Title ANALYTICAL GEOMETRY.pdf ✅

CLASS VII MATH WORKSHEET 01 CUQ 1. The horizontal axis is called as (a.)X-axis (b.) Y-axis (c.) Plane (d.) None 2. The point of intersection of axes is called as (a.)Plane (b.) X-axis (c.) Origin (d.) Y-axis 3. Of P(x, y) lies in first quadrant, then (a.)x < 0, y > 0 (b.) x < 0, y < 0 (c.) x > 0, y < 0 (d.) x > 0, y > 0 4. Q1 ∩ Q2 = (a.)X-axis (b.) Y-axis (c.) +ve Y-axis (d.)+ve X-axis 5. Distance between the points (1,2) and (3,4) is (a.)√2 units (b.) 2√2 units (c.) 3√2 units (d.) 4√2 units 6. The distance between the points P(x1, y1 ) and Q(x1, y2 ) is (a.)|y1 − y2 | (b.) |y1 + y2 | (c.) √|y1 + y2 | (d.) √|y1 − y2 | 7. The Co-ordinates of the point which divides the line segment joining A(x1, y1 ) and B(x2, y2 ) in the ratio m: n internally is (a.) ( mx2+nx1 m+n , my2+ny1 m+n ) (b.) ( mx2−nx1 m−n , myy2−ny m−n ) (c.) ( mx1+nx m+n , myy1+ny2 m+n ) (d.) ( mx1−nx2 m−n , myy1−ny2 m−n ) 8. If p(x, y) is any point on the line passing through A(x1, y1 ) and B(x2, y2 ) then the ra- tio in which ' p ' divided AB̅̅̅̅ is (a.)x1 − x: x − x2 (b.) y1 − y: y − y2 (c.) x − x1: x − x2 (d.) Both (1)and (2) 9. The ratio in which the line segment joining (x1, y1 ) and (x2, y2 ) is divided by x axis is (a.)y1: y2 (b.) y2: y1 (c.) −y1: y2 (d.) −y2: y1 10. If Q is the harmonic conjugate of ' P ' with respect to A, B, then AP, AB, AQ are in (a.)A.P (b.) G.P (c.) H.P (d.) A.G.P 11. The midpoint of (1,2) and (3,4) is (a.)(1,4) (b.) (2,3) (c.) (2,4) (d.) (3,2) JEE MAIN LEVEL - 1 1. Let A(acos θ, 0), B(0, asin θ) be any two points, then the distance between two points is (a.)|a| units (b.) a 2 units (c.) √a units (d.) √2a units 2. The ratio in which (2,3) divides the line segment joining (4,8), (−2, −7) is (a.)2 : 1 externally (b.) 2 : 3 internally (c.) 4: 3 externally (d.) 1: 2 internally. 3. The x - axis divides the line segment joining (2, −3), (5,7) in the ratio is (a.)1: 2 (b.) 3: 7 ANALYTICAL GEOMETRY
CLASS VII MATH (c.) 4: 5 (d.) 3: 4 4. The y - axis divides the line segment joining (3,5), (−4,7) in the ratio is (a.)1: 2 (b.) 3: 7 (c.) 4: 5 (d.) 3: 4 5. The centroid of the Δ le formed by (0,0)(1,4)(2,5) is (a.)(1,3) (b.) (3,1) (c.) (3,4) (d.) (3,9) 6. Distance from origin to (tan x, 1) is (a.)|1 + tan α| (b.) |sec α| (c.) |Tan2 α − 1| (d.) |cosec α| 7. Distance between (cos θ, sin θ), and (−sin θ, cos θ) is (a.)1 (b.) 2 + 2sin θ (c.) 1 + sin θ (d.) √2 8. If (−x, −y) ∈ Q2, then (x, −y) belongs to (a.)Q1 (b.) Q2 (c.) Q3 (d.) Q4 9. If (2x + 3,3y − 4) = (1,5), then (x, y) = (a.)(−1,5) (b.) (3, −1) (c.) (−1,3) (d.) (3, −4) 10. The points (7,9), (3, −7), (−3,3) are the vertices of (a.)equilateral triangle (b.) isosceles triangle (c.) right angled triangle (d.) right angled isosceles triangle JEE MAIN LEVEL - 2 11. The distance between the points (1,1) and ( 2t 2 1+t 2 , (1−t) 2 1+t 2 ) is (a.)4t (b.) 3t (c.) 1 (d.) 24 12. The coordinates of the point which divides the line segment joining points A(0,0) and B(9,12) in the ratio 1: 2 is (a.)(−3,4) (b.) (3,4) (c.) (3, −4) (d.) None of these 13. The points (7,1), (4,4), (−2, −2)(1, −5) taken in order, forms (a.)parallelogram (b.) rectangle (c.) rhombus (d.) square 14. The fourth vertex of the square whose con- secutive vertices are (2,1), (7,4), (2,5) is (a.)(2,-2)$ (b.) (17,13) (c.) (−3,2) (d.) (6,9) 15. If (k, 2)(2,3), (3,4) are collinear, then k = (a.)1 (b.) 2 (c.) 3 (d.) -1 JEE MAIN LEVEL - 3 16. If (2,4), (4,2) are the extremities of the hy- potenuse of a right angled isosceles triangle, then the third vertex is (a.)(2, (b. )or (4,4) (b.) (3,3) or (4,4) (c.) (2, (b. )or (3,3) (d.) (2, (c. )or (3,2) 17. If P(1,2),Q(4,6),R(5,7),S(a, b) are verti- ces of a parallelogram PQRS, then (a.)a = 2, b = 4 (b.) a = 3, b = 4 (c.) a = 2, b = 3 (d.) a = 3, b = 5 18. A line is of length 10 unit and one end is at (2, −3). If the abscissa of the other end is 10 , then its ordinate is
CLASS VII MATH (a.)9 (b.) 3 (c.)-3 (d.) 6 19. If the points (k − 1, k + 2), (k, k + 1) and (k + 1, k) are collinear, then k = (a.)1 (b.) 2 (c.) 3 (d.) All JEE MAIN LEVEL - 4 20. If A = (at22at), B = ( a t 2 , − 2a t ) ,S = (a, 0), then 1 SA + 1 SB = (a.)a (b.) 1/a (c.) 2/a (d.) a 2 (√5 + 1)/8 21. If P = (−5,4) and Q = (−2, −3). If PQ̅̅̅̅ is produced to R such that P divides QR̅̅̅̅ exter- nally in the ratio 1: 2, then R is (a.)(1,10) (b.) (1, −10) (c.) (10,1) (d.) (2, −10) 22. If the points (a, 0), (b, 0) and (1,1) are col- linear then (a.) 1 a2 + 1 b2 = 1 (b.) 1 a2 − 1 b2 = 1 (c.) 1 a + 1 b = 1 (d.) 1 a − 1 b = 1 JEE MATN LEVEL- 5 23. If the point [x1 + t(x2 − x1 ), y1 + t(y2 − y1 )] divide the join of (x1, y1 ) and (x2, y2 ) internally, then (a.)t < 0 (b.) 0 < t < 1 (c.) t > 1 (d.) t = 1 24. Area of quadrilateral formed by the points A(2,1), B(4, (c. )C(−1, (b. )&D(−3,2) is (a.)54Sq units (b.) 36 Sq.units (c.) 20 Sq.units (d.) 12 Sq.units 25. If A, B, C are collinear points such that A = (3,4),B = (7,7) and AC = 10. then C = (a.)(2,5) (b.) (−2, −5) (c.) (5, −2) (d.) (−5, −2) JEE ADVANCED LEVEL - 1 Multi Correct Choice Type: 26. Let A(x1, y1 )B(x2, y2 ) be any two points distance between two points (a.)√(x2 − x1 ) 2 + (y2 − y1 ) 2 (b.) √(x2 + x1 ) 2 + (y2 − y1 ) 2 (c.) √(x1 − x2 ) 2 + (y1 − y2 ) 2 (d.) √(x2 + x1 ) 2 − (y2 − y1 ) 2 COMPREHENSION TYPE: The points A, B and C are called collinear points if they lie on the same line. If three points are collin- ear then AB + BC = AC (or) AC + CB = AB (or) AC + AB = BC. Based on the above passage answer the following questions. 27. If A(2,7),B(8,3) and C(14, −1) are collin- ear then which of the following is true. (a.)AB + BC = AC (b.) AC + CB = AB (c.) AB + AC = BC (d.) All the above 28. If A, B and C are collinear then the area of △ ABC is (a.)Positive real (b.) Negative real (c.) 0 (d.) Complex number 29. If A(−1,3), B(2, p) and C(5, −1) are collin- ear then the value of p is (a.)0 (b.) 3 (c.) 2 (d.) 1 Matrix Match Type :
CLASS VII MATH 30. Match the following Column I Column II a) Distance between (5,3) and (8,7) is p) 5 b) Distance between (0,0) and (−4,3) is q) √5 c) Distance between ( 1 2 , 3 2 ) and ( 3 2 , −1 2 ) is r) 3 d) If (1, x) is at √10 units from (0,0), then x is s) 5 t) 4 JEE ADVANCED LEVEL-2&3 Matrix Match Type : 31. If Δ denotes area of Δ le formed by (p + 1,1), ((2p + 1),3) and (2p + 2,2p) Match the following Column I Column II a) p = 0 p) Δ = 7 2 b) p = ±1 q) Δ = 25 2 c) p = 3 r) Δ = 3 2 d) p = −3 s) Δ = 1 Multi Correct Choice Type: 32. ABC is an isosceles triangle whose base is BC. If B and C are (a + b, b − a) and (a − b, a + b) then coordinates of A may be (a.)(a.b) (b.) (b, a) (c.) ( a b , b a ) (d.) (1, b a ) JEE ADVANCED LEVEL-4&5 33. The centroid of Δ le formed by (p, q), (q, 1)&(1, p) is origin, if p 3 + q 3 + 1 = kpq, then k = Integer Type: 34. A(a + 1, a − 1), B(a 2 + 1, a 2 − 1) and C(a 3 + 1, a 3 − 1) are given points D(11,9) is the mid point of AB and E(41,39) is the mid point of BC. If F is the mid point of AC, then (BF) 2 is equal to WORKSHEET 02 CUQ 1. If ' θ ' is the inclination, then (a.)θ ∈ [0, π) (b.) θ ∈ [0, π] (c.) θ ∈ [0,2π) (d.) θ ∈ [0,2π] 2. Slope of the line with inclination ' θ ' is (a.)m = cot θ (b.) m = tan θ (c.) m = cos θ (d.) m = sec θ 3. Slope of the line passing thought (x1, y1 ) and (x2, y2 ) is (a.)m = y2−y1 x2−x1 (b.) m = x2−x1 y2−y1 (c.) m = y1−y2 x2−x1 (d.) m = x1−x2 y2−y1 4. Slope of the line ax + by + c = 0 is (a.)m = +a b (b.) m = −b a (c.) m = −a b (d.) m = b a 5. If ax + by +c = 0 is the general form of the line, then (a.)|a| + |b| = 0 (b.) |a| + |b| ≠ 0 (c.) a + b = 0 (d.) a + b ≠ 0 6. If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are two parallel lines, then the cor- rect statement is (a.)a1 = a2, b1 = b2, c1 ≠ c2 (b.) a1 ≠ a2, b1 = b2, c1 = c2 (c.) a1 ≠ a2, b1 ≠ b2, c1 = c2 (d.) a1 = a2, b1 ≠ b2, c1 = c2 7. Slope - intercept form of the line is (a.)y = mx (b.) y = mx + c