2 |
| C. | 3 |
| D. | -1 |
| Answer» B. 2 | |
| 7610. |
What is the perpendicular distance of the point P(6,7, 8) from xy-plane? |
| A. | 8 |
| B. | 7 |
| C. | 6 |
| D. | None of these |
| Answer» B. 7 | |
| 7611. |
The co-ordinates of the points A and B are (2, 3, 4) and (-2, 5, -4) respectively. If a point P moves so that \[P{{A}^{2}}-P{{B}^{2}}=k\] where k is a constant, then the locus of P is |
| A. | \[-8x+4y-16z+16=k\] |
| B. | \[-8x-4y-16z-16=k\] |
| C. | \[-8x+4y-16z-16=k\] |
| D. | None of these |
| Answer» D. None of these | |
| 7612. |
A parallelopiped is formed by planes drawn through the points (2, 4, 5) and (5, 9, 7) parallel to the coordinate planes. The length of the diagonal of the parallelepiped is |
| A. | 8 |
| B. | 4 |
| C. | 7 |
| D. | 11 |
| Answer» D. 11 | |
| 7613. |
Points (1, 1, 1), (-2, 4, 1), (-1, 5, 5) and (2, 2, 5) are the vertices of a |
| A. | Rectangle |
| B. | Square |
| C. | Parallelogram |
| D. | Trapezium |
| Answer» C. Parallelogram | |
| 7614. |
The ratio in which the join of points (1, -2, 3) and (4, 2, -1) is divided by XOY plane is |
| A. | 0.04375 |
| B. | 0.125694444444444 |
| C. | #VALUE! |
| D. | None of these |
| Answer» C. #VALUE! | |
| 7615. |
The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, -1) is |
| A. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6\] |
| B. | \[{{x}^{2}}-4x+2z+6=0\] |
| C. | \[{{y}^{2}}-2y-4x+2z+6=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-{{z}^{2}}=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}-{{z}^{2}}=0\] | |
| 7616. |
The equation of the plane passing through the point (?1, 3, 2) and perpendicular to each of the planes \[x+2y+3z=5\] and \[3x+3y+z=0\], is |
| A. | \[7x-8y+3z-25=0\] |
| B. | \[7x-8y+3z+25=0\] |
| C. | \[-7x+8y-3z+5=0\] |
| D. | \[7x-8y-3z+5=0\] |
| Answer» C. \[-7x+8y-3z+5=0\] | |
| 7617. |
The angle between two planes \[x+2y+2z=3\] and \[-5x+3y+4z=9\] is [MP PET 2004] |
| A. | \[{{\cos }^{-1}}\frac{3\sqrt{2}}{10}\] |
| B. | \[{{\cos }^{-1}}\frac{19\sqrt{2}}{30}\] |
| C. | \[{{\cos }^{-1}}\frac{9\sqrt{2}}{20}\] |
| D. | \[{{\cos }^{-1}}\frac{3\sqrt{2}}{5}\] |
| Answer» B. \[{{\cos }^{-1}}\frac{19\sqrt{2}}{30}\] | |
| 7618. |
The equation of the plane passing through (1, 1, 1) and (1, ?1, ?1) and perpendicular to \[2x-y+z+5=0\]is [EAMCET 2003] |
| A. | \[2x+5y+z-8=0\] |
| B. | \[x+y-z-1=0\] |
| C. | \[2x+5y+z+4=0\] |
| D. | \[x-y+z-1=0\] |
| Answer» C. \[2x+5y+z+4=0\] | |
| 7619. |
The value of k for which the planes \[3x-6y-2z=7\] and \[2x+y-kz=5\] are perpendicular to each other, is [MP PET 1992] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 7620. |
The equation of the plane passing through (2, 3, 4) and parallel to the plane \[5x-6y+7z=3\] [Kerala (Engg.) 2002] |
| A. | \[5x-6y+7z+20=0\] |
| B. | \[5x-6y+7z-20=0\] |
| C. | \[-5x+6y-7z+3=0\] |
| D. | \[5x+6y+7z+3=0\] |
| Answer» C. \[-5x+6y-7z+3=0\] | |
| 7621. |
In a three dimensional xyz space the equation \[{{x}^{2}}-5x+6=0\] represents [Orissa JEE 2002] |
| A. | Points |
| B. | Plane |
| C. | Curves |
| D. | Pair of straight line |
| Answer» C. Curves | |
| 7622. |
If the planes \[x+2y+kz=0\] and \[2x+y-2z=0\] are at right angles, then the value of k is [MP PET 1999] |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | ? 2 |
| D. | 2 |
| Answer» E. | |
| 7623. |
The equation of the plane through (2, 3, 4) and parallel to the plane \[x+2y+4z=5\]is [MP PET 1996] |
| A. | \[x+2y+4z=10\] |
| B. | \[x+2y+4z=3\] |
| C. | \[x+y+2z=2\] |
| D. | \[x+2y+4z=24\] |
| Answer» E. | |
| 7624. |
The equation of the plane through the three points (1, 1, 1), (1, ?1, 1) and (?7,?3,?5), is [AISSE 1984] |
| A. | \[3x-4z+1=0\] |
| B. | \[3x-4y+1=0\] |
| C. | \[3x+4y+1=0\] |
| D. | None of these |
| Answer» B. \[3x-4y+1=0\] | |
| 7625. |
A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron \[OABC\] is |
| A. | \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-2}}\] |
| B. | \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\] |
| C. | \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16\] |
| D. | None of these |
| Answer» B. \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\] | |
| 7626. |
A plane meets the co-ordinate axes in \[A,B,C\] and \[(\alpha ,\beta ,\gamma )\] is the centered of the triangle \[ABC\]. Then the equation of the plane is [MP PET 2004] |
| A. | \[\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=3\] |
| B. | \[\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=1\] |
| C. | \[\frac{3x}{\alpha }+\frac{3y}{\beta }+\frac{3z}{\gamma }=1\] |
| D. | \[\alpha x+\beta y+\gamma z=1\] |
| Answer» B. \[\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=1\] | |
| 7627. |
The equation of the plane passing through the line of intersection of the planes \[x+y+z=1\] and \[2x+3y-z+4=0\]and parallel to x-axis is |
| A. | \[y-3z-6=0\] |
| B. | \[y-3z+6=0\] |
| C. | \[y-z-1=0\] |
| D. | \[y-z+1=0\] |
| Answer» C. \[y-z-1=0\] | |
| 7628. |
The equation of the plane through (1, 2, 3) and parallel to the plane \[2x+3y-4z=0\]is [MP PET 1990] |
| A. | \[2x+3y+4z=4\] |
| B. | \[2x+3y+4z+4=0\] |
| C. | \[2x-3y+4z+4=0\] |
| D. | \[2x+3y-4z+4=0\] |
| Answer» E. | |
| 7629. |
The angle between the planes \[3x-4y+5z=0\] and \[2x-y-2z=5\] is [MP PET 1988] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | None of these |
| Answer» C. \[\frac{\pi }{6}\] | |
| 7630. |
The point of intersection of the line passing through (0, 0, 1) and intersecting the lines \[x+2y+z=1\], \[-x+y-2z=2\] and\[x+y=2,\,\,x+z=2\] with xy plane is |
| A. | \[\left( \frac{5}{3},-\frac{1}{3},0 \right)\] |
| B. | (1, 1, 0) |
| C. | \[\left( \frac{2}{3},-\frac{1}{3},0 \right)\] |
| D. | \[\left( -\frac{5}{3},\frac{1}{3},0 \right)\] |
| Answer» B. (1, 1, 0) | |
| 7631. |
If the foot of the perpendicular from the origin to a plane is P (a, b, c), the equation of the plane is |
| A. | \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3\] |
| B. | \[ax+by+cz=3\] |
| C. | \[ax+by+cz={{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| D. | \[ax+by+cz=a+b+c\] |
| Answer» D. \[ax+by+cz=a+b+c\] | |
| 7632. |
A(-1, 1), B(5, 3) are opposite vertices of a square in xy-plane. The equation of the other diagonal (not passing through (A, B) of the square is given by [EAMCET 1993] |
| A. | \[x-3y+4=0\] |
| B. | \[2x-y+3=0\] |
| C. | \[y+3x-8=0\] |
| D. | \[x+2y-1=0\] |
| Answer» D. \[x+2y-1=0\] | |
| 7633. |
The opposite angular points of a square are \[(3,\ 4)\] and \[(1,\ -\ 1)\]. Then the co-ordinates of other two points are [Roorkee 1985] |
| A. | \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( -\frac{1}{2},\,\,\frac{5}{2} \right)\] |
| B. | \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( \frac{1}{2},\,\,\frac{5}{2} \right)\] |
| C. | \[D\,\left( \frac{9}{2},\,\,\frac{1}{2} \right)\,,\,\,B\,\left( -\frac{1}{2},\,\,\frac{5}{2} \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 7634. |
The equation of the straight line which is perpendicular to \[y=x\] and passes through (3, 2) is [MP PET 2002] |
| A. | \[x-y=5\] |
| B. | \[x+y=5\] |
| C. | \[x+y=1\] |
| D. | \[x-y=1\] |
| Answer» C. \[x+y=1\] | |
| 7635. |
If the intercept made by the line between the axis is bisected at the point (5, 2), then its equation is [RPET 1996] |
| A. | \[5x+2y=20\] |
| B. | \[2x+5y=20\] |
| C. | \[5x-2y=20\] |
| D. | \[2x-5y=20\] |
| Answer» C. \[5x-2y=20\] | |
| 7636. |
Equations of lines which passes through the points of intersection of the lines \[4x-3y-1=0\] and \[2x-5y+3=0\] and are equally inclined to the axes are [AMU 1981] |
| A. | \[y\pm x=0\] |
| B. | \[y-1=\pm \ 1(x-1)\] |
| C. | \[x-1=\pm \ 2(y-1)\] |
| D. | None of these |
| Answer» C. \[x-1=\pm \ 2(y-1)\] | |
| 7637. |
The equation of the line passing through (4, -6) and makes an angle \[{{45}^{o}}\]with positive x-axis, is [RPET 1984] |
| A. | \[x-y-10=0\] |
| B. | \[x-2y-16=0\] |
| C. | \[x-3y-22=0\] |
| D. | None of these |
| Answer» B. \[x-2y-16=0\] | |
| 7638. |
If the transversal y = mr x; r = 1, 2, 3 cut off equal intercepts on the transversal \[x+y=1,\]then \[1+{{m}_{1}},\]\[1+{{m}_{2}},\] \[1+{{m}_{3}}\] are in |
| A. | A. P. |
| B. | G. P. |
| C. | H. P. |
| D. | None of these |
| Answer» D. None of these | |
| 7639. |
The equation of line whose mid point is \[({{x}_{1}},\ {{y}_{1}})\] in between the axes, is [RPET 1988] |
| A. | \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=2\] |
| B. | \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=\frac{1}{2}\] |
| C. | \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=1\] |
| D. | None of these |
| Answer» B. \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=\frac{1}{2}\] | |
| 7640. |
The points A (1, 3) and C (5, 1) are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient 2, is [RPET 1991] |
| A. | \[2x+y-8=0\] |
| B. | \[2x-y-4=0\] |
| C. | \[2x-y+4=0\] |
| D. | \[2x+y+7=0\] |
| Answer» C. \[2x-y+4=0\] | |
| 7641. |
The equation of the line joining the origin to the point (-4, 5), is [MP PET 1984] |
| A. | \[5x+4y=0\] |
| B. | \[3x+4y=2\] |
| C. | \[5x-4y=0\] |
| D. | \[4x-5y=0\] |
| Answer» B. \[3x+4y=2\] | |
| 7642. |
The equations of the lines which pass through the origin and are inclined at an angle \[{{\tan }^{-1}}m\] to the line \[y=mx+c,\] are |
| A. | \[x=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\] |
| B. | \[y=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\] |
| C. | \[y=0,\ \ 2mx+(1-{{m}^{2}})\ y=0\] |
| D. | None of these |
| Answer» C. \[y=0,\ \ 2mx+(1-{{m}^{2}})\ y=0\] | |
| 7643. |
If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is |
| A. | \[\frac{5}{4}\] |
| B. | \[\frac{\sqrt{10}}{4}\] |
| C. | \[\frac{\sqrt{13}}{3}\] |
| D. | None of these |
| Answer» B. \[\frac{\sqrt{10}}{4}\] | |
| 7644. |
The point \[({{t}^{2}}+2t+5,\,2{{t}^{2}}+t-2)\] lies on the line \[x+y=2\] for |
| A. | All real values of t |
| B. | Some real values of t |
| C. | \[t=\frac{-3\pm \sqrt{3}}{6}\] |
| D. | None of these |
| Answer» E. | |
| 7645. |
The indenter of a triangle with vertices (7, 1), (-1, 5) and \[(3+2\sqrt{3},\,\,3+4\sqrt{3})\] is |
| A. | \[\left( 3+\frac{2}{\sqrt{3}},3+\frac{4}{\sqrt{3}} \right)\] |
| B. | \[\left( 1+\frac{2}{3\sqrt{3}},1+\frac{4}{3\sqrt{3}} \right)\] |
| C. | \[(7,1)\] |
| D. | None of these |
| Answer» B. \[\left( 1+\frac{2}{3\sqrt{3}},1+\frac{4}{3\sqrt{3}} \right)\] | |
| 7646. |
If the slope of one of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is the square of the other, Then \[\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}=\] |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | None of these |
| Answer» C. 8 | |
| 7647. |
Let \[P=(-1,0),Q=(0,0)\] and \[R=(3,3\sqrt{3})\] be three point. The equation of the bisector of the angle PQR is |
| A. | \[\frac{\sqrt{3}}{2}x+y=0\] |
| B. | \[x+\sqrt{3y}=0\] |
| C. | \[\sqrt{3}x+y=0\] |
| D. | \[x+\frac{\sqrt{3}}{2}y=0\] |
| Answer» D. \[x+\frac{\sqrt{3}}{2}y=0\] | |
| 7648. |
The point \[({{t}^{2}}+2t+5,2{{t}^{2}}+t-2)\] lies on the line\[x+y=2\] for |
| A. | All real values of t |
| B. | Some real values of t |
| C. | \[t=\frac{-3\pm \sqrt{3}}{6}\] |
| D. | None of these |
| Answer» E. | |
| 7649. |
The area of the region bounded by the locus of a point P satisfying \[d(P,A)=4\], where A is (1, 2) is |
| A. | 64 sq. unit |
| B. | 54 sq. unit |
| C. | \[\,16\pi \,\,sq.\text{ }unit\] |
| D. | None of these |
| Answer» B. 54 sq. unit | |
| 7650. |
If \[(-4,5)\] is one vertex and \[7x-y+8=0\] is one diagonal of a square, then he equation of second diagonal is |
| A. | \[x+3y=21\] |
| B. | \[2x-3y=7\] |
| C. | \[x+7y=31\] |
| D. | \[2x+3y=21\] |
| Answer» D. \[2x+3y=21\] | |