Question 1: Palette 1/11

AP-EAPCET 2025 MCQ

Three vectors each of magnitude $3 \sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$, then the magnitude of the resultant vector of the three vector is

A

$9 \sqrt{3}$ units

B

9 units

C

$\sqrt{6}$ units

D

3 units

Question 2: Palette 2/11

AP-EAPCET 2025 MCQ

A vector perpendicular to the vector $(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}})$ is

A

$4 \hat{i}+3 \hat{j}$

B

$6 \hat{i}$

C

$3 \hat{i}-4 \hat{j}$

D

$7 \hat{\mathbf{k}}$

Question 3: Palette 3/11

AP-EAPCET 2025 MCQ

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively, then $\sin ^2 \alpha+\sin ^2 \beta=$

A

$\sin ^2 \gamma$

B

$\cos ^2 \gamma$

C

$1+\cos ^2 \gamma$

D

$1+\sin ^2 \gamma$

Question 4: Palette 4/11

AP-EAPCET 2025 MCQ

If the magnitude of a vector $\mathbf{P}$ is 25 units and its $y$-component is 7 units, then its $x$-component is

A

24 units

B

18 units

C

32 units

D

16 units

Question 5: Palette 5/11

AP-EAPCET 2025 MCQ

The magnitudes of two vectors are $A$ and $B(A>B)$. If the maximum resultant magnitude of the two vectors is ' $n$ ' times their minimum resultant magnitude, then $\frac{A}{B}=$

A

$\frac{n}{n-1}$

B

$\frac{n+1}{n}$

C

$\frac{n^2+1}{n-1}$

D

$\frac{n+1}{n-1}$

Question 6: Palette 6/11

AP-EAPCET 2024 MCQ

The angle made by the resultant vector of two vectors $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ with $X$-axis.

A

$60^{\circ}$

B

$45^{\circ}$

C

$90^{\circ}$

D

$120^{\circ}$

Question 7: Palette 7/11

AP-EAPCET 2024 MCQ

If $|\mathbf{P}+\mathbf{Q}|=|\mathbf{P}|=|\mathbf{Q}|$ then the angle between $\mathbf{P}$ and $\mathbf{Q}$ is

A

$0^{\circ}$

B

$120^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 8: Palette 8/11

AP-EAPCET 2022 MCQ

The component of a vector $\mathbf{P}=3 \hat{i}+4 \hat{j}$ along the direction $(\hat{i}+2 \hat{j})$ is

A

$\frac{8}{\sqrt{5}}$

B

$\frac{11}{\sqrt{5}}$

C

$\frac{11}{2}$

D

$\sqrt{10}$

Question 9: Palette 9/11

AP-EAPCET 2022 MCQ

If two vectors $\mathbf{A}$ and $\mathbf{B}$ are mutually perpendicular, then the component of $\mathbf{A}-\mathbf{B}$ along the direction of $\mathbf{A}+\mathbf{B}$ is

A

$\sqrt{|A|^2+|B|^2}$

B

$\sqrt{|A|^2-|B|^2}$

C

$\frac{|A|^2-|B|^2}{\sqrt{|A|^2+|B|^2}}$

D

$\frac{|A|^2+|B|^2}{\sqrt{|A|^2-|B|^2}}$

Question 10: Palette 10/11

AP-EAPCET 2022 MCQ

Which of the following is not true about vectors $\mathbf{A}, \mathbf{B}$ and $\mathbf{C}$ ?

A

$(\mathbf{A} \cdot \mathbf{A})(\mathbf{B} \cdot \mathbf{C})$ is a scalar value.

B

$(\mathbf{A} \times \mathbf{B}),(\mathbf{B} \times \mathbf{C})$ is a scalar value.

C

$(\mathbf{A} \times \mathbf{C}) \times(\mathbf{B} \times \mathbf{C})$ is a scalar value.

D

$\mathbf{A} \times(\mathbf{B} \times \mathbf{C})$ is a vector value.

Question 11: Palette 11/11

AP-EAPCET 2021 MCQ

One of the rectangular components of a force of 40 N is 20$\sqrt3$ N. What is the other rectangular component?

A

10 N

B

20 N

C

30 N

D

25 N