:رایض APEX STUDY CIRCLE:
PREPARED WITH PRECISION TO REFLECT THE EXAMINER’S MINDSET
Target Paper Class (XI) (MATHEMATICS) 2026
Section “B” (Short Q/Ans)
1. Find real and imaginary parts of each of the following by using any method:
1 −1 3+4𝑖 −1
*( ) *( ) ∗ (2𝑖 − √3)−1
4𝑖−5 5𝑖−4
2. Write the following polynomials as the product of linear factors:
∗ 𝑧³ − 7𝑧² + 19𝑧 – 13 ∗ 𝑧 3 + 3𝑧 2 + 19𝑧 + 17 *𝑧 3 + 3𝑧 2 + 𝑧 − 5
3. Solve the following quadratic equations by completing the squares, where z is a complex number.
∗ 𝑧 2 + 64 = 0 ∗ 34𝑧 2 − 6𝑧 = −1 *𝑧² − 6𝑧 + 34 = 0
4. Find the period of the following periodic matrix.
1 −2 −6
*[−3 2 9]
2 0 −3
5. Find the index of the following nilpotent matrices.
0 1 0 1 −3 −4
*[0 0 1] *[−1 3 4]
0 0 0 1 −3 −4
6. Find real numbers 𝑥, 𝑦, 𝑧 such that matrix A is Hermitian matrix.
3 𝑥 + 2𝑖 𝑦𝑖
𝐴=[ 3 − 2𝑖 0 1 + 𝑧𝑖 ]
𝑦𝑖 1 − 𝑥𝑖 −1
7. Without expanding determinants, prove that:|
1+𝑎 1 1
1 1 1
*| 1 1+𝑏 1 | = 𝑎𝑏𝑐 (1 + 𝑎 + 𝑏 + 𝑐 ) = 𝑎𝑏𝑐 + 𝑏𝑐 + 𝑐𝑎 + 𝑎𝑏
1 1 1+𝐶
𝛼 𝛽𝛾 𝛼𝛽𝛾 𝛼 𝛼2 𝛼3
*|𝛽 𝛼𝛾 𝛼𝛽𝛾| = |𝛽 𝛽 2 𝛽 3 |
𝛾 𝛼𝛽 𝛼𝛽𝛾 𝛾 𝛾2 𝛾3
8. 𝑃𝑟𝑜𝑣𝑒 𝐻𝑒𝑥𝑎𝑔𝑜𝑛 𝑙𝑎𝑤 𝑜𝑓 𝑣𝑒𝑐𝑡𝑜𝑟 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛.
9. 𝐼𝑓 𝑎, ẞ, 𝑦 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒𝑠 𝑜𝑓 𝑎 𝑣𝑒𝑐𝑡𝑜𝑟 𝑡ℎ𝑒𝑛 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡; 𝒔𝒊𝒏²𝒂 + 𝒔𝒊𝒏²𝑩 + 𝒔𝒊𝒏²𝒚 = 𝟐
10. Find the work done by the force 𝐹 = 7𝑖 + 9ĵ − 11𝑘 in moving an object along a straight line from (4,2,7) 𝑡𝑜 (6,4,9)
11. Calculate the work done by a Force 𝐹 = 3𝑖 + 4𝑗 + 5𝑘 in displacing a body from position B to position A along a straight path.
The position vectors of A and B are respectively given as 𝑟_𝑎 = 2𝑖 + 5𝑗 − 2𝑘 𝑎𝑛𝑑 𝑟_𝑏 = 7𝑖 + 3𝑗 − 5𝑘.
12. Find a unit vector which is orthogonal to both the vectors. . 𝑎 = 𝑖 − 2𝑗 + 3𝑘 𝑎𝑛𝑑 𝑏 = 3𝑖 − 2𝑗 + 𝑘
13. Find the moment about a point A(1,3,5) of the 𝑓𝑜𝑟𝑐𝑒 𝐹 = 𝑖 + 2𝑗 − 𝑘 , 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑎𝑡 𝐵 (3, −2,5).
Prepared By: MOHTASHAM Acc. To New Syllabus
PREPARED WITH PRECISION TO REFLECT THE EXAMINER’S MINDSET
Target Paper Class (XI) (MATHEMATICS) 2026
Section “B” (Short Q/Ans)
1. Find real and imaginary parts of each of the following by using any method:
1 −1 3+4𝑖 −1
*( ) *( ) ∗ (2𝑖 − √3)−1
4𝑖−5 5𝑖−4
2. Write the following polynomials as the product of linear factors:
∗ 𝑧³ − 7𝑧² + 19𝑧 – 13 ∗ 𝑧 3 + 3𝑧 2 + 19𝑧 + 17 *𝑧 3 + 3𝑧 2 + 𝑧 − 5
3. Solve the following quadratic equations by completing the squares, where z is a complex number.
∗ 𝑧 2 + 64 = 0 ∗ 34𝑧 2 − 6𝑧 = −1 *𝑧² − 6𝑧 + 34 = 0
4. Find the period of the following periodic matrix.
1 −2 −6
*[−3 2 9]
2 0 −3
5. Find the index of the following nilpotent matrices.
0 1 0 1 −3 −4
*[0 0 1] *[−1 3 4]
0 0 0 1 −3 −4
6. Find real numbers 𝑥, 𝑦, 𝑧 such that matrix A is Hermitian matrix.
3 𝑥 + 2𝑖 𝑦𝑖
𝐴=[ 3 − 2𝑖 0 1 + 𝑧𝑖 ]
𝑦𝑖 1 − 𝑥𝑖 −1
7. Without expanding determinants, prove that:|
1+𝑎 1 1
1 1 1
*| 1 1+𝑏 1 | = 𝑎𝑏𝑐 (1 + 𝑎 + 𝑏 + 𝑐 ) = 𝑎𝑏𝑐 + 𝑏𝑐 + 𝑐𝑎 + 𝑎𝑏
1 1 1+𝐶
𝛼 𝛽𝛾 𝛼𝛽𝛾 𝛼 𝛼2 𝛼3
*|𝛽 𝛼𝛾 𝛼𝛽𝛾| = |𝛽 𝛽 2 𝛽 3 |
𝛾 𝛼𝛽 𝛼𝛽𝛾 𝛾 𝛾2 𝛾3
8. 𝑃𝑟𝑜𝑣𝑒 𝐻𝑒𝑥𝑎𝑔𝑜𝑛 𝑙𝑎𝑤 𝑜𝑓 𝑣𝑒𝑐𝑡𝑜𝑟 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛.
9. 𝐼𝑓 𝑎, ẞ, 𝑦 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒𝑠 𝑜𝑓 𝑎 𝑣𝑒𝑐𝑡𝑜𝑟 𝑡ℎ𝑒𝑛 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡; 𝒔𝒊𝒏²𝒂 + 𝒔𝒊𝒏²𝑩 + 𝒔𝒊𝒏²𝒚 = 𝟐
10. Find the work done by the force 𝐹 = 7𝑖 + 9ĵ − 11𝑘 in moving an object along a straight line from (4,2,7) 𝑡𝑜 (6,4,9)
11. Calculate the work done by a Force 𝐹 = 3𝑖 + 4𝑗 + 5𝑘 in displacing a body from position B to position A along a straight path.
The position vectors of A and B are respectively given as 𝑟_𝑎 = 2𝑖 + 5𝑗 − 2𝑘 𝑎𝑛𝑑 𝑟_𝑏 = 7𝑖 + 3𝑗 − 5𝑘.
12. Find a unit vector which is orthogonal to both the vectors. . 𝑎 = 𝑖 − 2𝑗 + 3𝑘 𝑎𝑛𝑑 𝑏 = 3𝑖 − 2𝑗 + 𝑘
13. Find the moment about a point A(1,3,5) of the 𝑓𝑜𝑟𝑐𝑒 𝐹 = 𝑖 + 2𝑗 − 𝑘 , 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑎𝑡 𝐵 (3, −2,5).
Prepared By: MOHTASHAM Acc. To New Syllabus
