Students can access the CBSE Sample Papers for Class 11 Applied Mathematics with Solutions and marking scheme Term 2 Set 5 will help students in understanding the difficulty level of the exam.

## CBSE Sample Papers for Class 11 Applied Mathematics Term 2 Set 5 for Practice

Time : 2 Hours

Maximum Marks : 40

General Instructions:

- The question paper is divided into 3 sections -A, B and C.
- Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
- Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question.
- Section C comprises of 4 questions. It contains one case study-based question. Internal choice has been provided in one question.

Section – A [2 Marks each]

Question 1.

An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube is increasing when the edge is 5 cm long ?

OR

If (x^{2} + y^{2})^{2} = xy, find \(\frac{d y}{d x}\).

Question 2.

A product is sold from Kota (Rajasthan) to Gwalior (M.E) for ₹ 8,000 and then from Gwalior to Indore (M.P). If the rate of tax under GST system is 18% and the profit made by the dealer in Gwalior is ₹ 3,000, find net GST payable by the dealer in Gwalior.

Question 3.

₹16000 invested at 10% p.a. compounded semi-annually amounts to ₹18522. Find the time period of investment.

OR

Mr. Kohli, a citizen of India, is an export manager of Arjun Overseas Limited, an Indian Company, since 1.5.2014. He has been regularly going to U.S.A. for export promotion. He spent the following days in U.S.A. for the last five years:

Previous year ended | No. of days spent in U.S.A. |

31.3.2015 | 317 days |

31.3.2016 | 150 days |

31.3.2017 | 271 days |

31.3.2018 | 311 days |

31.3.2019 | 294 days |

Determine his residential status for assessment year 2019-20 assuming that prior to 1.5.2014 he had never travelled abroad.

Question 4.

A die is rolled. If E = {1, 3, 5}, F = {2, 3} and G = {2, 3,4, 5}, find (i) P[(E ∪ F)/G], (ii) P[(E ∩ F)/G]

Question 5.

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2). Find the centroid of the triangle.

Question 6.

If ^{n}P_{4}: ^{n}P_{2} = 12, find n.

Section – B [3 Marks each]

Question 7.

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that it is either a king or spade.

Question 8.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^{2} = 12y to the ends of its latus rectum.

OR

In what ratio the line joining (-1,1) and (5, 7) is divided by the line x + y = 4 ?

Question 9.

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random. Find the probability that

(i) The student opted for NCC or NSS.

(ii) The student has opted for neither NCC nor NSS.

(iii) The student has opted for NSS but not NCC.

Question 10.

(a) A man purchased a house valued at ₹300000. He paid ₹200000 at the time of purchased and agreed to pay the balance with the interest at 12% per annum compounded half yearly in 20 equal half yearly instalments. If first instalment is paid after six months from the date of purchase then find the amount of each instalment. [Given that (1.06)^{20} = 3.2071]

(b) A person invests ₹500 at the end of each year with a bank which pays interest at 10% p.a. compounded annually. Find the amount standing to his credit one year after he has made his yearly investment for the 12^{th} time. [Given that (1.1)^{12} = 3.1348]

Section – C [4 Marks each]

Question 11.

From 6 different novels and 3 different dictionaries, 4 novels and a dictionary is to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then find the number of such arrangements.

Question 12.

(a) A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest in how many years?

(b) Compound interest on a sum of money in 2 years at 4% per annum is ₹ 2448. Find simple interest on the same sum of money at the same rate of interest for 2 years.

OR

Leela is an athlete who believes that her playing career will last 3 years.

(a) To prepared for future, she deposits ₹ 24,000 at the end of each year for 3 years in an account paying 6% compounded annually. How much will she have on deposit after 3 years ? Also, find the value of interest earned.

(b) Instead of investing ₹ 24,000 at the end of each year, suppose Leela deposits ₹ 80,000 at the end of each year for 3 years in an account paying 5% compounded annually. How much will she have on deposit after 3 years ? Also, find the value of interest earned.

Question 13.

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm/sec. How fast is the area decreasing when two equal sides are equal to the base ?

Question 14.

Read the following text and answer the following questions on the basis of the same:

In XI standard, teacher was giving lecture on GST topic. Following points were discussed on this topic.

Goods and Services Tax (G.S.T.)

G.S.T. is known as the Goods and Services Tax. It is an indirect tax which has replaced many indirect taxes in India such as the excise duty, V.A.T., services tax, etc. The Goods and Services Tax Act was passed in the Parliament on 29th March 2017 and came into effect on 1st July 2017.

In other words, Goods and Services Tax (G.S.T.) is levied on the supply of goods and services. Goods and Services Tax Law in India is a comprehensive, multi-stage, destination-based tax that is levied on every value addition. G.S.T. is a single domestic indirect tax law for the entire country. In order to address the complex system in India, the Government introduced 4 types of G.S.T. which are given below.

(i) C.G.S.T. (Central Goods and Services Tax): Levied and collected by Central Government.

(ii) S.G.S.T. (State Goods and Services Tax): Levied and collected by State Governments/Union Territories with Legislatures.

(iii) U.T.G.S.T. (Union Territory Goods and Services Tax): Levied and collected by Union Territories without Legislatures, on intra-state supplies of taxable goods and/or services.

(iv) I.G.S.T. (Integrated Goods and Services Tax): Inter-state supplies of taxable goods and/or services are subject to Integrated Goods and Services Tax (I.G.S.T.). I.G.S.T. is the total sum of C.G.S.T. and S.G.S.T./U.T.G.S.T and is levied by Centre on all inter-state supplies.

- Intra-state means: Supply within the same state.

In case of intra-state sale of goods/services, or both If G.S.T. rate is 18%, then

C.G.S.T. = 9% of sales price S.G.S.T. = 9%of sales price I.G.S.T. = 0 - Inter-state means: Supply from one state to another state.

In case of inter-state of goods or services or both

If GST rate is 18%, then IGST = 18% of Sale price - Discount is never allowed on amount including GST.

Based on the information given above, solve the given questions:

(a) A dealer in Bhopal (M.E) supplies products and services worth ₹ 5,000 to another dealer in Kanpur (U.E). If the rate of G.S.T. is 28%, find the tax levied under C.G.S.T.

Also, A dealer in Agra (U.E), say Ramesh, supplies products and services worth ₹ 10,000 to Suresh a person in Lucknow (U.E). If the rate of GST is 28% find the S.G.S.T. (2)

(b) Let Amar, Ram and Rahim be three dealers belonging to different states. Dealer Amar sells some products/services to dealer Ram for ₹ 1000 dealer Rahim at a profit of ₹ 300. Calculate the tax liability of Ram, if the rate of G.S.T. is 12%. (2)