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Federal (FBISE) · Quarter book test · Free

10th Class Mathematics 1st Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: 01. Complex Numbers, 02. Quadratic Equations, 03. Matrices and Determinants.

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10th Class Mathematics 1st Quarter Book Paper

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. If A and B are two matrices, conformable for the product AB then (AB)t=(AB)^t =
    1. AtBtA^tB^t
    2. (BA)t(BA)^t
    3. BtAtB^tA^t
    4. AB
  2. Which of the following is a quadratic equation?
    1. ax + b = c
    2. ax² + bx + c
    3. ax² + bx + c = 0
    4. ax² + bx + c = 0, a = 0
  3. 21−i\frac{2}{1 - i} =?
    1. 1+i2\frac{1 + i}{2}
    2. (1+i)22\frac{(1+i)^2}{2}
    3. 1−i1 - i
    4. 1+i1 + i
  4. Matrix equation for y + x = 144 + y and x + 2y = x + 13 is
    1. [1112]×[xy]=[14413]\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
    2. [1012]×[xy]=[14413]\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
    3. d) [1012]×[xy]=[1413]\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 14 \\ 13 \end{bmatrix}
    4. [1002]×[yx]=[14413]\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} \times \begin{bmatrix} y \\ x \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
  5. Which of the following is a reciprocal equation?
    1. x2+2x+2=0x^2 + 2x + 2 = 0
    2. x4+x3+x2+x+1=0x^4 + x^3 + x^2 + x + 1 = 0
    3. 2x+3\sqrt{2x + 3}
    4. x4+2x3+x2+4x=0x^4 + 2x^3 + x^2 + 4x = 0
  6. 1+(i)91 + (i)^9 = ?
    1. 1+i1 + i
    2. 1+−11 +\sqrt{-1}
    3. 1−i1 - i
    4. −i-i
  7. Multiplicative inverse of a null matrix of order 2, is
    1. [0000] \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}
    2. [00] \begin{bmatrix} 0 & 0 \end{bmatrix}
    3. [00] \begin{bmatrix} 0 \\ 0 \end{bmatrix}
    4. Impossible
  8. Roots of the equation (x – 1)² – 9 are:
    1. –2, 4
    2. 2, 4
    3. –4, 2
    4. –2, –4
  9. (−xi)19(-xi)19 = ?
    1. −x19i-x^{19}i
    2. x19ix^{19}i
    3. −i19-i^{19}
    4. −x19-x^{19}
  10. If I3=[y0x0z0x01] I_3 = \begin{bmatrix} y & 0 & x \\ 0 & z & 0 \\ x & 0 & 1 \end{bmatrix} then
    1. y = x = 1
    2. x = z = 0
    3. x = z = 1
    4. y = z = 1 , x = 0
  11. 2 and –3 are roots of
    1. (x – 2)(x – 3) = 0
    2. (x + 2)(x + 3) = 0
    3. (x – 2)(x + 3) = 0
    4. (x + 2)(x – 3) = 0
  12. Conjugate of x−iy\sqrt{x} - i\sqrt{y} is:
    1. x+iy\sqrt{x} + i\sqrt{y}
    2. x - y
    3. x - y
    4. x + y

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Find all roots of 8x³− 7x³− 1 = 0
  2. Verify A(B + C) = AB + AC A=[52],B=[64] and C=[12]. A = \begin{bmatrix} 5 & 2 \end{bmatrix}, B = \begin{bmatrix} 6 \\ 4 \end{bmatrix} \text{ and } C = \begin{bmatrix} 1 \\ 2 \end{bmatrix}.
  3. Find z .zˉ:z=14−7i\bar{z} : {z} = 14 - 7i
  4. If S1,S2S_1 , S_2​ are the roots of 3x²− 2x + 4 = 0, find the value of S1S2+S2S1\frac{S_1}{S_2 } + \frac{S_2}{S_1 }
  5. If P=[5329] and Q=[7239]. P = \begin{bmatrix} 5 & 3 \\ 2 & 9 \end{bmatrix} \text{ and } Q = \begin{bmatrix} 7 & 2 \\ 3 & 9 \end{bmatrix}. , then verify the commutative property of matrix addition.
  6. Simplify:i9 i⁹
  7. Find the sum and product of the roots of the quadratic equation x²− 5x + 2 = 0
  8. If C=[2060],D=[26],E=[2266] C = \begin{bmatrix} 2 & 0 \\ 6 & 0 \end{bmatrix}, D = \begin{bmatrix} 2 \\ 6 \end{bmatrix}, E = \begin{bmatrix} 2 & 2 \\ 6 & 6 \end{bmatrix} . Then check whether C + D = E
  9. Express number in term of i.−−64 -\sqrt{-64}
  10. Write the quadratic equation in standard form. ax² + bx = c
  11. Write the most appropriate type of the matric. [15×39×5]\left[ \frac{15 \times 3}{9 \times 5} \right]
  12. Find the conjugate : 11i

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. The daily sum of labour and the material costs of Haani's and Massab's Home Industries are Rs. 20,000 and Rs. 40,000 respectively. If labour and the material rate, for both the Home Industries is same but Hanni's Home Industry has 6 workers who make 80 items and Massab's Home Industry has 12 workers who make 160 items, find the labour and the material cost.
  2. The difference of a positive number and its square is 380. Find the number.
  3. Represent z₁÷ z₂ graphically when z₁= -4 − 6i and z₂= 1 + i
  4. If A=[1023],B=[210−3], A = \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 1 \\ 0 & -3 \end{bmatrix}, then Verify that (AB)t=BtAtandA(AB)^t = B^tA^t and A