Practice Questions

Q88.The plane which bisects the line segment joining the points (−3, −3, 4) and (3, 7, 6) at right angles, passes through which one of the following points? (1) (2, 1, 3) (2) (4, 1, −2) (3) (4, −1, 7) (4) (−2, 3, 5) y−5

Q88.The plane containing the line x−3 2 = y+2−1 = z−13 and also containing its projection on the plane 2x + 3y −z = 5 , contains which one of the following points? (1) (2,2,0) (2) (-2,2,2) (3) (0,-2,2) (4) (2,0,-2)

Q88.Let A be a point on the line →r= (1 −3μ)ˆi + (μ −1)ˆj + (2 + 5μ)ˆk and B(3, 2, 6) be a point in the space. −→ Then the value of μ for which the vector AB is parallel to the plane x −4y + 3z = 1 is (1) 1 (2) 1 2 4 (3) −14 (4) 81

Q88.If the lines x = ay + b, z = cy + d and x = a′z + b′, y = c′ z + d′ are perpendicular, then (1) cc’ + a + a’ = 0 (2) aa’ + c + c’ = 0 (3) bb’ + cc’ + 1 = 0 (4) ab’ + bc’ + 1 = 0

Q88.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 2x −5y = 15, then 2α −3β is equal to : (1) 12 (2) 7 (3) 5 (4) 17

Q88.The plane through the intersection of the planes 𝑥+ 𝑦+ 𝑧= 1 and 2𝑥+ 3𝑦- 𝑧+ 4 = 0 and parallel to 𝑦- axis also passes through the point (1) 3, 3, - 1 (2) -3, 1, 1 (3) 3, 2, 1 (4) -3, 0, - 1

Q88.If the length of the perpendicular from the point (β, 0, β), (β ≠0) to the line, x1 = y−10 = z+1−1 is √32 is equal to (1) 2 (2) −1 (3) −2 (4) 1

Q88.The length of the perpendicular from the point ( 2, - 1, 4 ) on the straight line 𝑥+ 3 = 𝑦- 2 = 𝑧 is 10 -7 1 (1) greater than 3 but less (2) greater than 4 (3) less than 2 (4) greater than 2 but less than 4 than 3

Q88.The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines is + + + + →r= (ˆi ˆj) λ(ˆi + 2ˆj −ˆk) and →r= (ˆi ˆj) μ(−ˆi + ˆj −2ˆk) (1) 1 (2) 3 3 (3) √3 (4) 1 √3

Q88.The vertices B and C of a ΔABC lie on the line, x+2 3 = y−10 = 4z such that BC = 5 units. Then the area (in sq. units) of this triangle, given the point A(1, −1, 2), is (1) 6 (2) 2√34 (3) √34 (4) 5√17

Q88.Let →𝑎= 3^𝑖+ 2^𝑗+ 2^𝑘 and →𝑏= ^𝑖+ 2^𝑗- 2^𝑘 be two vectors. If a vector perpendicular to both the vectors →𝑎+ →𝑏 and →𝑎- →𝑏 has the magnitude 12 then one such vector is: (1) 4(2^𝑖+ 2^𝑗+ ^𝑘) (2) 4(2^𝑖- 2^𝑗- ^𝑘) (3) 4( - 2^𝑖- 2^𝑗+ ^𝑘) (4) 4(2^𝑖+ 2^𝑗- ^𝑘)

Q88.A plane passing though the points (0, −1, 0) and (0, 0, 1) and making an angle π4 with the plane y–z + 5 = 0, also passes through the point −1, 1, (1) (√2, 4) (2) (√2, 4) −1, 1, (3) (−√2, −4) (4) (−√2, −4)

Q88.Let S be the set of all real values of λ such that a plane passing through the points (−λ2, 1, 1), (1, −λ2, 1) and (1, 1, −λ2) also passes through the point (−1, −1, 1). Then S is equal to : (1) {√3} (2) {3, −3} (3) {1, −1} (4) {√3, −√3}

Q88.The vector equation of the plane through the line of intersection of the planes 𝑥+ 𝑦+ 𝑧= 1 and 2𝑥+ 3𝑦+ 4𝑧= 5 which is perpendicular to the plane 𝑥- 𝑦+ 𝑧= 0 is (1) →𝑟× ^𝑖+ ^𝑘+ 2 = 0 (2) →𝑟⋅^𝑖- ^𝑘- 2 = 0 (3) →𝑟× ^𝑖- ^𝑘+ 2 = 0 (4) →𝑟⋅(^𝑖- ^𝑘) + 2 = 0

Q88.A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(−1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) cos−1( 317 ) (2) cos−1( 3117 ) (3) cos−1( 3519 ) (4) cos−1( 359 )

Q89.The direction ratios of normal to the plane through the points (0,-1,0) and (0,0,1) and making an angle π with 4 the plane y −z + 5 = 0 are; 2,-1,1 2, √2 −√2 √2, 1, −1 2√3, 1, −1 (1) option 1 and 2 (2) option 2 and 3 (3) option 3 and 4 (4) all the options

Q89.On which of the following lines lies the point of intersection of the line, x−4 2 = 2 = z−31 and the plane, x + y + z = 2? y−5 (1) x−4 1 = 1 = z−5−1 (2) x−11 = y−32 = z+4−5 (3) x−2 2 = y−32 = z+33 (4) x+33 = 4−y3 = z+1−2

Q89.If a point 𝑅4, 𝑦, 𝑧 lies on the line segment joining the points 𝑃2, - 3,4 and 𝑄8,0, 10, then the distance of 𝑅 from the origin is (1) 2√21 (2) √53 (3) 6 (4) 2√14 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q89.The equation of a plane containing the line of intersection of the planes 2𝑥- 𝑦- 4 = 0 and 𝑦+ 2𝑧- 4 = 0 and passing through the point 1,1, 0 is JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 𝑥- 3𝑦- 2𝑧= - 2 (2) 𝑥+ 3𝑦+ 𝑧= 4 (3) 𝑥- 𝑦- 𝑧= 0 (4) 2𝑥- 𝑧= 2

Q89.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is : (1) 1 (2) 5 6 6 (3) 1 (4) 2 3 3

Q89.Let P be the plane, which contains the line of intersection of the planes, x + y + z −6 = 0 and 2x + 3y + z + 5 = 0 and it is perpendicular to the xy-plane. Then the distance of the point (0, 0, 256) from P is equal to: JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) 205√5 units (2) 17 units √5 (3) 11 units (4) 63√5 units √5

Q89.The perpendicular distance from the origin to the plane containing the two lines, x + 3 2 = y −5 2 = z +7 5 and x − 1 1 = y −4 4 = z +7 4 , is (1) 11√6 (2) 11 √6 (3) 11 (4) 6√11

Q89.A perpendicular is drawn from a point on the line = = to the plane 𝑥+ 𝑦+ 𝑧= 3 such that the 2 -1 1 foot of the perpendicular 𝑄 also lies on the plane 𝑥- 𝑦+ 𝑧= 3. Then the coordinates of 𝑄 are (1) 2, 0, 1 (2) – 1, 0, 4 (3) 4, 0, – 1 (4) 1, 0, 2

Q89.If the line, x−1 2 = y+13 = z−24 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is, (1) 2√5 (2) 92 (3) √5 (4) 7 2 2

Q89.The equation of the line passing through -4, 3, 1, parallel to the plane 𝑥+ 2𝑦- 𝑧- 5 = 0 and intersecting the 𝑥 + 1 𝑦- 3 𝑧- 2 line = = is -3 2 -1 𝑥+ 4 𝑦- 3 𝑧- 1 𝑥+ 4 𝑦- 3 𝑧- 1 (1) = = (2) = = 3 -1 1 1 1 3 (3) 𝑥+ 4 = 𝑦- 3 = 𝑧- 1 (4) 𝑥- 4 = 𝑦+ 3 = 𝑧+ 1 -1 1 1 2 1 4