{"id":121679,"date":"2022-05-18T16:22:54","date_gmt":"2022-05-18T10:52:54","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=121679"},"modified":"2022-05-18T16:38:03","modified_gmt":"2022-05-18T11:08:03","slug":"mathematics-ncert-sample-question-paper-semester-ii-code041-2021-2022-class-xii","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/mathematics-ncert-sample-question-paper-semester-ii-code041-2021-2022-class-xii","title":{"rendered":"Mathematics NCERT SAMPLE QUESTION PAPER-SEMESTER-II Code(041) 2021-2022 Class XII"},"content":{"rendered":"

1. \"\"<\/h2>\n

OR<\/p>\n

\"\"<\/p>\n

Answer.<\/h3>\n

\"\"<\/p>\n

OR<\/p>\n

\"\"<\/p>\n

2. Write the sum of the order and the degree of the following differential equation:<\/h2>\n

\"\"<\/p>\n

Answer.<\/h3>\n

Write the sum of the order and the degree of the following differential<\/h3>\n

\"\"<\/p>\n

Solution: Order = 2
\nDegree = 1
\nSum = 3<\/h3>\n

3. If \ud835\udc4e\u0302 and \ud835\udc4f\u0302 are unit vectors, then prove that
\n|\ud835\udc4e\u0302 + \ud835\udc4f\u0302| = 2\ud835\udc50\ud835\udc5c\ud835\udc60 0\/2 , where \ud835\udf03 is the angle between them.<\/h2>\n

Answer.
\nIf \ud835\udc4e\u0302 and \ud835\udc4f\u0302 are unit vectors, then prove that<\/h3>\n

\"\"<\/p>\n

4. Find the direction cosines of the following line:<\/h2>\n

\"\"<\/p>\n

Answer.<\/h3>\n

Find the direction cosines of the following line:<\/h3>\n

\"\"<\/p>\n

5. A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-byone without replacement.<\/h2>\n

Answer.
\nA bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement. Solution: Let X be the random variable defined as the number of red balls.
\nThen X = 0, 1<\/h3>\n

\"\"<\/p>\n

6. Two cards are drawn at random from a pack of 52 cards one-by-one without replacement. What is the probability of getting first card red and second card Jack?<\/h2>\n

Answer.
\nTwo cards are drawn at random from a pack of 52 cards one-by-one without replacement. What is the probability of getting first card red and second card Jack? Solution: The required probability = P((The first is a red jack card and The second is a jack card) or (The first is a red non-jack card and The second is a jack card))<\/h3>\n

\"\"<\/p>\n

7. \"\"<\/h2>\n

Answer.<\/h3>\n

\"\"<\/p>\n

8. Find the general solution of the following differential equation:<\/h2>\n

\"\"<\/p>\n

OR<\/p>\n

Find the particular solution of the following differential equation, given that<\/h2>\n

\"\"<\/p>\n

Answer.<\/h3>\n

\"\"
\n\ud835\udc59\ud835\udc5c\ud835\udc54|\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc63 \u2212 \ud835\udc50\ud835\udc5c\ud835\udc61\ud835\udc63| = \u2212\ud835\udc59\ud835\udc5c\ud835\udc54|\ud835\udc65| + \ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc3e,\ud835\udc3e > 0 (Here, \ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc3e is an arbitrary
\nconstant.)
\n\u21d2 \ud835\udc59\ud835\udc5c\ud835\udc54|(\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc63 \u2212 \ud835\udc50\ud835\udc5c\ud835\udc61\ud835\udc63)\ud835\udc65| = \ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc3e
\n\u21d2 |(\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc63 \u2212 \ud835\udc50\ud835\udc5c\ud835\udc61\ud835\udc63)\ud835\udc65| = \ud835\udc3e
\n\u21d2 (\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc63 \u2212 \ud835\udc50\ud835\udc5c\ud835\udc61\ud835\udc63)\ud835\udc65 = \u00b1\ud835\udc3e
\n\u21d2 (\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc52\ud835\udc50 \ud835\udc66\/\ud835\udc65\u2212 \ud835\udc50\ud835\udc5c\ud835\udc61 \ud835\udc66\/\ud835\udc65) \ud835\udc65 = \ud835\udc36, which is the required general solution.<\/h3>\n

OR<\/p>\n

\"\"<\/p>\n

9. If \ud835\udc4e\u20d7 \u2260 0,
\n\u20d7\u20d7\u20d7 \ud835\udc4e\u20d7. \ud835\udc4f\u20d7\u20d7 = \ud835\udc4e\u20d7. \ud835\udc50\u20d7, \ud835\udc4e\u20d7 \u00d7 \ud835\udc4f\u20d7\u20d7 = \ud835\udc4e\u20d7 \u00d7 \ud835\udc50\u20d7, then show that \ud835\udc4f\u20d7\u20d7 = \ud835\udc50\u20d7.<\/h2>\n

Answer.<\/h3>\n

If \ud835\udc4e\u20d7 \u2260 0,
\n\u20d7\u20d7\u20d7 \ud835\udc4e\u20d7. \ud835\udc4f\u20d7\u20d7 = \ud835\udc4e\u20d7. \ud835\udc50\u20d7, \ud835\udc4e\u20d7 \u00d7 \ud835\udc4f\u20d7\u20d7 = \ud835\udc4e\u20d7 \u00d7 \ud835\udc50\u20d7, then show that \ud835\udc4f\u20d7\u20d7 = \ud835\udc50\u20d7.
\nSolution: We have \ud835\udc4e\u20d7. (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7) = 0
\n\u21d2 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7) = \u20d70\u20d7 or \ud835\udc4e\u20d7 \u22a5 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7)
\n\u21d2 \ud835\udc4f\u20d7\u20d7 = \ud835\udc50\u20d7 or \ud835\udc4e\u20d7 \u22a5 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7)
\nAlso, \ud835\udc4e\u20d7 \u00d7 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7) = \u20d70\u20d7
\n\u21d2 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7) = \u20d70\u20d7 or \ud835\udc4e\u20d7 \u2225 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7)
\n\u21d2 \ud835\udc4f\u20d7\u20d7 = \ud835\udc50\u20d7 or \ud835\udc4e\u20d7 \u2225 (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7)
\n\ud835\udc4e\u20d7 \ud835\udc50\ud835\udc4e\ud835\udc5b \ud835\udc5b\ud835\udc5c\ud835\udc61 \ud835\udc4f\ud835\udc52 \ud835\udc4f\ud835\udc5c\ud835\udc61\u210e \ud835\udc5d\ud835\udc52\ud835\udc5f\ud835\udc5d\ud835\udc52\ud835\udc5b\ud835\udc51\ud835\udc56\ud835\udc50\ud835\udc62\ud835\udc59\ud835\udc4e\ud835\udc5f \ud835\udc61\ud835\udc5c (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7) \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc5d\ud835\udc4e\ud835\udc5f\ud835\udc4e\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc59 \ud835\udc61\ud835\udc5c (\ud835\udc4f\u20d7\u20d7 \u2212 \ud835\udc50\u20d7)
\nHence, \ud835\udc4f\u20d7\u20d7 = \ud835\udc50\u20d7.<\/h3>\n

10. Find the shortest distance between the following lines:
\n\ud835\udc5f\u20d7 = (\ud835\udc56\u0302+ \ud835\udc57\u0302\u2212 \ud835\udc58\u0302) + \ud835\udc60(2\ud835\udc56\u0302+ \ud835\udc57\u0302+ \ud835\udc58\u0302)
\n\ud835\udc5f\u20d7 = (\ud835\udc56\u0302+ \ud835\udc57\u0302+ 2\ud835\udc58\u0302) + \ud835\udc61(4\ud835\udc56\u0302+ 2\ud835\udc57\u0302+ 2\ud835\udc58\u0302)<\/h2>\n

OR<\/p>\n

Find the vector and the cartesian equations of the plane containing the point
\n\ud835\udc56\u0302+ 2\ud835\udc57\u0302\u2212 \ud835\udc58\u0302 and parallel to the lines \ud835\udc5f\u20d7 = (\ud835\udc56\u0302+ 2\ud835\udc57\u0302+ 2\ud835\udc58\u0302) + \ud835\udc60(2\ud835\udc56\u0302\u2212 3\ud835\udc57\u0302+ 2\ud835\udc58\u0302) and
\n\ud835\udc5f\u20d7 = (3\ud835\udc56\u0302+ \ud835\udc57\u0302\u2212 2\ud835\udc58\u0302) + \ud835\udc61(\ud835\udc56\u0302\u2212 3\ud835\udc57\u0302+ \ud835\udc58\u0302)<\/h2>\n

Answer.
\nFind the shortest distance between the following lines:
\n\ud835\udc5f\u20d7 = (\ud835\udc56\u0302+ \ud835\udc57\u0302\u2212 \ud835\udc58\u0302) + \ud835\udc60(2\ud835\udc56\u0302+ \ud835\udc57\u0302+ \ud835\udc58\u0302)
\n\ud835\udc5f\u20d7 = (\ud835\udc56\u0302+ \ud835\udc57\u0302+ 2\ud835\udc58\u0302) + \ud835\udc61(4\ud835\udc56\u0302+ 2\ud835\udc57\u0302+ 2\ud835\udc58\u0302)<\/h3>\n

\"\"<\/p>\n

OR<\/p>\n

\"\"<\/p>\n

11. Evaluate: \u222b |\ud835\udc65
\n3 \u2212 3\ud835\udc65
\n2 + 2\ud835\udc65|\ud835\udc51\ufffd<\/h2>\n

Answer.<\/h3>\n

\"\"<\/p>\n

12. Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y 2 = x and the x-axis.<\/h2>\n

OR<\/p>\n

Using integration, find the area of the region
\n{(\ud835\udc65, \ud835\udc66): 0 \u2264 \ud835\udc66 \u2264 \u221a3\ud835\udc65, \ud835\udc65
\n2 + \ud835\udc66
\n2 \u2264 4}<\/h2>\n

Answer.<\/h3>\n

Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y 2 = x and the x-axis.
\nSolution: Solving x + y = 2 and y 2 = x simultaneously, we get the points of intersection as (1, 1) and (4, -2).<\/h3>\n

\"\"<\/p>\n

OR<\/p>\n

Using integration, find the area of the region: {(\ud835\udc65, \ud835\udc66): 0 \u2264 \ud835\udc66 \u2264 \u221a3\ud835\udc65, \ud835\udc65 2 + \ud835\udc66 2 \u2264 4}<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

13. Find the foot of the perpendicular from the point (1, 2, 0) upon the plane x \u2013 3y + 2z = 9. Hence, find the distance of the point (1, 2, 0) from the given plane.<\/h2>\n

Answer.
\nFind the foot of the perpendicular from the point (1, 2, 0) upon the plane x \u2013 3y + 2z = 9. Hence, find the distance of the point (1, 2, 0) from the given plane. Solution: The equation of the line perpendicular to the plane and passing
\nthrough the point (1, 2, 0) is<\/h3>\n

\"\"<\/p>\n

14.\"\"<\/h2>\n

Fig 1
\nAn insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. The company\u2019s statistics show that an accident-prone person will have an accident at sometime within a fixed one-year period with probability 0.6, whereas this probability is 0.2 for a person who is not accident prone. The company knows that 20 percent of the population is accident prone. Based on the given information, answer the followin questions.
\n(i)what is the probability that a new policyholder will have an accident within a year of purchasing a policy?
\n(ii) Suppose that a new policyholder has an accident within a year of purchasing a policy. What is the probability that he or she is accident prone?<\/h2>\n

Answer.<\/h3>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

1. OR Answer. OR 2. Write the sum of the order and the degree of the following differential equation: Answer. Write the sum of the order and the degree of the following differential Solution: Order = 2 Degree = 1 Sum = 3 3. If \ud835\udc4e\u0302 and \ud835\udc4f\u0302 are unit vectors, then prove that |\ud835\udc4e\u0302 […]<\/p>\n","protected":false},"author":21830,"featured_media":121721,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-121679","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/121679","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=121679"}],"version-history":[{"count":3,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/121679\/revisions"}],"predecessor-version":[{"id":121729,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/121679\/revisions\/121729"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/121721"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=121679"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=121679"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=121679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}