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Model Paper 7 Applied Maths - Model Paper 7

CBSE - STD 12 Science - Applied Maths (CBSE - English Medium). 47 questions in this chapter.

Question types

Model Paper 7 question types

47 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.

47
Questions
6
Question groups
5
Question types
Sample Questions

Model Paper 7 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The most commonly use mathematical method for measuring the trend is:
  • A
    Semi average method
  • B
    Time series method
  • ✓
    Method of least squares
  • D
    Moving average method

Answer: C.

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Q 2MCQ1 Mark
$\int e^x\left(\frac{1-x}{1+x^2}\right)^2 d x$ is equal to
  • A
    $-\frac{e^x}{1+x^2}+C$
  • B
    $-\frac{e^x}{\left(1+x^2\right)^2}+C$
  • ✓
    $\frac{e^x}{1+x^2}+C$
  • D
    $\frac{e^x}{\left(1+x^2\right)^2}+C$

Answer: C.

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Q 3MCQ1 Mark
A sample of 50 bulbs is taken at random. Out of 50 we found 15 bulbs are of Bajaj, 17 are of Surya and 18 are of Crompton. What is the point estimate of population proportion of Surya?
  • A
    0.3
  • ✓
    0.34
  • C
    0.36
  • D
    0.4

Answer: B.

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Q 4MCQ1 Mark
The necessary condition for third quadrant region in xy plane is:
  • A
    x > 0, y < 0
  • ✓
    x < 0, y < 0
  • C
    x < 0, y = 0
  • D
    x < 0, y > 0

Answer: B.

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Q 5MCQ1 Mark
If the objective function for an L.P.P. is Z = 3x + 4y and the comer points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of Z occurs at
  • ✓
    (4, 3)
  • B
    (9, 0)
  • C
    (2, 5)
  • D
    (0, 8)

Answer: A.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If the average cost (AC) of producing x units of an item is given by $AC =3 x ^2-7 x +5-\frac{11}{x}$, then the marginal cost (MC) of producing 5 units is ₹160.
Reason (R): $MC =\frac{d}{d x}( C )$.
  • ✓
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.

Answer: A.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Let A be a non-singular matrix of order n.
Assertion (A): $\operatorname{adj}(\operatorname{adj} A )=| A |^{ n -2} A$
Reason (R): $|\operatorname{adj} A |=| A |^{ n -1}$.
  • A
    Both A and R are true and R is the correct explanation of A.
  • ✓
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.

Answer: B.

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Q 82 Marks Questions2 Marks
A vessel contains a mixture of two liquids X and Y in the ratio 3 : 5. 8 litres of mixture are drawn off from the vessel and 8 liters of liquid X is filled in the vessel. If the ratio of liquids X and Y is now becomes 7: 10, how many litres of liquids X and Y were contained by the vessel initially?
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Q 122 Marks Questions2 Marks
Mrs Vandana invested ₹ 35000 in a shares of a company and reinvested the earnings every year in buying the shares of the same company. At the end of 5 years, the value of shares increased to ₹ 56000. Calculate the compound annual growth rate of her investment.
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Q 133 Marks Question3 Marks
Consider the following hypothesis test:
$\begin{array}{l} H _0: p \geq 0.75 \\ H _{ a }: p <0.75\end{array}$
A sample of 300 provided a sample proportion of 0.68.
i. Compute the value of the test statistic.
ii. What is the p-value?
iii. At $\alpha=0.05$, what is your conclusion?
iv. What is the rejection rule using critical value? What is your conclusion?
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Q 143 Marks Question3 Marks
For the following data, use the weighted average of price relative method to construct the index number for theyear 2010, taking the year 2005 as the base year.
CommodityWeight (W)Price in $2005\left( P _0\right)$Price in $2007\left( P _1\right)$
E152230
F121518
G81720
H171215
I202532
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Q 153 Marks Question3 Marks
A traffic engineer records the number of bicycle riders that use a particular cycle track. He records that an average of 3.2 bicycle riders use the cycle track every hour. Given that the number of bicycles that use the cycle track follow a Poisson distribution, what is the probability that
a. 2 or less bicycle riders will use the cycle track within an hour?
b. 3 or more bicycle riders will use the cycle track within an hour?
Also, write the mean expectation and variance for the random variable X.
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Q 185 Marks Questions5 Marks
A machine costing ₹ 50,000 has a useful life of 4 years. The estimated scrap value is ₹ 10,000. Using the straightline method, find the annual depreciation and construct a schedule for depreciation. Also, find the depreciation rate percent.
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Q 195 Marks Questions5 Marks
If the diameters of ball bearings are normally distributed with mean 0.6140 inches and standard deviation of 0.0025 inches, determine the percentage of ball bearings with diameters
i. between 0.610 and 0.618 inches inclusive
ii. greater than 0.617 inches
iii. less than 0.608 inches
iv. equal to 0.615 inches.
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Q 215 Marks Questions5 Marks
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
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Q 225 Marks Questions5 Marks
A firm makes items A and B and the total number of items it can make in a day is 24. It takes one hour to make an item of A and half an hour to make an item of B. The maximum time available per day is 16 hours. The profit on an item of A is ₹ 300 and on one item of B is ₹ 160. How many items of each type should be produced to maximize the profit? Solve the problem graphically.
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Q 23Case study (4 Marks)4 Marks
Show that the matrix, $A=\left[\begin{array}{rrr}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]$ satisfies the equation, $A^3-A^2-3 A-I_3=O$. Hence, find $A^{-1}$.
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Q 24Case study (4 Marks)4 Marks
An amount of ₹ 5000 is put into three investments at the rate of interest of 6%, 7% and 8% per annum respectively. The total annual income is ₹ 358. If the combined income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment by matrix method.
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Q 26Case study (4 Marks)4 Marks
In the year 2010, Mr. Aggarwal took a home loan of ₹ 30,00,000 from State Bank of India at 7.5% p.a. compounded monthly for 20 years.
Based on the above information, answer the following questions:
(a) Determine the EMI.
(b) Find the principal paid by Mr. Aggarwal in the $150^{\text {th }}$ instalment.
(c) Find the total interest paid by Mr. Aggarwal.
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Q 27Case study (4 Marks)4 Marks
The CEO of the multi-national company is interested in maximizing the area of the whole floor including the semicircular ends. Find the value of x for which the whole area is maximum.
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