Board Paper of Class 12Commerce 2015 Maths (SET 3)  Solutions
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Marks for each question are indicated against it.
(iv) Questions 1 to 6 in SectionA are Very Short Answer Type Questions carrying one mark each.
(v) Questions 7 to 19 in SectionB are Long Answer I Type Questions carrying 4 marks each.
(vi) Questions 20 to 26 in SectionC are Long Answer II Type Questions carrying 6 marks each.
(vii) Please write down the serial number of the Question before attempting it.
* Kindly update your browser if you are unable to view the equations.
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Marks for each question are indicated against it.
(iv) Questions 1 to 6 in SectionA are Very Short Answer Type Questions carrying one mark each.
(v) Questions 7 to 19 in SectionB are Long Answer I Type Questions carrying 4 marks each.
(vi) Questions 20 to 26 in SectionC are Long Answer II Type Questions carrying 6 marks each.
(vii) Please write down the serial number of the Question before attempting it.
* Kindly update your browser if you are unable to view the equations.
 Question 1
Find the differential equation representing the family of curves $\mathrm{v}=\frac{\mathrm{A}}{\mathrm{r}}$+ B, where A and B are arbitrary constants. VIEW SOLUTION
 Question 2
Find the integrating factor of the differential equation
$\left(\frac{{{e}^{2}}^{\sqrt{x}}}{\sqrt{x}}\frac{y}{\sqrt{x}}\right)\frac{dx}{dy}=1$. VIEW SOLUTION
 Question 3
If $\overrightarrow{\mathrm{a}}=7\hat{\mathrm{i}}+\hat{\mathrm{j}}4\hat{\mathrm{k}}\mathrm{and}\overrightarrow{\mathrm{b}}=2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+3\hat{\mathrm{k}},$then find the projection of $\overrightarrow{\mathrm{a}}\mathrm{on}\overrightarrow{\mathrm{b}}$. VIEW SOLUTION
 Question 4
Find λ, if the vectors $\overrightarrow{a}=\hat{i}+3\hat{j}+\hat{k},\overrightarrow{b}=2\hat{i}\hat{j}\hat{k}\mathrm{and}\overrightarrow{c}=\lambda \hat{j}+3\hat{k}$ are coplanar. VIEW SOLUTION
 Question 5
If a line makes angles 90°, 60° and θ with x, y and zaxis respectively, where θ is acute, then find θ. VIEW SOLUTION
 Question 6
Write the element a_{23}_{ }of a 3 ✕ 3 matrix A = (a_{ij}) whose elements a_{ij} are given by ${a}_{ij}=\frac{\leftij\right}{2}.$ VIEW SOLUTION
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