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CBSE Class 11 Maths Question of the Day: chapters 9–11

30 CBSE Class 11 Mathematics puzzles from the Question of the Day rotation, chapters 9–11. Each puzzle is three board-style questions on one chapter, shown as an image with the question text written out below it; the answers, hints and step-marked solutions are on the daily puzzle page.

Chapter 9: Straight Lines

Chapter 9: Straight Lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The slope of the line through (2, 3) and (6, 11) is Options: A) 12; B) 2; C) 8; D) -2
2. The slope of a line inclined at 135^∘ to the positive x-axis is Options: A) -1; B) 1; C) √3; D) -1/(√3)
3. The line through (1, -2) with slope 3 is Options: A) x - 3y - 7 = 0; B) 3x - y + 5 = 0; C) 3x - y - 5 = 0; D) 3x + y - 1 = 0
Chapter 9: Straight Lines · Slopes
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator. Let A = (1, 2) and B = (4, 8).
1. The slope of AB is Options: A) 3; B) 6; C) 2; D) 1/2
2. The slope of a line perpendicular to AB is Options: A) 1/2; B) -2; C) 2; D) - 1/2
3. The inclination of a line is 150^∘. Its slope is Options: A) 1/(√3); B) -√3; C) -1; D) -1/(√3)
Chapter 9: Straight Lines · Equations of lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The line through (2, -1) with slope 3 is Options: A) y = 3x + 7; B) y = -x + 3; C) y = 3x - 7; D) y = 3x - 1
2. The line with x-intercept 4 and y-intercept -2 is Options: A) x + 2y = 4; B) x - 2y = -4; C) x - 2y = 4; D) 2x - y = 4
3. The y-intercept of the line 3x + 4y = 12 is Options: A) 3/4; B) 3; C) 4; D) 12
Chapter 9: Straight Lines · The line through two points
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator. A line passes through (-1, 3) and (2, -3).
1. Its equation is Options: A) 2x - y = -5; B) x + 2y = 5; C) 2x + y = 5; D) 2x + y = 1
2. Its x-intercept is Options: A) 1; B) -2; C) 2; D) 1/2
3. The area of the triangle formed by the line and the coordinate axes is Options: A) 1/4; B) 1/2; C) 1; D) 1/8
Chapter 9: Straight Lines · Collinear points, parallel and perpendicular lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The points (1, 2), (3, 8) and (k, 11) lie on one line. Then k equals Options: A) 3; B) 5; C) 11/3; D) 4
2. The line through (0, 5) parallel to 2x - y + 3 = 0 is Options: A) y = 2x + 5; B) y = -2x + 5; C) y = 12 x + 5; D) y = 2x + 3
3. The line through (1, 1) perpendicular to x + 2y = 7 is Options: A) y = 2x + 1; B) y = 2x - 1; C) y = -12 x + 32; D) y = -2x + 3
Chapter 9: Straight Lines · Angles between lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The acute angle between the lines y = x and y = √3 x is Options: A) 45^∘; B) 60^∘; C) 15^∘; D) 30^∘
2. The acute angle between y = 2x + 1 and y = -3x + 4 is Options: A) 30^∘; B) 60^∘; C) 90^∘; D) 45^∘
3. The angle between 3x - 4y = 5 and 8x + 6y = 1 is Options: A) 90^∘; B) 45^∘; C) 60^∘; D) 0^∘
Chapter 9: Straight Lines · Distances from lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The distance of the point (3, -2) from the line 4x + 3y - 1 = 0 is Options: A) 1/5; B) 1; C) 5; D) 17/5
2. The distance between the parallel lines 3x + 4y = 9 and 6x + 8y = -2 is Options: A) 2; B) 11/5; C) 8/5; D) 10
3. The distance of the origin from the line x3 + y4 = 1 is Options: A) 12; B) 12/5; C) 5; D) 7/5
Chapter 9: Straight Lines · Lines in a triangle
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator. A triangle has vertices A(0, 0), B(6, 0) and C(2, 4).
1. The median from C has equation Options: A) y = 2x; B) 4x + y = 12; C) x + 4y = 18; D) 4x - y = 4
2. The length of the perpendicular from C to AB is Options: A) 2 √5; B) 6; C) 4; D) 2
3. The foot of the perpendicular from B to the line AC is Options: A) (125, 65); B) (1, 2); C) (65, 125); D) (2, 4)
Chapter 9: Straight Lines · Through a point of intersection
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator. The lines x + y = 5 and 2x - y = 1 meet at P.
1. P is Options: A) (1, 4); B) (2, -3); C) (2, 3); D) (3, 2)
2. The line through P and the origin is Options: A) x - y = 0; B) 3x + 2y = 0; C) 3x - 2y = 0; D) 2x - 3y = 0
3. The line through P perpendicular to x - 3y + 4 = 0 is Options: A) 3x - y = 3; B) x + 3y = 11; C) 3x + y = 9; D) x - 3y + 7 = 0
Chapter 9: Straight Lines · Images, distances and parallel lines
Three board-style questions on Straight Lines (CBSE Class 11 Mathematics). No calculator.
1. The image of the point (1, 2) in the line x + y = 5 is Options: A) (5, 5); B) (3, 4); C) (4, 3); D) (2, 1)
2. The points on the x-axis at distance 4 from the line 3x - 4y + 3 = 0 have x-coordinates Options: A) 17/3 only; B) 23/3 and -17/3; C) 4 and -4; D) 17/3 and -23/3
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The lines 2x + 3y = 5 and 4x + 6y = 7 do not meet. Reason (R): Two different lines with equal slopes are parallel. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.

Chapter 10: Conic Sections

Chapter 10: Conic Sections
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator.
1. The centre and radius of x² + y² - 6x + 4y - 12 = 0 are Options: A) (3, -2) and 5; B) (-3, 2) and 5; C) (3, -2) and √12; D) (6, -4) and 5
2. The focus of the parabola y² = 12x is Options: A) (12, 0); B) (-3, 0); C) (0, 3); D) (3, 0)
3. The eccentricity of the ellipse (x²)/25 + (y²)/16 = 1 is Options: A) 45; B) 35; C) 53; D) (√41)/5
Chapter 10: Conic Sections · A parabola
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. Consider the parabola y² = 12x.
1. Its focus is Options: A) (12, 0); B) (0, 3); C) (-3, 0); D) (3, 0)
2. Its directrix is Options: A) y = -3; B) x = -12; C) x = -3; D) x = 3
3. The length of its latus rectum is Options: A) 24; B) 12; C) 3; D) 6
Chapter 10: Conic Sections · An ellipse
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. Consider the ellipse (x²)/25 + (y²)/9 = 1.
1. Its foci are Options: A) (± 4, 0); B) (0, ± 4); C) (± 5, 0); D) (± √34, 0)
2. Its eccentricity is Options: A) 3/5; B) 5/4; C) 3/4; D) 4/5
3. The length of its latus rectum is Options: A) 50/3; B) 6; C) 18/5; D) 9/5
Chapter 10: Conic Sections · A hyperbola
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. Consider the hyperbola (x²)/16 - (y²)/9 = 1.
1. Its foci are Options: A) (± √7, 0); B) (0, ± 5); C) (± 4, 0); D) (± 5, 0)
2. Its eccentricity is Options: A) 4/5; B) 5/3; C) (√7)/4; D) 5/4
3. The length of its transverse axis is Options: A) 10; B) 8; C) 6; D) 4
Chapter 10: Conic Sections · Circles from given conditions
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator.
1. The circle with centre (2, -1) passing through (5, 3) is Options: A) (x - 5)² + (y - 3)² = 25; B) (x - 2)² + (y + 1)² = 25; C) (x + 2)² + (y - 1)² = 25; D) (x - 2)² + (y + 1)² = 5
2. The circle on the line segment joining (1, 2) and (7, 10) as diameter is Options: A) (x - 3)² + (y - 4)² = 25; B) (x - 1)² + (y - 2)² = 100; C) (x - 4)² + (y - 6)² = 25; D) (x - 4)² + (y - 6)² = 100
3. The radius of the circle through (0, 0), (4, 0) and (0, 6) is Options: A) 2 √13; B) √13; C) 13; D) 5
Chapter 10: Conic Sections · Parabolas from given conditions
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator.
1. The parabola with vertex at the origin, axis along the x-axis, passing through (2, 4) is Options: A) y² = 2x; B) x² = 4y; C) y² = 16x; D) y² = 8x
2. The parabola with focus (0, -2) and directrix y = 2 is Options: A) y² = -8x; B) x² = -2y; C) x² = -8y; D) x² = 8y
3. The point P on y² = 8x with y = 8 is at what distance from the focus? Options: A) 10; B) 8; C) 6; D) 12
Chapter 10: Conic Sections · An ellipse from its foci
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. An ellipse has foci (0, ± 3) and major axis of length 10.
1. Its equation is Options: A) (x²)/16 + (y²)/25 = 1; B) (x²)/25 + (y²)/16 = 1; C) (x²)/9 + (y²)/25 = 1; D) (x²)/16 + (y²)/9 = 1
2. Its eccentricity is Options: A) 3/5; B) 4/5; C) 5/3; D) 3/4
3. The length of its latus rectum is Options: A) 18/5; B) 25/2; C) 8; D) 32/5
Chapter 10: Conic Sections · A hyperbola from its vertices and foci
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. A hyperbola has vertices (± 2, 0) and foci (± 3, 0).
1. Its equation is Options: A) (x²)/9 - (y²)/4 = 1; B) (x²)/4 + (y²)/5 = 1; C) (x²)/4 - (y²)/5 = 1; D) (x²)/4 - (y²)/9 = 1
2. Its eccentricity is Options: A) 2/3; B) (√5)/2; C) 9/4; D) 3/2
3. The length of its latus rectum is Options: A) 5; B) 5/2; C) 10; D) 4/3
Chapter 10: Conic Sections · Recognising conics
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator.
1. A double cone has semi-vertical angle 30^∘. A plane not through the vertex makes an angle of 60^∘ with the axis. The section is Options: A) a circle; B) an ellipse; C) a parabola; D) a hyperbola
2. The length of the major axis of the ellipse 9x² + 4y² = 36 is Options: A) 6; B) 4; C) 3; D) 9
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The eccentricity of every ellipse is less than 1. Reason (R): For an ellipse, c² = a² - b² with b > 0, so c < a. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 10: Conic Sections · Centre and radius of a circle
Three board-style questions on Conic Sections (CBSE Class 11 Mathematics). No calculator. Consider the circle x² + y² - 6x + 8y = 0.
1. Its centre is Options: A) (-3, 4); B) (6, -8); C) (-6, 8); D) (3, -4)
2. Its radius is Options: A) 10; B) 5; C) 25; D) 7
3. The length of the chord it cuts off on the x-axis is Options: A) 6; B) 3; C) 8; D) 10

Chapter 11: Introduction to Three Dimensional Geometry

Chapter 11: Introduction to Three Dimensional Geometry
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator.
1. The point (-2, 3, -5) lies in octant Options: A) II; B) VI; C) III; D) VII
2. Every point on the y-axis has coordinates of the form Options: A) (x, 0, 0); B) (x, y, 0); C) (0, 0, z); D) (0, y, 0)
3. The distance between (1, -2, 3) and (4, 2, 3) is Options: A) √7; B) 7; C) 5; D) 25
Chapter 11: Introduction to Three Dimensional Geometry · Perpendiculars to planes and axes
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator. Let P = (3, -4, 5).
1. The foot of the perpendicular from P to the xy-plane is Options: A) (0, -4, 5); B) (3, -4, 0); C) (0, 0, 5); D) (3, 0, 5)
2. The distance of P from the xz-plane is Options: A) 3; B) -4; C) 4; D) 5
3. The distance of P from the x-axis is Options: A) 9; B) √41; C) 5; D) √34
Chapter 11: Introduction to Three Dimensional Geometry · Three points on a line
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator. Let A = (1, 2, 3), B = (3, 5, 9) and C = (5, 8, 15).
1. AB equals Options: A) 49; B) √13; C) 5; D) 7
2. AC equals Options: A) 14; B) 7; C) 196; D) 2 √13
3. Which statement is true? Options: A) A, B, C are collinear with A between B and C; B) ABC is an equilateral triangle; C) ABC is a right-angled triangle; D) A, B, C are collinear with B between A and C
Chapter 11: Introduction to Three Dimensional Geometry · What kind of triangle?
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator. Let A = (2, 1, 0), B = (4, 3, 1) and C = (3, 3, -2).
1. AB equals Options: A) 9; B) √5; C) 5; D) 3
2. BC equals Options: A) √10; B) 10; C) 3; D) 2 √2
3. Triangle ABC is Options: A) right-angled; B) scalene; C) equilateral; D) isosceles but not right-angled
Chapter 11: Introduction to Three Dimensional Geometry · Finding an unknown coordinate
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator.
1. The point on the x-axis equidistant from (1, 2, 3) and (3, 5, -2) has x-coordinate Options: A) -6; B) 4; C) 6; D) 2
2. That common distance is Options: A) √29; B) 6; C) √38; D) 38
3. If the distance between (2, k, 1) and (5, 1, -3) is 5, then k equals Options: A) 1; B) 0; C) -1; D) 5
Chapter 11: Introduction to Three Dimensional Geometry · Points equidistant from two points
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator. Let A = (1, 0, 2) and B = (3, 2, 0). The set of points P(x, y, z) with PA = PB is a plane.
1. Its equation is Options: A) x - y - z = 0; B) x + y - z = 4; C) x + y - z = 2; D) x + y + z = 2
2. Which point is equidistant from A and B? Options: A) (0, 0, 0); B) (3, 0, 0); C) (2, 1, 1); D) (1, 1, 2)
3. The point of the y-axis that is equidistant from A and B is Options: A) (0, -2, 0); B) (0, 1, 0); C) (2, 0, 0); D) (0, 2, 0)
Chapter 11: Introduction to Three Dimensional Geometry · A triangle in space
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator. Let A = (1, 2, 2), B = (3, 4, 3) and C = (5, 2, 4).
1. AB equals Options: A) 9; B) √5; C) 5; D) 3
2. AC equals Options: A) 6; B) 3 √2; C) 2 √5; D) 20
3. The perimeter of triangle ABC is Options: A) 6 + 2√5; B) 12; C) 3 + 2√5; D) 9 + 2√5
Chapter 11: Introduction to Three Dimensional Geometry · Planes, axes and lattice points
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator.
1. The distance of (1, -2, 2) from the origin is Options: A) 9; B) 1; C) √5; D) 3
2. How many points with integer coordinates are at distance exactly 1 from the origin? Options: A) 8; B) 3; C) 26; D) 6
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The point (-3, 0, 4) lies in the xz-plane. Reason (R): Every point of the xz-plane has z = 0. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 11: Introduction to Three Dimensional Geometry · Octants and coordinate planes
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator.
1. The point (-1, 5, -2) lies in octant Options: A) VI; B) II; C) VII; D) III
2. The point (4, -1, 2) lies in octant Options: A) II; B) I; C) IV; D) VIII
3. Which point lies in the yz-plane? Options: A) (3, -2, 0); B) (1, 1, 1); C) (0, 3, -2); D) (3, 0, -2)
Chapter 11: Introduction to Three Dimensional Geometry · The distance formula
Three board-style questions on Introduction to Three Dimensional Geometry (CBSE Class 11 Mathematics). No calculator.
1. The distance between (1, 2, 3) and (4, 6, 15) is Options: A) 12; B) 13; C) 169; D) 19
2. The distance of (2, -3, 6) from the origin is Options: A) 5; B) 49; C) 11; D) 7
3. The distance of (3, 4, 12) from the z-axis is Options: A) 4; B) 5; C) 12; D) 13

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Other chapters: Chapters 1–4 · Chapters 5–8 · Chapters 9–11 · Chapters 12–14. See all CBSE Maths daily and weekly questions.