Three-Dimensional Geometry PYQs Set 5 (PDF)

Set 5 of 16 · Questions 121-150 of 471

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Three-Dimensional Geometry · Set 5 (Q121-150)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
121. $The coordinates of the foot of perpendicular drawn from origin to the plane 2 x - y + 5 z - 3 = 0 are$ (1) $(\frac{2}{30}, \frac{- 1}{30}, \frac{5}{30})$ (2) $(2, - 1, 5)$ (3) $(\frac{2}{3}, \frac{- 1}{3}, \frac{5}{3})$ (4) $(\frac{1}{5}, \frac{- 1}{10}, \frac{1}{2})$ 122. $If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a & b and perpendicular to a is$ (1) $(0, 1, 0)$ (2) $(1, - 1, 0)$ (3) $k$ (4) $(1, 0, 1)$ 123. $A (2, 3, 5), B (α, 3, 3) and C (7, 5, β) are the vertices of a triangle. If the median through A is equally inclined with the coordinate axes, then \frac{β}{α} =$ (1) $-9$ (2) $\frac{- 1}{9}$ (3) $\frac{- 2}{9}$ (4) $\frac{9}{2}$ 124. $If A = (1, - 1, 2), B = (3, 4, - 2), C = (0, 3, 2) and D = (3, 5, 6) then the angle between the lines AB and CD is$ (1) $30^{\circ}$ (2) $45^{\circ}$ (3) $60^{\circ}$ (4) $90^{\circ}$ 125. $A vector parallel to the line of intersection of the planes r \cdot (3 i - j + k) = 1 and r \cdot (i + 4 j - 2 k) = 2 is$ (1) $- 2 i + 7 j + 13 k$ (2) $2 i - 7 j + 13 k$ (3) $- i + 4 j + 7 k$ (4) $i - 4 j + 7 k$ 126. $If the mirror image of the point (2, 4, 7) in the plane 3x - y + 4z = 2 is (a, b, c), the 2a + b + 2c is equal to :$ (1) $54$ (2) $50$ (3) $-6$ (4) $-42$ 127. $If for some α \in R the lines L_{1} : \frac{x + 1}{2} = \frac{y - 2}{- 1} = \frac{z - 1}{1} and L_{2} : \frac{x + 2}{α} = \frac{y + 1}{5 - α} = \frac{z + 1}{1} are coplanarthen the line L_{2} passes through the point:$ (1) $(10, 2, 2)$ (2) $(2, - 10, - 2)$ (3) $(10, - 2 - 2)$ (4) $(- 2, 10, 2)$ 128. $The equation of a plane containing the line of intersection of the planes 2 x - y - 4 = 0 and y + 2 z - 4 = 0 and passing through the point (1, 1, 0) is:$ (1) $x - 3 y - 2 z = - 2$ (2) $2 x - z = 2$ (3) $x - y - z = 0$ (4) $x + 3 y + z = 4$ 129. $The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2 x = 3 y, z = 1 also passes through the point:$ (1) $(0, 6, - 2)$ (2) $(- 2, 0, 1)$ (3) $(0, - 6, 2)$ (4) $(2, 0 - 1)$ 130. $The equation of a plane passing through (- 1, 2, 3) and whose normal makes cqual angles with the coordinate axes is$ (1) $x + y + z + 4 = 0$ (2) $x - y + z + 4 = 0$ (3) $x + y + z - 4 = 0$ (4) $x + y + z = 0$ 131. $If α, 2 α, 3 α are angles made by a ray with OX, OY, OZ axes respectively then all the possible values of α are$ (1) $\frac{π}{6}, \frac{π}{12}$ (2) $\frac{π}{6}, \frac{π}{3}$ (3) $\frac{π}{4}, \frac{π}{3}$ (4) $\frac{π}{6}, \frac{π}{4}$ 132. $The co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2 x + 6 y - 3 z = 63 are$ (1) $(\frac{2}{7}, \frac{6}{7}, \frac{- 3}{7})$ (2) $(4, 2, - 4)$ (3) $(\frac{9}{7}, \frac{6}{7}, \frac{- 3}{7})$ (4) $(\frac{18}{7}, \frac{54}{7}, \frac{- 27}{7})$ 133. $Each of the angles β and γ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible values of the angle β is$ (1) $\frac{π}{2}$ (2) $π$ (3) $\frac{3 π}{4}$ (4) $\frac{3 π}{2}$ 134. $Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2 x - y + z + 3 = 0 is$ (1) $(- 1, 4, 3)$ (2) $(1, 2, - 3)$ (3) $(0, - 4, - 7)$ (4) $(- 3, 5, 2)$ 135. $In △ ABC, ∠ A = 90^{\circ} and co-ordinates of points B and C are (2, - 4) and (1, 5) . Then the equation of the circuricircle of △ ABC is$ (1) $x^{2} + y^{2} + 3 x + y + 18 = 0$ (2) $x^{2} + y^{2} - 3 x + y - 18 = 0$ (3) $x^{2} + y^{2} - 3 x - y - 18 = 0$ (4) $x^{2} + y^{2} + 3 x - y + 18 = 0$ 136. $A plane π passing through the point 3 i - 4 j + 5 k is parallel to the plane which passes through the point i + j - k and perpendicular to the vector i + 2 j - 3 k . Then the cartesian equation of π is$ (1) $3 x - 4 y + 5 z + 20 = 0$ (2) $2 x - y + 3 z - 25 = 0$ (3) $x + 2 y - 3 z + 20 = 0$ (4) $4 x + 5 y - 6 z + 38 = 0$ 137. $A ray makes angles \frac{π}{3} and \frac{π}{4} with Y and Z -axes respectively. Then the value of the sine of the angle made by the ray with X -axis is$ (1) $\frac{3}{2}$ (2) $\frac{1}{2}$ (3) $\frac{1}{2}$ (4) $1$ 138. $The length of perpendicular from the origin to the plane which makes intercepts \frac{1}{3}, \frac{1}{4} and \frac{1}{5} respectively on the coordinate axes is$ (1) $\frac{1}{5 2}$ (2) $\frac{1}{10}$ (3) $52$ (4) $5$ 139. $Let π_{1} be the plane determined by the vectors i + 2 j and 3 j - 2 k . Let π_{2} be the plane determined by the vectors j + 2 k and 3 k - 2 i . If θ is the angle between π_{1} and π_{2}, then cos θ =$ (1) $\frac{7}{26}$ (2) $- \frac{14}{29}$ (3) $- \frac{32}{5 2}$ (4) $\frac{23}{38}$ 140. $Let Q (a, b, c) be the image of the point P (3, 2, 1) in the line \frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1} . Then the distance of Q from the line \frac{x - 9}{3} = \frac{y - 9}{2} = \frac{z - 5}{- 2} is$ (1) $8$ (2) $5$ (3) $7$ (4) $6$ 141. $If r = b + ta, r = d + sc are the two skew lines, then the shortest distance between them is$ (1) $Magnitude of vector b \times d$ (2) $Sum of orthogonal projection of b on d and projection of d and b$ (3) $Orthogonal projection of (a - c) on (b\timesd)$ (4) $Orthogonal projection of (b - d) on (a \times c)$ 142. $If A (1, 2, 3), B (3, 7, - 2), C (6, 7, 7) and D (- 1, 0, - 1) are points in a plane, then the vector equation of the line passing through the centroids of △ ABD and △ ACD is$ (1) $r = 2 i + 3 j + 3 k + t (i + 3 j)$ (2) $r = (1 + t) i + 3 j + 3 t k$ (3) $r = i + j + k + t (2 i - j)$ (4) $r = 2 i - j + t (j + 4 k)$ 143. $If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2 x - 5 y = 15 then 2 α - 3 β is equal to$ (1) $12$ (2) $7$ (3) $5$ (4) $17$ 144. $Let P be the plane, which contains the line of intersection of the planes, x + y + z - 6 = 0 and 2 x + 3 y + z + 5 = 0 and it is perpendicular to the x y - plane. Then the distance of the point (0, 0, 256) from P is equal to:$ (1) $17/ 5$ (2) $635$ (3) $2055$ (4) $11/ 5$ 145. $The distance, of the point (7, - 2, 11) from the line \frac{x - 6}{1} = \frac{y - 4}{0} = \frac{z - 8}{3} along the line \frac{x - 5}{2} = \frac{y - 1}{- 3} = \frac{z - 5}{6}, is$ (1) $12$ (2) $14$ (3) $18$ (4) $21$ 146. $If the position vectors of the vertices of a △ ABC are OA = 3 i + j + 2 k, OB = i + 2 j + 3 k and OC = 2 i + 3 j + k then the length of the altitude of △ ABC drawn from A is$ (1) $\frac{3}{2}$ (2) $\frac{3}{2}$ (3) $\frac{3}{2}$ (4) $\frac{3}{2}$ 147. $If the equation of the plane passing through the point A (- 2, 1, 3) and perpendicular to the vector 3 i + j + 5 k is ax + bv + cz + d = 0 then \frac{a + b}{c + d} =$ (1) $4/5$ (2) $2/3$ (3) $1$ (4) $- 4/5$ 148. $If the equation of a plane P, passing through the intersection of the planes x + 4 y - z + 7 = 0 and 3 x + y + 5 z = 8 is ax + by + 6 z = 15 for some a, b \in R, then the distance of the point (3, 2, - 1) from the plane P is$ 149. $If the shortest distance between the lines \frac{x - λ}{3} = \frac{y - 2}{- 1} = \frac{z - 1}{1} and \frac{x + 2}{- 3} = \frac{y + 5}{2} = \frac{z - 4}{4} is \frac{44}{30}, then the largest possible value of \| λ \| is equal to ______$ 150. $Let the equation of the plane P containing the line x + 10 = \frac{8 - y}{2} = z be ax + by + 3 z = 2 (a + b) and the distance of the plane P from the point (1, 27, 7) be c. Then a^{2} + b^{2} + c^{2} is equal to$