AKUEB Prep - Question Bank & Past Papers

Class 11 - Mathematics / Unit 9 - Trigonometric Functions and their Graphs / 9.1 Trigonometric Functions / 9.1.5

Past Paper 2024HARD

Q1

The function $2 - 3\sin(\theta + 40°)$ has the minimum value when $\theta$ is equal to

90°

60°

50°

30°

Class 11 - Mathematics / Unit 10 - Inverse Trigonometric Functions and Trigonometric Equations / 10.3 Trigonometric Equations / 10.3.2

Past Paper 2024HARD

Q2

The solution set of $3\cot x = \sqrt{3}$ in the interval of $[0, 2\pi]$ will be

\left\{\dfrac{\pi}{3}, \dfrac{4\pi}{3}\right\}

\left\{\dfrac{\pi}{3}, \dfrac{7\pi}{6}\right\}

\left\{\dfrac{\pi}{3}+n\pi\right\} \cup \left\{\dfrac{4\pi}{3}+n\pi\right\}

\left\{\dfrac{\pi}{3}+n\pi\right\} \cup \left\{\dfrac{7\pi}{6}+n\pi\right\}

Class 11 - Mathematics / Unit 9 - Trigonometric Functions and their Graphs / 9.1 Trigonometric Functions / 9.1.4

Past Paper 2024MEDIUM

Q3

If the period of $f(x) = \sin(ax)$ is $\dfrac{\pi}{2}$ , then the value of $a$ is

\dfrac{1}{4}

\dfrac{1}{2}

2

4

Class 11 - Mathematics / Unit 9 - Trigonometric Functions and their Graphs / 9.1 Trigonometric Functions / 9.1.2

Past Paper 2024EASY

Q4

The range of $\cosec x$ is

[-1,1]

(-1,1)

\mathbb{R} - [-1,1]

\mathbb{R} - (-1,1)

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.4 Sum/Difference and Product of Sine and Cosine / 8.4.1

Past Paper 2024EASY

Q5

$2\sin 4x \cos 3x$ is equal to

\sin 7x - \sin x

\sin 7x + \sin x

\sin x - \sin 7x

-\sin x - \sin 7x

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.2 Trigonometric Ratios of Allied Angles / 8.2.3

Past Paper 2024MEDIUM

Q6

If $3\sin x + 4\cos x = r\sin(x+y)$ , then $r$ will be

3

4

5

7

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.2 Trigonometric Ratios of Allied Angles / 8.2.2

Past Paper 2024EASY

Q7

Which of the following trigonometric ratios has a positive sign?

\sin 210°

\cos 350°

\tan 310°

\cosec 240°

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.1 Fundamental Law of Trigonometry / 8.1.2

Past Paper 2024MEDIUM

Q8

If the distance between $(2, 0)$ and $(0, \sqrt{a})$ is $c$ , then the expression for $a$ will be

c^2+4

-c^2-4

c^2-4

-c^2+4

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.1 Fundamental Law of Trigonometry / 8.1.4

Past Paper 2024HARD

Q9

$\sin\theta$ can be represented as

\dfrac{\sqrt{\sec^2\theta - 1}}{\sec\theta}

\dfrac{\sec\theta}{\sqrt{\sec^2\theta - 1}}

\dfrac{\cosec\theta}{\sqrt{\cosec^2\theta - 1}}

\dfrac{\sqrt{\cosec^2\theta - 1}}{\cosec\theta}

Class 11 - Mathematics / Unit 9 - Trigonometric Functions and their Graphs / 9.1 Trigonometric Functions / 9.1.1

Past Paper 2024EASY

Q10

$3\pi$ radians can be expressed in degrees as

0.16°

9.42°

180°

540°

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.2 Binomial Theorem / 6.2.5

Past Paper 2024MEDIUM

Q11

The coefficient of the 3rd term of the expression $(1-2x)^6$ will be

-60

60

-160

160

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.3 Binomial Series / 6.3.2

Past Paper 2024HARD

Q12

Which of the following conditions is valid for the convergence of $(2+5x)^{-2}$ ?

|x| < \dfrac{2}{5}

|x| > \dfrac{2}{5}

|x| < \dfrac{5}{2}

|x| > \dfrac{5}{2}

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.1 Mathematical Induction / 6.1.3

Past Paper 2024HARD

Q13

If the statement $x^{2k} - y^{2k}$ is true for $(k+1)$ terms, then it must be divisible by
I. $x+y$
II. $x-y$
III. $x^2+y^2$

I onlyIII onlyI and IIII and III

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.2 Binomial Theorem / 6.2.3

Past Paper 2024MEDIUM

Q14

The general term of the binomial expansion of $(3x+7y)^{10}$ is

\dbinom{10}{r}(3x)^{r-10}(7y)^{r}

\dbinom{10}{r}(3x)^{r}(7y)^{r-10}

\dbinom{10}{r}(3x)^{r}(7y)^{10-r}

\dbinom{10}{r}(3x)^{10-r}(7y)^{r}