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.
| 5401. |
If a circle and a square have the same perimeter, then [Pb. CET 2001] |
| A. | Their area are equal |
| B. | Area of circle is larger |
| C. | Area of square is larger |
| D. | None of these |
| Answer» C. Area of square is larger | |
| 5402. |
If the lines \[2x+3y+1=0\]and \[3x-y-4=0\]lie along diameters of a circle of circumference \[10\pi \], then the equation of the circle is [AIEEE 2004] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\] |
| Answer» E. | |
| 5403. |
The radius of the circle passing through the point (6, 2) and two of whose diameters are \[x+y=6\]and \[x+2y=4\]is [Karnataka CET 2004] |
| A. | 4 |
| B. | 6 |
| C. | 20 |
| D. | \[\sqrt{20}\] |
| Answer» E. | |
| 5404. |
The four distinct points (0, 0),(2, 0), (0, -2) and (k, -2)are con-cyclic, if k = [EAMCET 2002] |
| A. | - 2 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 5405. |
For what value of k, the points (0, 0), (1, 3), (2, 4) and (k, 3) are con-cyclic [RPET 1997] |
| A. | 2 |
| B. | 1 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 5406. |
The centre of circle inscribed in square formed by the lines \[{{x}^{2}}-8x+12=0\]and \[{{y}^{2}}-14y+45=0\], is [IIT Screening 2003] |
| A. | (4, 7) |
| B. | (7, 4) |
| C. | (9, 4) |
| D. | (4, 9) |
| Answer» B. (7, 4) | |
| 5407. |
The equation of the circle which touches both axes and whose centre is \[({{x}_{1}},\ {{y}_{1}})\] is [MP PET 1988] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2{{x}_{1}}(x+y)+x_{1}^{2}=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-2{{x}_{1}}(x+y)+x_{1}^{2}=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+2x{{x}_{1}}+2y{{y}_{1}}=0\] |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\] | |
| 5408. |
The limit of the perimeter of the regular n-gons inscribed in a circle of radius R as \[n\to \infty \]is [MP PET 2003] |
| A. | \[2\,\pi \,R\] |
| B. | \[\pi \,R\] |
| C. | \[4R\] |
| D. | \[\pi \,{{R}^{2}}\] |
| Answer» B. \[\pi \,R\] | |
| 5409. |
The centre of a circle is (2, ?3) and the circumference is \[10\pi \]. Then the equation of the circle is [Kerala (Engg.) 2002] |
| A. | \[{{x}^{2}}+{{y}^{2}}+4x+6y+12=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-4x+6y+12=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-4x+6y-12=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] | |
| 5410. |
If \[{{g}^{2}}+{{f}^{2}}=c\], then the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]will represent [MP PET 2003] |
| A. | A circle of radius g |
| B. | A circle of radius f |
| C. | A circle of diameter \[\sqrt{c}\] |
| D. | A circle of radius 0 |
| Answer» E. | |
| 5411. |
The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is [EAMCET 2002] |
| A. | \[{{(x-5)}^{2}}+{{(y+5)}^{2}}=25\] |
| B. | \[{{(x+4)}^{2}}+{{(y+4)}^{2}}=25\] |
| C. | \[{{(x+6)}^{2}}+{{(y+6)}^{2}}=25\] |
| D. | \[{{(x+5)}^{2}}+{{(y+5)}^{2}}=25\] |
| Answer» E. | |
| 5412. |
The equation of the circle passing through the point (?2, 4) and through the points of intersection of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+6=0\] and the line \[3x+2y-5=0\], is [RPET 1996] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2x-4y-4=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+4x-2y-4=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-4x-2y=0\] |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] | |
| 5413. |
The equation of circle with centre (1, 2) and tangent \[x+y-5=0\]is [MP PET 2001] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2x-4y+6=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2x+4y+8=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-2x-4y+8=0\] |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-2x+4y+8=0\] | |
| 5414. |
The circle \[{{x}^{2}}+{{y}^{2}}-8x+4y+4=0\]touches [Karnataka CET 1999, 2004; Pb. CET 2000] |
| A. | x-axis only |
| B. | y- axis only |
| C. | Both x and y- axis |
| D. | Does not touch any axis |
| Answer» C. Both x and y- axis | |
| 5415. |
The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] touches [MP PET 1988] |
| A. | x-axis |
| B. | y-axis |
| C. | x-axis and y-axis |
| D. | None of these |
| Answer» D. None of these | |
| 5416. |
Radius of the circle \[(x-1)(x-3)+(y-2)(y-4)\] \[=0\] is |
| A. | 2 |
| B. | \[\sqrt{2}\] |
| C. | 3 |
| D. | \[2\sqrt{2}\] |
| Answer» C. 3 | |
| 5417. |
The area of the curve \[{{x}^{2}}+{{y}^{2}}=2ax\]is [MP PET 1996] |
| A. | \[\pi {{a}^{2}}\] |
| B. | \[2\pi {{a}^{2}}\] |
| C. | \[4\pi {{a}^{2}}\] |
| D. | \[\frac{1}{2}\pi {{a}^{2}}\] |
| Answer» B. \[2\pi {{a}^{2}}\] | |
| 5418. |
The equation of the circle whose diameter lies on \[2x+3y=3\]and \[16x-y=4\] which passes through (4,6) is [Kurukshetra CEE 1998] |
| A. | \[5\text{ }({{x}^{2}}+{{y}^{2}})-3x-8y=200\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-4x-8y=200\] |
| C. | \[5\text{ }({{x}^{2}}+{{y}^{2}})-4x=200\] |
| D. | \[{{x}^{2}}+{{y}^{2}}=40\] |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}-4x-8y=200\] | |
| 5419. |
The equation \[2{{x}^{2}}+2{{y}^{2}}+4x+8y+15=0\] represents [Roorkee 1999] |
| A. | A pair of straight lines |
| B. | A circle |
| C. | An ellipse |
| D. | None of these |
| Answer» E. | |
| 5420. |
If \[(\alpha ,\beta )\]is the centre of a circle passing through the origin, then its equation is [MP PET 1999] |
| A. | \[{{x}^{2}}+{{y}^{2}}-\alpha x-\beta y=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2\beta y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2\alpha x-2\beta y=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+\alpha x+\beta y=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}+\alpha x+\beta y=0\] | |
| 5421. |
The equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible, is |
| A. | \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-x-y=0\] |
| C. | \[2{{x}^{2}}+2{{y}^{2}}-3x-3y+1=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-3x-3y+2=0\] |
| Answer» C. \[2{{x}^{2}}+2{{y}^{2}}-3x-3y+1=0\] | |
| 5422. |
The equation of the circumcircle of the triangle formed by the lines \[x=0,y=0,2x+3y=5\] is [MP PET 2004] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2x+3y-5=0\] |
| B. | \[6({{x}^{2}}+{{y}^{2}})-5\text{ }(3x+2y)=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2x-3y+5=0\] |
| D. | \[6({{x}^{2}}+{{y}^{2}})+5\text{ }(3x+2y)=0\] |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-2x-3y+5=0\] | |
| 5423. |
Equations to the circles which touch the lines \[3x-4y+1=0\], \[4x+3y-7=0\]and pass through (2, 3) are [EAMCET 1989] |
| A. | \[{{(x-2)}^{2}}+{{(y-8)}^{2}}=25\] |
| B. | \[5{{x}^{2}}+5{{y}^{2}}-12x-24y+31=0\] |
| C. | Both (a) and (b) |
| D. | None of these |
| Answer» D. None of these | |
| 5424. |
Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is |
| A. | \[{{x}^{2}}+{{y}^{2}}+9x+2fy+14=0\] |
| B. | \[3{{x}^{2}}+3{{y}^{2}}+27x-2fy+42=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-9x+2fy+14=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-2fy-9y+14=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}-2fy-9y+14=0\] | |
| 5425. |
The equation of the circle whose centre is (1, ?3) and which touches the line \[2x-y-4=0\] is |
| A. | \[5{{x}^{2}}+5{{y}^{2}}-10x+30y+49=0\] |
| B. | \[5{{x}^{2}}+5{{y}^{2}}+10x-30y+49=0\] |
| C. | \[5{{x}^{2}}+5{{y}^{2}}-10x+30y-49=0\] |
| D. | None of these |
| Answer» B. \[5{{x}^{2}}+5{{y}^{2}}+10x-30y+49=0\] | |
| 5426. |
The equation \[{{(x-5)}^{2}}+(x-5)\,(y-6)\,-2\,{{(y-6)}^{2}}=0\] represents |
| A. | A circle |
| B. | Two straight lines passing through origin |
| C. | Two straight lines passing through the point (5, 6) |
| D. | None of these |
| Answer» D. None of these | |
| 5427. |
The equation of the lines represented by the equation \[ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0\] are |
| A. | \[ax-by=0,\ bx+ay=0\] |
| B. | \[ax-by=0,\ bx-ay=0\] |
| C. | \[ax+by=0,\ bx+ay=0\] |
| D. | \[ax+by=0,\ bx-ay=0\] |
| Answer» B. \[ax-by=0,\ bx-ay=0\] | |
| 5428. |
If \[\frac{{{x}^{2}}}{a}+\frac{{{y}^{2}}}{b}+\frac{2xy}{h}=0\] represent pair of straight lines and slope of one line is twice the other. Then \[ab:{{h}^{2}}\] is [DCE 2005] |
| A. | 9 : 8 |
| B. | 8 : 9 |
| C. | 1 : 2 |
| D. | 2 : 1 |
| Answer» B. 8 : 9 | |
| 5429. |
If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then c has the value [AIEEE 2004] |
| A. | - 2 |
| B. | - 1 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 5430. |
If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET 2004] |
| A. | - 16 |
| B. | 16 |
| C. | 4 |
| D. | - 4 |
| Answer» C. 4 | |
| 5431. |
If one of the lines given by \[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is \[3x+4y=0\], then c equals [AIEEE 2004] |
| A. | - 3 |
| B. | - 1 |
| C. | 3 |
| D. | 1 |
| Answer» B. - 1 | |
| 5432. |
The equation of lines passing through the origin and parallel to the lines \[y={{m}_{1}}x+{{c}_{1}}\] and \[y={{m}_{2}}x+{{c}_{2}}\] is |
| A. | \[{{m}_{1}}{{m}_{2}}{{x}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] |
| B. | \[{{m}_{1}}{{m}_{2}}{{x}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] |
| C. | \[{{m}_{1}}{{m}_{2}}{{y}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] |
| D. | \[{{m}_{1}}{{m}_{2}}{{y}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] |
| Answer» B. \[{{m}_{1}}{{m}_{2}}{{x}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] | |
| 5433. |
The value of \[\lambda ,\] for which the equation \[{{x}^{2}}-{{y}^{2}}-x\]?\[\lambda y-2=0\]represent a pair of straight line, are [MP PET 2004] |
| A. | 3, - 3 |
| B. | - 3, 1 |
| C. | 3, 1 |
| D. | -1, 1 |
| Answer» B. - 3, 1 | |
| 5434. |
Difference of slopes of the lines represented by equation \[{{x}^{2}}({{\sec }^{2}}\theta -{{\sin }^{2}}\theta )-2xy\tan \theta +{{y}^{2}}{{\sin }^{2}}\theta =0\]is [Kurukshetra CEE 2002] |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | None of these |
| Answer» D. None of these | |
| 5435. |
The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\]and \[x=a\], is |
| A. | \[2{{a}^{2}}\] |
| B. | \[\frac{{{a}^{2}}}{2}\] |
| C. | \[\frac{\sqrt{3}{{a}^{2}}}{2}\] |
| D. | \[\frac{2{{a}^{2}}}{\sqrt{3}}\] |
| Answer» C. \[\frac{\sqrt{3}{{a}^{2}}}{2}\] | |
| 5436. |
The equation to the pair of straight lines through the origin which are perpendicular to the lines \[2{{x}^{2}}-5xy+{{y}^{2}}=0,\]is [MP PET 1990] |
| A. | \[2{{x}^{2}}+5xy+{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+2{{y}^{2}}+5xy=0\] |
| C. | \[{{x}^{2}}-5xy+2{{y}^{2}}=0\] |
| D. | \[2{{x}^{2}}+{{y}^{2}}-5xy=0\] |
| Answer» C. \[{{x}^{2}}-5xy+2{{y}^{2}}=0\] | |
| 5437. |
If the slope of one of the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is 5 times the other, then [Karnataka CET 2003] |
| A. | \[5{{h}^{2}}=ab\] |
| B. | \[5{{h}^{2}}=9ab\] |
| C. | \[9{{h}^{2}}=5ab\] |
| D. | \[{{h}^{2}}=ab\] |
| Answer» C. \[9{{h}^{2}}=5ab\] | |
| 5438. |
The equation \[4{{x}^{2}}-24xy+11{{y}^{2}}=0\]represents [Orissa JEE 2003] |
| A. | Two parallel lines |
| B. | Two perpendicular lines |
| C. | Two lines through the origin |
| D. | A circle |
| Answer» D. A circle | |
| 5439. |
If two sides of a triangle are represented by \[{{x}^{2}}-7xy+6{{y}^{2}}=0\] and the centroid is (1, 0) then the equation of third side is |
| A. | \[2x+7y+3=0\] |
| B. | \[2x-7y+3=0\] |
| C. | \[2x+7y-3=0\] |
| D. | \[2x-7y-3=0\] |
| Answer» E. | |
| 5440. |
If the equation \[12{{x}^{2}}-10xy+2{{y}^{2}}+11x-5y+k=0\] represents two straight lines, then the value of k is [MP PET 2003] |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | 3 |
| Answer» C. 0 | |
| 5441. |
If the equation \[2{{x}^{2}}+7xy+3{{y}^{2}}-9x-7y+k=0\] represents a pair of lines, then k is equal to [Kerala (Engg.) 2002] |
| A. | 4 |
| B. | 2 |
| C. | 1 |
| D. | - 4 |
| Answer» B. 2 | |
| 5442. |
Equation \[3{{x}^{2}}+7xy+2{{y}^{2}}+5x+5y+2=0\] represents [UPSEAT 2002] |
| A. | Pair of straight line |
| B. | Ellipse |
| C. | Hyperbola |
| D. | None of these |
| Answer» B. Ellipse | |
| 5443. |
If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to [Karnataka CET 2002] |
| A. | 9 |
| B. | 1 |
| C. | 0 |
| D. | - 9 |
| Answer» E. | |
| 5444. |
The value of k so that the equation \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+k=0\] represents a pair of straight lines, is [Kurukshetra CEE 2002] |
| A. | 4 |
| B. | 6 |
| C. | 0 |
| D. | 8 |
| Answer» B. 6 | |
| 5445. |
Separate equations of lines, for a pair of lines, whose equation is \[{{x}^{2}}+xy-12{{y}^{2}}=0\], are [Karnataka CET 2001; Pb. CET 2000] |
| A. | \[x+4y=0\]and \[x+3y=0\] |
| B. | \[2x-3y=0\] and \[x-4y=0\] |
| C. | \[x-6y=0\]and \[x-3y=0\] |
| D. | \[x+4y=0\]and \[x-3y=0\] |
| Answer» E. | |
| 5446. |
The equation \[2{{x}^{2}}+4xy-k{{y}^{2}}+4x+2y-1=0\] represents a pair of lines. The value of k is [Karnataka CET 2001] |
| A. | \[-\frac{5}{3}\] |
| B. | \[\frac{5}{3}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[-\frac{1}{3}\] |
| Answer» B. \[\frac{5}{3}\] | |
| 5447. |
The equation \[{{x}^{2}}+kxy+{{y}^{2}}-5x-7y+6=0\] represents a pair of straight lines, then k is [MP PET 2000] |
| A. | 5/3 |
| B. | 10/3 |
| C. | 3/2 |
| D. | 3/10 |
| Answer» C. 3/2 | |
| 5448. |
The gradient of one of the lines of \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is twice that of the other, then [MP PET 2000; Pb. CET 2002] |
| A. | \[{{h}^{2}}=ab\] |
| B. | \[h=a+b\] |
| C. | \[8{{h}^{2}}=9ab\] |
| D. | \[9{{h}^{2}}=8ab\] |
| Answer» D. \[9{{h}^{2}}=8ab\] | |
| 5449. |
If the slope of one line of the pair of lines represented by \[a{{x}^{2}}+4xy+{{y}^{2}}=0\]is 3 times the slope of the other line, then a is [DCE 1999] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 5450. |
The equation of pair of straight lines perpendicular to the pair \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is [MP PET 1989] |
| A. | \[a{{x}^{2}}-2hxy+b{{y}^{2}}=0\] |
| B. | \[b{{x}^{2}}+2hxy+a{{y}^{2}}=0\] |
| C. | \[a{{y}^{2}}-2hxy+b{{x}^{2}}=0\] |
| D. | \[a{{y}^{2}}-b{{x}^{2}}=0\] |
| Answer» D. \[a{{y}^{2}}-b{{x}^{2}}=0\] | |