MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 66 Mcqs, each offering curated multiple-choice questions to sharpen your BITSAT knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
A point on the line \(\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+2}{7}\) has coordinates |
| A. | (3, 5, 4) |
| B. | (2, 5, 5) |
| C. | (-1, -1, 5) |
| D. | (2, -1, 0) |
| Answer» C. (-1, -1, 5) | |
| 52. |
A plane passing through the points(0, -1, 0) and (0, 0, 1) and making an angle \(\frac{\pi }{4}\) with the planey – z + 5 = 0, also passes through the point: |
| A. | \(\left( { - \sqrt 2 ,{\rm{\;}}1,{\rm{\;}} - 4} \right)\) |
| B. | \(\left( {\sqrt 2 , - 1,{\rm{\;}}4} \right)\) |
| C. | \(\left( { - \sqrt 2 , - 1, - 4} \right)\) |
| D. | \(\left( {\sqrt 2 ,{\rm{\;}}1,{\rm{\;}}4} \right)\) |
| Answer» E. | |
| 53. |
If a straight line passing through the point P(-3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is |
| A. | x – y + 7 = 0 |
| B. | 4x – 3y + 24 = 0 |
| C. | 3x – 4y + 25 = 0 |
| D. | 4x + 3y = 0 |
| Answer» C. 3x – 4y + 25 = 0 | |
| 54. |
Find the equation of the circle x2 + y2 = 1 in terms of x' y' coordinates, assuming that the xy coordinate system results from a scaling of 3 units in the x’ direction and 4 units in the y' direction. |
| A. | 3(x')2 + 4(y)2 = 1 |
| B. | \({\left( {\frac{{x'}}{3}} \right)^2} + {\left( {\frac{{y'}}{4}} \right)^2} = 1\) |
| C. | (3x')2 + (4y')2 = 1 |
| D. | \(\frac{1}{3}(x')^2+\frac{1}{4}(y')^2 = 1\) |
| Answer» C. (3x')2 + (4y')2 = 1 | |
| 55. |
On which of the following lines lies the point of intersection of the line, \(\frac{{x - 4}}{2} = \frac{{y - 5}}{2} = \frac{{z - 3}}{1}\) and the plane, x + y + z = 2 |
| A. | \(\frac{{x + 3}}{3} = \frac{{4 - y}}{3} = \frac{{z + 1}}{{ - 2}}\) |
| B. | \(\frac{{x - 4}}{1} = \frac{{y - 5}}{1} = \frac{{z - 5}}{{ - 1}}\) |
| C. | \(\frac{{x - 1}}{1} = \frac{{y - 3}}{2} = \frac{{z + 4}}{{ - 5}}\) |
| D. | \(\frac{{x - 2}}{2} = \frac{{y - 3}}{2} = \frac{{z + 3}}{3}\) |
| Answer» D. \(\frac{{x - 2}}{2} = \frac{{y - 3}}{2} = \frac{{z + 3}}{3}\) | |
| 56. |
Consider the following:Let P (-2, 1, -5) & Q (4, -3, -1) be two points in a 3D space1. The direction ration of the line segment PQ are < 3, -2, 2>2. The sum of the squares of direction cosines of the line segment PQ is unity.Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 57. |
If the foot of the perpendicular drawn from (-2, 1, 0) on a plane is (1, -2, 1), then the equation of the plane is |
| A. | 3x + 3y + z = 10 |
| B. | 3x + 3y - z = 10 |
| C. | 3x - 3y + z = 10 |
| D. | 3x - 3y - z = 10 |
| Answer» D. 3x - 3y - z = 10 | |
| 58. |
If an angle between the line, \(\frac{{{\rm{x}} + 1}}{2} = \frac{{{\rm{y}} - 2}}{1} = \frac{{{\rm{z}} - 3}}{{ - 2}}{\rm{\;}}\) and the plane, x – 2y – kz = 3 is \({\rm{co}}{{\rm{s}}^{ - 1}}\left( {\frac{{2\sqrt 2 }}{3}} \right),\) then a value of k is |
| A. | \(\begin{array}{*{20}{c}} {{\rm{\;}}\sqrt {\frac{5}{3}} }&{\rm{\;}} \end{array}\) |
| B. | \({\rm{\;}}\sqrt {\frac{3}{5}}\) |
| C. | \(- \frac{3}{5}\) |
| D. | \(- \frac{5}{3}\) |
| Answer» B. \({\rm{\;}}\sqrt {\frac{3}{5}}\) | |
| 59. |
If l, m, n are the direction cosines of the line x - 1 = 2(y + 3) = 1 - z, then what is l4 + m4 + n4 equal to? |
| A. | 1 |
| B. | \(\dfrac{11}{27}\) |
| C. | \(\dfrac{13}{27}\) |
| D. | 4 |
| Answer» C. \(\dfrac{13}{27}\) | |
| 60. |
If the system of equations 2x + 3y – z = 0, x + ky - 2z = 0 and 2x – y + z = 0 has a non-trivial solution (x, y, z), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to: |
| A. | 3/4 |
| B. | 1/2 |
| C. | \(\frac{{ - 1}}{4}\) |
| D. | -4 |
| Answer» C. \(\frac{{ - 1}}{4}\) | |
| 61. |
If the angle between the lines whose direction ratios are \(\left\langle {2, - 1,\;2} \right\rangle \) and \(\left\langle {x,\;3,\;5\;} \right\rangle\) is \(\frac{\pi }{4}\), then the smaller value of x is |
| A. | 52 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» C. 2 | |
| 62. |
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min] of the ice decreases, is: |
| A. | \(\frac{1}{{18\;\pi }}\) |
| B. | \(\frac{1}{{36{\rm{\;}}\pi }}\) |
| C. | \(\frac{5}{{6{\rm{\;}}\pi }}\) |
| D. | \(\frac{1}{{9{\rm{\;}}\pi }}\) |
| Answer» B. \(\frac{1}{{36{\rm{\;}}\pi }}\) | |
| 63. |
If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is: |
| A. | 5 : 9 : 13 |
| B. | 4 : 5 : 6 |
| C. | 3 : 4 : 5 |
| D. | 5 : 6 : 7 |
| Answer» C. 3 : 4 : 5 | |
| 64. |
If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the squares of its direction cosines? |
| A. | (a + b + c)2 |
| B. | 2 (a + b + c) |
| C. | 3 |
| D. | 1 |
| Answer» E. | |
| 65. |
If the tangent to the curve \(y = \frac{x}{{{x^2} - 3}},\;x \in {\rm{R}},\left( {x \ne \pm \sqrt 3 } \right),{\rm{\;}}\)at a point (α, β) ≠ (0, 0) on it is parallel to the line 2x + 6y - 11 = 0, then: |
| A. | |6α + 2β| = 19 |
| B. | |6α + 2β| = 9 |
| C. | |2α + 6β| = 19 |
| D. | |2α + 6β| = 11 |
| Answer» B. |6α + 2β| = 9 | |
| 66. |
If α, β and γ are the angles which the vector \(\overrightarrow {OP} \) (O being the origin) makes with the positive direction of the coordinate axes, then which of the following are correct?1. cos2 α + cos2 β = sin2 γ2. sin2 α + sin2 β = cos2 γ3. sin2 α + sin2 β + sin2 γ = 2Select the correct answer using the code given below. |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» D. 1, 2 and 3 | |