Explore topic-wise MCQs in Mathematics Questions and Answers.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the angle between the pair of lines \(\frac{x-3}{5}=\frac{y+7}{3}=\frac{z-2}{2} \,and \,\frac{x+1}{3}=\frac{y-5}{4}=\frac{z+2}{8}\).

A. \(cos^{-1}⁡\frac{43}{\sqrt{3482}}\)
B. \(cos^{-1}⁡⁡\frac{43}{\sqrt{3382}}\)
C. \(cos^{-1}⁡⁡\frac{85}{\sqrt{3382}}\)
D. \(cos^{-1}⁡⁡\frac{34}{\sqrt{3382}}\)
Answer» C. \(cos^{-1}⁡⁡\frac{85}{\sqrt{3382}}\)
Discussion
2.

If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then what is the angle between the two lines?

A. cot⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)
B. sin⁡θ=\(\left |l_1 \,l_2+m_1 \,n_2+n_1 \,m_2\right |\)
C. tan⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)
D. cos⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)
Answer» E.
Discussion
3.

Find the angle between the lines \(\vec{r}=2\hat{i}+6\hat{j}-\hat{k}+λ(\hat{i}-2\hat{j}+3\hat{k})\) and \(\vec{r}=4\hat{i}-7\hat{j}+3\hat{k}+μ(5\hat{i}-3\hat{j}+3\hat{k})\).

A. θ=\(cos^{-1}\frac{⁡20}{\sqrt{602}}\)
B. θ=\(cos^{-1}\frac{⁡20}{\sqrt{682}}\)
C. θ=\(cos^{-1}\frac{⁡8}{\sqrt{602}}\)
D. θ=\(cos^{-1}⁡\frac{14}{\sqrt{598}}\)
Answer» B. θ=\(cos^{-1}\frac{⁡20}{\sqrt{682}}\)
Discussion
4.

If the equations of two lines L1 and L2 are \(\vec{r}=\vec{a_1}+λ\vec{b_1}\) and \(\vec{r}=\vec{a_2}+μ\vec{b_2}\), then which of the following is the correct formula for the angle between the two lines?

A. cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{b_1}||\vec{a_2}|}\right |\)
B. cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{a_1}||\vec{a_2}|}\right |\)
C. cos⁡θ=\(\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |\)
D. cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |\)
Answer» D. cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |\)
Discussion
5.

Find the value of p such that the lines \(\frac{x+11}{4}=\frac{y+3}{-2}=\frac{z-3}{4} \,and \,\frac{x-3}{p}=\frac{y+12}{2}=\frac{z-3}{-12}\) are at right angles to each other.

A. p=11
B. p=12
C. p=13
D. p=4
Answer» D. p=4
Discussion
6.

If two lines L1 and L2 with direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively are perpendicular to each other then

A. \(a_1 a_2+b_1 b_2+c_1 c_2=0\)
B. True
C. False
Answer» B. True
Discussion
7.

Find the angle between the two lines if the equations of the lines are

A. \(\vec{r}=\hat{i}+\hat{j}+\hat{k}+λ(3\hat{i}-\hat{j}+\hat{k}) \,and \,\vec{r}=4\hat{i}+\hat{j}-2\hat{k}+μ(2\hat{i}+3\hat{j}+\hat{k})\)
B. \(cos^{-1}\frac{⁡4}{\sqrt{14}}\)
C. \(cos^{-1}⁡\frac{7}{\sqrt{154}}\)
D. \(cos^{-1}⁡\frac{4}{154}\)
E. \(cos^{-1}⁡\frac{4}{\sqrt{154}}\)
Answer» E. \(cos^{-1}⁡\frac{4}{\sqrt{154}}\)
Discussion
8.

If L1 and L2 have the direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively then what is the angle between the lines?

A. \(θ=tan^{-1}⁡\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\)
B. \(θ=2tan^{-1}⁡\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\)
C. \(θ=cos^{-1}⁡\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\)
D. \(θ=2 \,cos^{-1}⁡\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\)
Answer» D. \(θ=2 \,cos^{-1}⁡\left|\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\right |\)
Discussion