Board Boosters
The questions your board exam loves to ask
800 most-asked Class 11 & 12 (+1 / +2) questions across Physics, Chemistry, Maths and Biology — each with a model answer and the exact marking-scheme points examiners reward. Revise smart, walk in calm.
MathsClass 112 markseasy
Straight Lines
Find the equation of the line with slope 2 that passes through the point (1, -3).
Reveal model answer + marking pointsHide answer▾
Using the point-slope form y - y1 = m(x - x1) with m = 2 and (x1, y1) = (1, -3): y - (-3) = 2(x - 1), so y + 3 = 2x - 2, giving y = 2x - 5 or 2x - y - 5 = 0.
y - y1 = m(x - x1)
Marking-scheme points
- ✓Point-slope form: y - y1 = m(x - x1)
- ✓y + 3 = 2(x - 1)
- ✓y = 2x - 5
MathsClass 113 marksmedium
Straight Lines
Find the equation of the line passing through the points (1, 2) and (3, 6).
Reveal model answer + marking pointsHide answer▾
Slope m = (6 - 2)/(3 - 1) = 4/2 = 2. Using point-slope form with point (1, 2): y - 2 = 2(x - 1), so y - 2 = 2x - 2, giving y = 2x, or 2x - y = 0.
y - y1 = m(x - x1)
Marking-scheme points
- ✓Slope = (6 - 2)/(3 - 1) = 2
- ✓y - 2 = 2(x - 1)
- ✓Equation: 2x - y = 0
MathsClass 113 marksmedium
Straight Lines
Find the acute angle between the lines x + sqrt(3) y = 1 and sqrt(3) x + y = 1.
Reveal model answer + marking pointsHide answer▾
Slope of first line m1 = -1/sqrt3; slope of second line m2 = -sqrt3. The angle between them satisfies tan(theta) = |(m1 - m2)/(1 + m1 m2)| = |(-1/sqrt3 + sqrt3)/(1 + (-1/sqrt3)(-sqrt3))| = |((-1 + 3)/sqrt3)/(1 + 1)| = |(2/sqrt3)/2| = 1/sqrt3. So theta = 30 degrees.
tan theta = |(m1 - m2)/(1 + m1 m2)|
Marking-scheme points
- ✓m1 = -1/sqrt3, m2 = -sqrt3
- ✓tan theta = |(m1 - m2)/(1 + m1 m2)| = 1/sqrt3
- ✓theta = 30 degrees
MathsClass 113 marksmedium
Straight Lines
Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 marksmedium
Straight Lines
Find the distance between the parallel lines 3x - 4y + 7 = 0 and 3x - 4y + 5 = 0.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Straight Lines
Find the equation of the line which makes intercepts -3 and 2 on the x-axis and y-axis respectively.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Straight Lines
Find the equation of the perpendicular bisector of the line segment joining the points (1, 1) and (3, 5).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 115 markshard
Straight Lines
Find the image (reflection) of the point (3, 8) in the line x + 3y - 7 = 0.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 markseasy
Conic Sections
Find the centre and radius of the circle x^2 + y^2 - 4x + 6y - 12 = 0.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 markseasy
Conic Sections
Find the equation of the circle with centre (2, -3) and radius 5.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Conic Sections
For the parabola y^2 = 12x, find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Conic Sections
For the ellipse x^2/25 + y^2/9 = 1, find the vertices, foci, eccentricity and length of the latus rectum.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Conic Sections
For the hyperbola x^2/16 - y^2/9 = 1, find the vertices, foci and eccentricity.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 marksmedium
Conic Sections
Find the equation of the parabola with focus (0, 3) and directrix y = -3.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Conic Sections
Find the equation of the ellipse with vertices (+/-5, 0) and foci (+/-4, 0).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 markshard
Conic Sections
Find the eccentricity of an ellipse whose latus rectum is half of its major axis.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 markseasy
Introduction to Three Dimensional Geometry
Find the distance between the points (2, 3, 5) and (4, 3, 1).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 112 markseasy
Introduction to Three Dimensional Geometry
Find the distance of the point (1, -2, 3) from the origin.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Introduction to Three Dimensional Geometry
Find the coordinates of the point which divides the line segment joining (1, -2, 3) and (3, 4, -5) internally in the ratio 2 : 3.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Introduction to Three Dimensional Geometry
Find the centroid of the triangle whose vertices are (1, 2, 3), (3, -1, 5) and (4, 0, -2).
🔒 Model answer + marking pointsUnlock with Premium →You are more ready than you feel.
One question at a time is how every topper started. Bookmark this, revise a few each day, and watch the fear shrink. And if a friend is stressing about boards — send this their way. You both win.