🏆 Daily Math Board Challenge (2026 Edition)
Check whether (x + 1)² = 2(x − 3) is a quadratic equation.
🎯 Chapter Readiness Score35%
⚡ Key Formulas at a Glance
Formula (Hover/Click)
Matrix Product Order
Formula (Hover/Click)
Transpose Property
Formula (Hover/Click)
Symmetric Condition
Aᵀ = A (Symmetric), Aᵀ = −A (Skew-Symmetric)
Formula (Hover/Click)
Invertibility Theorem
Matrix A is invertible ↔ A is non-singular (|A| ≠ 0)
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📊 Chapter Weightage Analytics: High Yield Topic in Board Papers
Years Included: Year 2024, Year 2023
📅 Year 2024 Board Examination Paper
Q1NCERT Ex 3.1 Q4 • 2 Marks2 Marks
Construct a 2x2 matrix A = [a_ij] whose elements are given by a_ij = (i + 2j)² / 2.
▶ Show Detailed Solution
Step 1 (Calculate Elements):
a_11 = (1 + 2)²/2 = 9/2
a_12 = (1 + 4)²/2 = 25/2
a_21 = (2 + 2)²/2 = 8
a_22 = (2 + 4)²/2 = 18.
Step 2 (Form Matrix):
A = [[9/2, 25/2], [8, 18]].
✔ Final Answer: A = [[9/2, 25/2], [8, 18]]
Q2CBSE Board 2024 • 2 Marks2 Marks
If A = [[1, 2], [3, 4]] and B = [[-1, 3], [2, 1]], find matrix C such that 3A - 2B + C = O.
▶ Show Detailed Solution
Step 1 (Compute 3A and 2B):
3A = [[3, 6], [9, 12]]
2B = [[-2, 6], [4, 2]]
3A - 2B = [[5, 0], [5, 10]].
Step 2 (Solve for C):
C = -(3A - 2B) = [[-5, 0], [-5, -10]].
✔ Final Answer: C = [[-5, 0], [-5, -10]]
Q3NCERT Ex 3.2 Q9 • 3 Marks3 Marks
Find the values of x and y from the matrix equation: 2[[x, 5], [7, y-3]] + [[3, -4], [1, 2]] = [[7, 6], [15, 14]].
▶ Show Detailed Solution
Step 1 (Scalar Multiplication):
[[2x, 10], [14, 2y-6]] + [[3, -4], [1, 2]] = [[2x+3, 6], [15, 2y-4]].
Step 2 (Equate Entries):
2x + 3 = 7 ⟹ 2x = 4 ⟹ x = 2
2y - 4 = 14 ⟹ 2y = 18 ⟹ y = 9.
✔ Final Answer: x = 2, y = 9
Q4CBSE Board 2023 • 4 Marks4 Marks
If A = [[1, 2, 2], [2, 1, 2], [2, 2, 1]], prove that A² - 4A - 5I = O.
▶ Show Detailed Solution
Step 1 (Compute A²):
A² = [[9, 8, 8], [8, 9, 8], [8, 8, 9]].
Step 2 (Compute 4A + 5I):
4A + 5I = [[9, 8, 8], [8, 9, 8], [8, 8, 9]].
A² - 4A - 5I = O. ✓
✔ Hence Proved.
Q5NCERT Ex 3.3 Q10 • 4 Marks4 Marks
Express matrix A = [[3, 5], [1, -1]] as the sum of a symmetric and a skew-symmetric matrix.
▶ Show Detailed Solution
Step 1 (Symmetric Matrix P):
A' = [[3, 1], [5, -1]].
P = (1/2)(A + A') = [[3, 3], [3, -1]].
Step 2 (Skew-Symmetric Matrix Q):
Q = (1/2)(A - A') = [[0, 2], [-2, 0]].
Verify A = P + Q. ✓
✔ Final Answer: P = [[3, 3], [3, -1]], Q = [[0, 2], [-2, 0]]
📅 Year 2023 Board Examination Paper
Q1CBSE Board 2024 • 3 Marks3 Marks
Find the inverse of matrix A = [[2, 1], [7, 4]] using adjoint method.
▶ Show Detailed Solution
Step 1 (Determinant):
|A| = (2)(4) - (1)(7) = 8 - 7 = 1 ≠ 0.
Step 2 (Adjoint Matrix):
adj(A) = [[4, -1], [-7, 2]].
A⁻¹ = adj(A)/|A| = [[4, -1], [-7, 2]].
✔ Final Answer: A⁻¹ = [[4, -1], [-7, 2]]
Q2CBSE Board 2022 • 4 Marks4 Marks
Solve for x: [1, 2, 1] [[1, 2, 0], [2, 0, 1], [1, 0, 2]] [[0], [2], [x]] = O.
▶ Show Detailed Solution
Step 1 (First Multiplication):
[1, 2, 1] [[1, 2, 0], [2, 0, 1], [1, 0, 2]] = [6, 2, 4].
Step 2 (Second Multiplication):
[6, 2, 4] [[0], [2], [x]] = 4 + 4x = 0 ⟹ 4x = -4 ⟹ x = -1.
✔ Final Answer: x = -1
Q3NCERT Ex 3.1 Q4 (Variant #8) • 2 Marks2 Marks
Construct a 2x2 matrix A = [a_ij] whose elements are given by a_ij = (i + 2j)² / 2.
▶ Show Detailed Solution
Step 1 (Calculate Elements):
a_11 = (1 + 2)²/2 = 9/2
a_12 = (1 + 4)²/2 = 25/2
a_21 = (2 + 2)²/2 = 8
a_22 = (2 + 4)²/2 = 18.
Step 2 (Form Matrix):
A = [[9/2, 25/2], [8, 18]].
✔ Final Answer: A = [[9/2, 25/2], [8, 18]]
Q4CBSE Board 2024 (Variant #9) • 2 Marks2 Marks
If A = [[1, 2], [3, 4]] and B = [[-1, 3], [2, 1]], find matrix C such that 3A - 2B + C = O.
▶ Show Detailed Solution
Step 1 (Compute 3A and 2B):
3A = [[3, 6], [9, 12]]
2B = [[-2, 6], [4, 2]]
3A - 2B = [[5, 0], [5, 10]].
Step 2 (Solve for C):
C = -(3A - 2B) = [[-5, 0], [-5, -10]].
✔ Final Answer: C = [[-5, 0], [-5, -10]]
Q5NCERT Ex 3.2 Q9 (Variant #10) • 3 Marks3 Marks
Find the values of x and y from the matrix equation: 2[[x, 5], [7, y-3]] + [[3, -4], [1, 2]] = [[7, 6], [15, 14]].
▶ Show Detailed Solution
Step 1 (Scalar Multiplication):
[[2x, 10], [14, 2y-6]] + [[3, -4], [1, 2]] = [[2x+3, 6], [15, 2y-4]].
Step 2 (Equate Entries):
2x + 3 = 7 ⟹ 2x = 4 ⟹ x = 2
2y - 4 = 14 ⟹ 2y = 18 ⟹ y = 9.
✔ Final Answer: x = 2, y = 9