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Federal (FBISE) · Quarter book test · Free

1st Year Mathematics 3rd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: 7. Mathematical Induction and Binomial Theorem, 8. Fundamentals of Trigonometry, 9. Trigonometric Functions.

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1st Year Mathematics 3rd Quarter Book Paper

1st Year · 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 f(x) f(x) is a periodic function and its period is π\pi , then f(x) f(x) could be :
    1. sin⁡2x \sin 2x
    2. tan⁡2x \tan 2x
    3. cos⁡2x \cos 2x
    4. All
  2. If cos⁡θ=−310 \cos \theta = -\frac{3}{\sqrt{10}} and 90∘<θ<180∘ 90^\circ < \theta < 180^\circ than tan⁡2θ= \tan 2\theta =
    1. 34\frac{3}{4}
    2. ±34\pm\frac{3}{4}
    3. −43\frac{-4}{3}
    4. −34\frac{-3}{4}
  3. If n is even positive integer then the middle term in the expansion of (a + b)ⁿ is.
    1. (n2)thterm\left( \frac{n}{2} \right)^{\text{th}} \text{term}
    2. (n+12)thterm\left( \frac{n + 1}{2} \right)^{\text{th}} \text{term}
    3. (n−12)thterm\left( \frac{n - 1}{2} \right)^{\text{th}} \text{term}
    4. (n2+1)thterm\left( \frac{n}{2} + 1 \right)^{\text{th}} \text{term}
  4. If x, - x belongs to domain of f(x) f(x) ,then functionf(x) f(x) is said to be an even function if :
    1. f(−x) f(-x) =f(x) f(x)
    2. f(−x) f(-x) =-f(x) f(x)
    3. f(−x) f(-x) \neqf(x) f(x)
    4. f(−x) f(-x)
  5. The exact value of sin⁡7.5∘cos⁡7.5∘cos⁡15∘ \sin 7.5^\circ \cos 7.5^\circ \cos 15^\circ is ?
    1. 14\frac{1}{4}
    2. 12\frac{1}{2}
    3. 18\frac{1}{8}
    4. 116\frac{1}{16}
  6. (110)+(112)+(114)+⋯+(1110) \left( \begin{array}{c} 11 \\ 0 \end{array} \right) + \left( \begin{array}{c} 11 \\ 2 \end{array} \right) + \left( \begin{array}{c} 11 \\ 4 \end{array} \right) + \cdots + \left( \begin{array}{c} 11 \\ 10 \end{array} \right) is equal to
    1. 2¹¹
    2. 2¹²
    3. 2¹⁰
    4. 2¹¹- 1
  7. The graph of which of the trigonometric function does not crosses the x - axis?
    1. sin⁡x{\sin x}
    2. cos⁡x{\cos x}
    3. tanx{tanx}
    4. secx{secx}
  8. sin⁡(π2−θ)sin⁡(π2+θ)=\sin\left(\frac{\pi}{2} - \theta\right) \sin\left(\frac{\pi}{2} + \theta\right) =
    1. 1+cos⁡2θ1 +\cos 2\theta
    2. sin⁡2θ\sin 2\theta
    3. 1+cos⁡2θ2\frac{1 +\cos 2\theta}{2}
    4. 12sin⁡2θ\frac{1}{ 2}\sin2\theta
  9. Middle term (s) in the expansion of (2x2−15x)11 \left( 2x^2 - \frac{1}{5x} \right)^{11} is :
    1. T₅ , T₆
    2. T₄ , T₅
    3. T₆ , T₇
    4. T₇ , T₈
  10. Which of the two trigonometric functions have the domain x=R−{(2n+1)π2},n∈Z? x = R - \left\{ (2n + 1) \frac{\pi}{2} \right\}, n \in \mathbb{Z} ?
    1. sin⁡θ\sin\theta and cos⁡θ\cos\theta
    2. tan⁡θ\tan\theta and sec⁡θ\sec\theta
    3. cot⁡θ\cot\theta and cosecθcosec\theta
    4. tan⁡θ\tan\theta and cosecθcosec\theta
  11. If sin⁡A=15 \sin A = \frac{1}{5} and sin⁡B=13 \sin B = \frac{1}{3} and 0<A,B<π2 0 < A, B < \frac{\pi}{2} , then cos⁡(A+B)= \cos(A + B) =
    1. 83−115\frac{8\sqrt{3} - 1}{15}
    2. −83+115-\frac{8\sqrt{3} + 1}{15}
    3. 83+115\frac{8\sqrt{3} + 1}{15}
    4. −83+115\frac{-8\sqrt{3} + 1}{15}
  12. In the binomial expansion of ( a + x ) ⁿ the exponent of x _________ from zero to index .
    1. Remain Same
    2. Increases
    3. Decrease
    4. Varies

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

  1. Use the product-to-sum formula to change the sum or difference. sin (- u) sin 5u
  2. Find the last one or two digit of the number where applicable. 29¹⁰
  3. Check whether the function is odd or even? y = 3 Sin x + 4 Cos x
  4. Verify:sin⁡(π2−α)=cos⁡α\sin\left(\frac{\pi}{2} - \alpha\right) = \cos\alpha
  5. Which of the following is a larger number? 98⁵⁰ + 100⁵⁰ or 102⁵⁰
  6. Find the maximum and minimum values of the following trigonometric function.y=11+3 Sin(2θ−15) y = \frac{1}{1 + 3 \, \text{Sin}(2\theta - 15)}
  7. Rewrite as a single expression.tan⁡75∘−tan⁡45∘1+tan⁡75∘tan⁡45∘\frac{\tan 75^\circ - \tan 45^\circ}{1 + \tan 75^\circ \tan 45^\circ}
  8. Expand the followings by using binomial theorem. (-x + y⁻¹)⁶
  9. Find the maximum and minimum value of the reciprocal trigonometric function.y=112−5cos⁡θ y = \frac{1}{\frac{1}{2} - 5 \cos \theta}
  10. Verify the following identity. 8 sin⁴ θ = 3 + cos 4θ - 4 cos 2θ
  11. Approximate the value upto four place of decimal.1. (1.03)13 (1.03)^{\frac{1}{3}}
  12. Check whether the function is odd or even?y=tan⁡x−sin⁡xsin⁡3x y = \frac{\tan x - \sin x}{\sin^3 x}

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

  1. Find the domain, range, and period of the trigonometric function. 5 sin 3x
  2. Verify the following identity.1−tan⁡2x21+tan⁡2x2=cos⁡x\frac{1 - \tan^2 \frac{x}{2}}{1 + \tan^2 \frac{x}{2}} = \cos x
  3. Find the middle term in the expansion of the following. .(a−3x2)12(a - \frac{3}{x^2})^{12}
  4. Find the domain, range, and period of the trigonometric function.11−sin⁡x\frac{1}{1 - \sin x}