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 122 marksmedium
Determinants
Evaluate the determinant of the matrix [[1, 2, 3],[0, 1, 4],[5, 6, 0]].
Reveal model answer + marking pointsHide answer▾
Expand along the first row: |A| = 1 x (1 x 0 - 4 x 6) - 2 x (0 x 0 - 4 x 5) + 3 x (0 x 6 - 1 x 5) = 1 x (0 - 24) - 2 x (0 - 20) + 3 x (0 - 5) = -24 + 40 - 15 = 1. So the value of the determinant is 1.
Marking-scheme points
- ✓Expand along the first row
- ✓= 1(0 - 24) - 2(0 - 20) + 3(0 - 5)
- ✓= -24 + 40 - 15 = 1
MathsClass 122 marksmedium
Determinants
State any three properties of determinants.
Reveal model answer + marking pointsHide answer▾
(1) The value of a determinant remains unchanged if its rows and columns are interchanged (that is, |A'| = |A|). (2) If any two rows (or two columns) of a determinant are interchanged, the sign of the determinant changes. (3) If any two rows (or columns) of a determinant are identical (or proportional), the value of the determinant is zero. Also, if each element of a row (or column) is multiplied by a constant k, the determinant is multiplied by k.
Marking-scheme points
- ✓Interchanging rows and columns does not change the value
- ✓Interchanging two rows/columns changes the sign
- ✓Two identical/proportional rows or columns give value zero
MathsClass 123 marksmedium
Determinants
Using determinants, find the area of the triangle whose vertices are (1, 0), (6, 0) and (4, 3).
Reveal model answer + marking pointsHide answer▾
The area of a triangle with vertices (x1, y1), (x2, y2), (x3, y3) is (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Substituting: area = (1/2)|1(0 - 3) + 6(3 - 0) + 4(0 - 0)| = (1/2)|-3 + 18 + 0| = (1/2)(15) = 7.5 square units.
Area = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
Marking-scheme points
- ✓Area = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
- ✓= (1/2)|-3 + 18 + 0|
- ✓= 7.5 square units
MathsClass 122 markseasy
Determinants
Define the minor and the cofactor of an element of a determinant.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 marksmedium
Determinants
Find the inverse of the matrix A = [[2, 3],[1, 4]] using the adjoint method.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 markseasy
Determinants
What is a singular and a non-singular matrix? State the condition for a matrix to be invertible.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 markshard
Determinants
Solve the system of equations 2x + 3y = 8 and x + 2y = 5 using determinants (Cramer's rule).
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 marksmedium
Determinants
If A is a 3 x 3 matrix with |A| = 5, find the values of |adj A| and |2A|.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 markseasy
Continuity and Differentiability
State the conditions for a function f(x) to be continuous at a point x = a.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 marksmedium
Continuity and Differentiability
Find the value of k for which the function f(x) = kx + 1 for x <= 5 and f(x) = 3x - 5 for x > 5 is continuous at x = 5.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 marksmedium
Continuity and Differentiability
What is the relationship between continuity and differentiability of a function?
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 markseasy
Continuity and Differentiability
Differentiate sin(x^2) with respect to x.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 marksmedium
Continuity and Differentiability
If x^2 + y^2 = 25, find dy/dx by implicit differentiation.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 markshard
Continuity and Differentiability
Differentiate y = x^x with respect to x using logarithmic differentiation.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 marksmedium
Continuity and Differentiability
Write the derivatives of sin inverse (x) and tan inverse (x) with respect to x.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 marksmedium
Continuity and Differentiability
If x = a cos t and y = a sin t, find dy/dx.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 marksmedium
Continuity and Differentiability
State Rolle's theorem and the Lagrange mean value theorem.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 marksmedium
Continuity and Differentiability
If y = e^x sin x, find the second order derivative d2y/dx2.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 122 markseasy
Application of Derivatives
What is meant by the derivative as a rate of change? Write the rate of change of the area of a circle with respect to its radius.
🔒 Model answer + marking pointsUnlock with Premium →MathsClass 123 marksmedium
Application of Derivatives
The radius of a circle is increasing at the rate of 3 cm/s. Find the rate at which the area is increasing when the radius is 10 cm.
🔒 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.