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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.
| 2251. |
If the extremities of the base of an isosceles triangle are the points \[(2a,0)\] and \[(0,a)\] and the equation of one of the sides is \[x=2a\], then the area of the triangle is |
| A. | \[5{{a}^{2}}sq\]. units |
| B. | \[\frac{5}{2}{{a}^{2}}sq.\]units |
| C. | \[\frac{25{{a}^{2}}}{2}sq.\]units |
| D. | None of these |
| Answer» C. \[\frac{25{{a}^{2}}}{2}sq.\]units | |
| 2252. |
The incentre of the triangle formed by (0, 0), (5,12), (16, 12) is [EAMCET 1984] |
| A. | (7, 9) |
| B. | (9, 7) |
| C. | (-9, 7) |
| D. | (-7, 9) |
| Answer» B. (9, 7) | |
| 2253. |
The centroid of a triangle, whose vertices are (2,1), (5,2) and (3,4), is [IIT 1964] |
| A. | \[\left( \frac{8}{3},\frac{7}{3} \right)\] |
| B. | \[\left( \frac{10}{3},\frac{7}{3} \right)\] |
| C. | \[\left( -\frac{10}{3},\frac{7}{3} \right)\] |
| D. | \[\left( \frac{10}{3},-\frac{7}{3} \right)\] |
| Answer» C. \[\left( -\frac{10}{3},\frac{7}{3} \right)\] | |
| 2254. |
All points lying inside the triangle formed by the points (1, 3), (5,0) and (-1,2) satisfy [IIT 1986; Kurukshetra CEE 1998] |
| A. | \[3x+2y\ge 0\] |
| B. | \[2x+y-13\le 0\] |
| C. | \[2x-3y-12\le 0\] |
| D. | All the above |
| Answer» E. | |
| 2255. |
The area of triangle formed by the points \[(a,b+c),\] \[(b,c+a),\] \[(c,\,a+b)\] is equal to [Pb. CET 2003] |
| A. | \[abc\] |
| B. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| C. | \[ab+bc+ca\] |
| D. | 0 |
| Answer» E. | |
| 2256. |
Orthocentre of the triangle whose vertices are (0, 0) (2, -1) and (1, 3) is [ISM Dhanbad1970; IIT 1967, 74] |
| A. | \[\left( \frac{4}{7},\,\frac{1}{7} \right)\] |
| B. | \[\left( -\frac{4}{7},\,-\frac{1}{7} \right)\] |
| C. | (-4, -1) |
| D. | (4, 1) |
| Answer» C. (-4, -1) | |
| 2257. |
Two vertices of a triangle are (4, -3) and (-2, 5). If the orthocentre of the triangle is at (1, 2), then the third vertex is [Roorkee 1987] |
| A. | (- 33, -26) |
| B. | (33, 26) |
| C. | (26, 33) |
| D. | None of these |
| Answer» C. (26, 33) | |
| 2258. |
The vertices of a triangle are \[[a{{t}_{1}}{{t}_{2}},\,a({{t}_{1}}+{{t}_{2}})],\,\]\[[a{{t}_{2}}{{t}_{3}},\,a({{t}_{2}}+{{t}_{3}})]\], \[[a{{t}_{3}}{{t}_{1}},\,a({{t}_{3}}+{{t}_{1}})]\], then the coordinates of its orthocentre are [IIT 1983] |
| A. | \[[a,\,a({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\] |
| B. | \[[-a,a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\] |
| C. | \[[-a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}}),\,a]\] |
| D. | None of these |
| Answer» C. \[[-a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}}),\,a]\] | |
| 2259. |
Coordinates of the orthocentre of the triangle whose sides are \[x=3,\,y=4\] and \[3x+4y=6\] is [MNR 1989] |
| A. | (0, 0) |
| B. | (3, 0) |
| C. | (0, 4) |
| D. | (3, 4) |
| Answer» E. | |
| 2260. |
If \[A(4,-3)\], \[B(3,-2)\]and\[C\,(2,\text{ }8)\]are the vertices of a triangle, then its centroid will be [RPET 1984, 86] |
| A. | (-3, 3) |
| B. | (3, 3) |
| C. | (3, 1) |
| D. | (1, 3) |
| Answer» D. (1, 3) | |
| 2261. |
The orthocentre of triangle formed by lines \[4x-7y+10=0,\] \[x+y=5\] and \[7x+4y=15\] is [IIT 1969, 76] |
| A. | (1, 2) |
| B. | (1, -2) |
| C. | (-1, -2) |
| D. | (-1, 2) |
| Answer» B. (1, -2) | |
| 2262. |
Orthorcentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is [IIT Screening 2003] |
| A. | \[\left( 3,\,\frac{5}{4} \right)\] |
| B. | (3, 12) |
| C. | \[\left( 3,\,\frac{3}{4} \right)\] |
| D. | (3, 9) |
| Answer» D. (3, 9) | |
| 2263. |
The incentre of triangle formed by the lines \[x=0,\] \[y=0\] and \[3x+4y=12\] is [RPET 1990] |
| A. | \[\left( \frac{1}{2},\,\frac{1}{2} \right)\] |
| B. | (1, 1) |
| C. | \[\left( 1,\,\frac{1}{2} \right)\] |
| D. | \[\left( \frac{11}{2},\,1 \right)\] |
| Answer» C. \[\left( 1,\,\frac{1}{2} \right)\] | |
| 2264. |
The orthocentre of the triangle formed by (0, 0), (8, 0), (4 6) is [EAMCET 1991] |
| A. | \[\left( 4,\,\frac{8}{3} \right)\] |
| B. | (3, 4) |
| C. | (4, 3) |
| D. | (-3, 4) |
| Answer» B. (3, 4) | |
| 2265. |
If equation of three sides of a triangle are \[x=2,\] \[y+1=0\] and \[x+2y=4\] then co-ordinates of circumcentre of this triangle are [AMU 2005] |
| A. | (4, 0) |
| B. | (2, -1) |
| C. | (0, 4) |
| D. | (-1, 2) |
| Answer» B. (2, -1) | |
| 2266. |
The circumcentre of a triangle formed by the line \[xy+2x+2y+4=0\] and \[x+y+2=0\] is [Orissa JEE 2005] |
| A. | (-1, -1) |
| B. | (0, -1) |
| C. | (1, 1) |
| D. | (-1, 0) |
| Answer» B. (0, -1) | |
| 2267. |
Orthocentre of the triangle whose vertices are (0, 0) (3, 0) and (0, 4) is [MNR 1982; RPET 1997] |
| A. | (0, 0) |
| B. | (1, 1) |
| C. | (2, 2) |
| D. | (3, 3) |
| Answer» B. (1, 1) | |
| 2268. |
The incentre of a triangle with vertices (7, 1) (-1, 5) and \[(3+2\sqrt{3},\,3+4\sqrt{3})\] is [J & K 2005] |
| 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. \[\left( 1+\frac{2}{3\sqrt{3}},\,1+\frac{4}{3\sqrt{3}} \right)\] | |
| 2269. |
The orthocentre of the triangle with vertices (-2, -6), (-2, 4) and (1, 3) is [J & K 2005] |
| A. | (-3, 1) |
| B. | (-1, 1/3) |
| C. | (1, 3) |
| D. | None of these |
| Answer» D. None of these | |
| 2270. |
If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is [AIEEE 2005] |
| A. | \[\left( 1,\,\frac{7}{3} \right)\] |
| B. | \[\left( \frac{1}{3},\,\frac{7}{3} \right)\] |
| C. | \[\left( -1,\,\frac{7}{3} \right)\] |
| D. | \[\left( \frac{-1}{3},\,\frac{7}{3} \right)\] |
| Answer» B. \[\left( \frac{1}{3},\,\frac{7}{3} \right)\] | |
| 2271. |
If the points \[(x+1,\,2),\ (1,x+2),\ \left( \frac{1}{x+1},\frac{2}{x+1} \right)\]are collinear, then x is [RPET 2002] |
| A. | 4 |
| B. | 0 |
| C. | -4 |
| D. | None of these |
| Answer» D. None of these | |
| 2272. |
If points (5, 5), (10, k) and (-5, 1) are collinear, then k = [MP PET 1994, 99; RPET 2003] |
| A. | 3 |
| B. | 5 |
| C. | 7 |
| D. | 9 |
| Answer» D. 9 | |
| 2273. |
If the points (-2,-5), (2,-2), (8,a) are collinear, then the value of a is [MP PET 2002] |
| A. | \[-\frac{5}{2}\] |
| B. | \[\frac{5}{2}\] |
| C. | \[\frac{3}{2}\] |
| D. | \[\frac{1}{2}\] |
| Answer» C. \[\frac{3}{2}\] | |
| 2274. |
If the points \[(-5,\,1),\,(p,\,5)\]and \[(10,\,7)\]are collinear, then the value of p will be [MP PET 1984] |
| A. | 5 |
| B. | 3 |
| C. | 4 |
| D. | 7 |
| Answer» B. 3 | |
| 2275. |
If the points \[(a,\,0),\ (0,\,b)\]and (1, 1) are collinear, then |
| A. | \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\] |
| B. | \[\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}=1\] |
| C. | \[\frac{1}{a}+\frac{1}{b}=1\] |
| D. | \[\frac{1}{a}-\frac{1}{b}=1\] |
| Answer» D. \[\frac{1}{a}-\frac{1}{b}=1\] | |
| 2276. |
If the points \[(a,b),\,(a',b')\]and \[(a-a',b-b')\]are collinear, then [RPET 1999] |
| A. | \[ab'=a'b\] |
| B. | \[ab=a'b'\] |
| C. | \[aa'=bb'\] |
| D. | \[{{a}^{2}}+{{b}^{2}}=1\] |
| Answer» B. \[ab=a'b'\] | |
| 2277. |
If the points \[(k,\,2-2k)\], \[(1-k,\text{ }2k)\] and \[(-k-4,\text{ }6-2k)\] be collinear, then the possible values of k are [AMU 1978; RPET 1997] |
| A. | \[\frac{1}{2},-1\] |
| B. | \[1,-\frac{1}{2}\] |
| C. | \[1,-2\] |
| D. | \[2,-1\] |
| Answer» B. \[1,-\frac{1}{2}\] | |
| 2278. |
If the points \[A(3,\text{ }4),\,B(7,\text{ }7),\,C(a,\text{ }b)\] be collinear and \[AC=10\], then \[(a,\text{ }b)\]= |
| A. | \[(11,\text{ }10)\] |
| B. | \[(10,\text{ }11)\] |
| C. | \[(11/2,\,5)\] |
| D. | \[(5,\text{ }11/2)\] |
| Answer» B. \[(10,\text{ }11)\] | |
| 2279. |
Circumcentre of the triangle formed by the line \[y=x,\ \ y=2x\] and \[y=3x+4\]is |
| A. | (6, 8) |
| B. | (6, - 8) |
| C. | (3, 4) |
| D. | (- 3, - 4) |
| Answer» C. (3, 4) | |
| 2280. |
If the area of the triangle with vertices \[(x,\text{ }0),\,(1,\text{ }1)\] and \[(0,\text{ }2)\] is 4 square units then a value of x is [Karnataka CET 2004] |
| A. | -2 |
| B. | -4 |
| C. | -6 |
| D. | 8 |
| Answer» B. -4 | |
| 2281. |
If the vertices of a triangle are \[(5,2),\,(2/3,2)\] and \[(-4,\text{ }3)\], then the area of the triangle is [Kurukshetra CEE 2002] |
| A. | 44375 |
| B. | 44232 |
| C. | \[43\] |
| D. | 44360 |
| Answer» E. | |
| 2282. |
The vertices of the triangle ABC are (2,1), (4,3) and (2,5). \[D,\,E,\,F\]are the mid-points of the sides. The area of the triangle DEF is |
| A. | 1 |
| B. | 1.5 |
| C. | 3 |
| D. | 4 |
| Answer» B. 1.5 | |
| 2283. |
\[P(2,1),\,Q(4,-1),\,R(3,2)\] are the vertices of triangle and if through P and R lines parallel to opposite sides are drawn to intersect in S, then the area of PQRS is |
| A. | 6 |
| B. | 4 |
| C. | 8 |
| D. | 12 |
| Answer» C. 8 | |
| 2284. |
The area of the triangle with vertices at \[(-4,\text{ }1),\,(1,\text{ }2),\,(4,\text{ }-3)\] is [EAMCET 1980] |
| A. | 14 |
| B. | 16 |
| C. | 15 |
| D. | None of these |
| Answer» B. 16 | |
| 2285. |
The area of the triangle enclosed by the straight lines \[x=0,\] \[y=0\,\]and\[x+2y+3=0\]in sq. unit is |
| A. | \[\frac{9}{2}\] |
| B. | \[\frac{9}{4}\] |
| C. | \[\frac{3}{4}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{4}\] | |
| 2286. |
Area of a triangle whose vertices are \[(a\cos \theta ,b\sin \theta ),\] \[(-a\sin \theta ,b\cos \theta )\] and \[(-a\cos \theta ,-b\sin \theta )\] is |
| A. | \[a\cos \theta \sin \theta \] |
| B. | \[ab\sin \theta \cos \theta \] |
| C. | \[\frac{1}{2}ab\] |
| D. | \[ab\] |
| Answer» E. | |
| 2287. |
Three points are \[A(6,\text{ }3),\,B\text{ }(-\,3,\text{ }5),\,C\text{ }(4,\text{ }-2)\]and P (x, y) is a point, then the ratio of area of \[\Delta \]PBC and \[\Delta \]ABC is [IIT 1983] |
| A. | \[\left| \frac{x+y-2}{7} \right|\] |
| B. | \[\left| \frac{x-y+2}{2} \right|\] |
| C. | \[\left| \frac{x-y-2}{7} \right|\] |
| D. | None of these |
| Answer» B. \[\left| \frac{x-y+2}{2} \right|\] | |
| 2288. |
The area of a triangle whose vertices are (1, -1), (-1, 1) and (-1, -1) is given by [AMU 1981; RPET 1989; MP PET 1993; Pb. CET 2001] |
| A. | \[2\] |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | 3 |
| Answer» B. \[\frac{1}{2}\] | |
| 2289. |
If the vertices of a triangle be \[(a,\,1),\ (b,\,3)\]and \[(4,\,c),\]then the centroid of the triangle will lie on x-axis, if |
| A. | \[a+c=-4\] |
| B. | \[a+b=-4\] |
| C. | \[c=-4\] |
| D. | \[b+c=-4\] |
| Answer» D. \[b+c=-4\] | |
| 2290. |
If x\[\left| \begin{matrix} {{x}_{1}} & {{y}_{1}} & 1 \\ {{x}_{2}} & {{y}_{2}} & 1 \\ {{x}_{3}} & {{y}_{3}} & 1 \\ \end{matrix} \right|=\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & 1 \\ {{a}_{2}} & {{b}_{2}} & 1 \\ {{a}_{3}} & {{b}_{3}} & 1 \\ \end{matrix} \right|\]., then the two triangle with vertices \[({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}}),\,\] \[({{x}_{3}},{{y}_{3}})\] and \[({{a}_{1}},{{b}_{1}}),\,\]\[\,({{a}_{2}},{{b}_{2}}),\] \[({{a}_{3}},{{b}_{3}})\] must be [IIT 1985] |
| A. | Similar |
| B. | Congruent |
| C. | Never congruent |
| D. | None of these |
| Answer» E. | |
| 2291. |
The area of the triangle formed by the lines \[7x-2y+10=0,\] \[7x+2y-10=0\] and \[y+2=0\] is [IIT 1977] |
| A. | 8 sq. unit |
| B. | 12 sq. unit |
| C. | 14 sq. unit |
| D. | None of these |
| Answer» D. None of these | |
| 2292. |
If the coordinates of the points A, B, C, be (4,4), (3,-2) and (3,-16) respectively, then the area of the triangle ABC is [MP PET 1982] |
| A. | 27 |
| B. | 15 |
| C. | 18 |
| D. | 7 |
| Answer» E. | |
| 2293. |
If \[A({{x}_{1}},{{y}_{1}}),\ B({{x}_{2}},{{y}_{2}})\] and \[C({{x}_{3}},{{y}_{3}})\] are the vertices of a triangle, then the excentre with respect to B is [RPET 2000] |
| A. | \[\left( \frac{a{{x}_{1}}-b{{x}_{2}}+c{{x}_{3}}}{a-b+c},\,\frac{a{{y}_{1}}-b{{y}_{2}}+c{{y}_{3}}}{a-b+c} \right)\] |
| B. | \[\left( \frac{a{{x}_{1}}+b{{x}_{2}}-c{{x}_{3}}}{a+b-c},\,\frac{a{{y}_{1}}+b{{y}_{2}}-c{{y}_{3}}}{a+b-c} \right)\] |
| C. | \[\left( \frac{a{{x}_{1}}-b{{x}_{2}}-c{{x}_{3}}}{a-b-c},\,\frac{a{{y}_{1}}-b{{y}_{2}}-c{{y}_{3}}}{a-b-c} \right)\] |
| D. | None of these |
| Answer» B. \[\left( \frac{a{{x}_{1}}+b{{x}_{2}}-c{{x}_{3}}}{a+b-c},\,\frac{a{{y}_{1}}+b{{y}_{2}}-c{{y}_{3}}}{a+b-c} \right)\] | |
| 2294. |
Orthocentre of the triangle formed by the lines \[x+y=1\]and \[xy=0\]is [Orissa JEE 2004] |
| A. | (0, 0) |
| B. | (0, 1) |
| C. | (1, 0) |
| D. | (-1, 1) |
| Answer» B. (0, 1) | |
| 2295. |
If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then the third vertex is [RPET 1996] |
| A. | (4, 8) |
| B. | (8, 4) |
| C. | (6, 4) |
| D. | None of these |
| Answer» B. (8, 4) | |
| 2296. |
If a plane cuts off intercepts \[OA=a,OB=b,\] \[OC=c\] from the co-ordinate axes, then the area of the triangle \[ABC\]= |
| A. | \[\frac{1}{2}\sqrt{{{b}^{2}}{{c}^{2}}+{{c}^{2}}{{a}^{2}}+{{a}^{2}}{{b}^{2}}}\] |
| B. | \[\frac{1}{2}(bc+ca+ab)\] |
| C. | \[\frac{1}{2}abc\] |
| D. | \[\frac{1}{2}\sqrt{{{(b-c)}^{2}}+{{(c-a)}^{2}}+{{(a-b)}^{2}}}\] |
| Answer» B. \[\frac{1}{2}(bc+ca+ab)\] | |
| 2297. |
The distance between the planes \[x+2y+3z+7=0\] and \[2x+4y+6z+7=0\] is [MP PET 1991] |
| A. | \[\frac{\sqrt{7}}{2\sqrt{2}}\] |
| B. | \[\frac{7}{2}\] |
| C. | \[\frac{\sqrt{7}}{2}\] |
| D. | \[\frac{7}{2\sqrt{2}}\] |
| Answer» B. \[\frac{7}{2}\] | |
| 2298. |
If for a plane, the intercepts on the coordinate axes are 8, 4, 4 then the length of the perpendicular from the origin on to the plane is [Kerala (Engg.) 2005] |
| A. | 8/3 |
| B. | 3/8 |
| C. | 3 |
| D. | 4/3 |
| E. | 4/5 |
| Answer» B. 3/8 | |
| 2299. |
If a plane meets the co-ordinate axes at A,B and C such that the centroid of the triangle is (1, 2, 4) then the equation of the plane is [Kerala (Engg.) 2005] |
| A. | \[x+2y+4z=12\] |
| B. | \[4x+2y+z=12\] |
| C. | \[x+2y+4z=3\] |
| D. | \[4x+2y+z=3\] |
| E. | \[x+y+z=12\] |
| Answer» C. \[x+2y+4z=3\] | |
| 2300. |
If the distance of the point (1, 1,1) from the origin is half its distance from the plane \[x+y+z+k=0\], then \[k=\] [Kerala (Engg.)2005] |
| A. | \[\pm 3\] |
| B. | \[\pm 6\] |
| C. | ?3, 9 |
| D. | \[3,\,-9\] |
| Answer» E. | |