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 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.
Reveal model answer + marking pointsHide answer▾
The distance of point (x1, y1) from line Ax + By + C = 0 is d = |A x1 + B y1 + C|/sqrt(A^2 + B^2). Here A = 3, B = -4, C = -26 and (x1, y1) = (3, -5). d = |3(3) - 4(-5) - 26|/sqrt(9 + 16) = |9 + 20 - 26|/sqrt25 = |3|/5 = 3/5.
d = |A x1 + B y1 + C|/sqrt(A^2 + B^2)
Marking-scheme points
- ✓d = |A x1 + B y1 + C|/sqrt(A^2 + B^2)
- ✓Numerator = |9 + 20 - 26| = 3; denominator = 5
- ✓d = 3/5 units
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 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 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 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 →MathsClass 113 marksmedium
Limits and Derivatives
Evaluate lim as x approaches 0 of (sin 3x)/(sin 5x).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Limits and Derivatives
Evaluate lim as x approaches 3 of (x^2 - 9)/(x^2 - x - 6).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Limits and Derivatives
Evaluate lim as x approaches 0 of (sqrt(1 + x) - 1)/x.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Limits and Derivatives
Differentiate y = (x^2 + 1)(x - 3) using the product rule.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Limits and Derivatives
Differentiate y = (x + 1)/(x - 1) using the quotient rule.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 markshard
Limits and Derivatives
Find the derivative of sin x from first principles.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Statistics
Find the mean deviation about the mean for the data 6, 7, 10, 12, 13, 4, 8, 12.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 113 marksmedium
Statistics
Find the variance and standard deviation of the data 2, 4, 6, 8, 10.
🔒 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.