Board Paper of Class 12Science 2019 Math Abroad(Set 3)  Solutions
General Instructions:
(i) All questions are compulsory.
(ii) This question paper contains 29 questions divided into four sections A, B, C and D. Section A comprises of 4 questions of one mark each, Section B comprises of 8 questions of two marks each, Section C comprises of 11 questions of four marks each and Section D comprises of 6 questions of six marks each.
(iii) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
(iv) There is no overall choice. However, internal choice has been provided in 1 question of Section A, 3 questions of Section B, 3 questions of Section C and 3 questions of Section D. You have to attempt only one of the alternatives in all such questions.
(v) Use of calculators is not permitted. You may ask logarithmic tables, if required.
 Question 1
Find the acute angle between the planes $\overrightarrow{r}.\left(\hat{i}2\hat{j}2\hat{k}\right)=1\mathrm{and}\overrightarrow{r}.\left(3\hat{i}6\hat{j}+2\hat{k}\right)=0$ .
ORVIEW SOLUTION
Find the length of the intercept, cut off by the plane 2x + y − z = 5 on the xaxis
 Question 2
If y = log (cos e^{x}) then find $\frac{dy}{dx}$. VIEW SOLUTION
 Question 3
A is a square matrix with ∣A∣ = 4. then find the value of ∣A. (adj A)∣. VIEW SOLUTION
 Question 4
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A. VIEW SOLUTION

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