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Model Paper 9 Applied Maths - Model Paper 9

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

Question types

Model Paper 9 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 9 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
For the given values 15, 23, 28, 36, 41, 46, the 3-yearly moving averages are:
  • ✓
    22, 29, 35, 41
  • B
    24, 29, 35, 41
  • C
    24, 28, 35, 41
  • D
    22, 28, 35, 41

Answer: A.

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Q 2MCQ1 Mark
The value of $\int \frac{1}{x+x \log x} d x$ is
  • ✓
    log (1 + log x)
  • B
    x + log x
  • C
    x log (1 + log x)
  • D
    1 + log x

Answer: A.

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Q 3MCQ1 Mark
A specific characteristic of a sample is known as a
  • A
    parameter
  • B
    variance
  • ✓
    statistic
  • D
    population

Answer: C.

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Q 4MCQ1 Mark
Corner points of the feasible region for an LPP are: (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let z = 4x + 6y the objective function. The minimum value of z occurs at
  • ✓
    any point on the line segment joining the points (0, 2) and (3, 0)
  • B
    the mid-point of the line segment joining the points (0, 2) and (3, 0) only
  • C
    (3, 0) only
  • D
    (0, 2) only

Answer: A.

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Q 5MCQ1 Mark
Solution set of inequations $x-2 y \geq 0,2 x-y \leq-2, x \geq 0, y \geq 0$ is:
  • A
    First quadrant
  • ✓
    Empty
  • C
    Closed halfplane
  • D
    Infinite

Answer: B.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Let $f(x)=x^4-2 x^2+5$ be defined on $[-2,2]$.
Assertion (A): The range of f(x) is [2, 13].
Reason (R): The greatest value of f is attained at x = 2.
  • A
    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.
  • ✓
    A is false but R is true.

Answer: D.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ and $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, then the value of k such that $A ^2= kA -2 I$, is -1.
Reason (R): If A and B are square matrices of same order, then (A + B)(A + B) is equal to $A^2+A B+B A+B^2$
  • A
    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.
  • ✓
    A is false but R is true.

Answer: D.

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Q 82 Marks Questions2 Marks
In what ratio must a grocer mix two varieties of tea worth ₹ 60 per kg and ₹ 65 per kg so that by selling the mixture at ₹ 68.20 per kg may gain 10%?
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Q 92 Marks Questions2 Marks
Find the values of x , if $\left|\begin{array}{ll}x+1 & x-1 \\ x-3 & x+2\end{array}\right|=\left|\begin{array}{cc}4 & -1 \\ 1 & 3\end{array}\right|$
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Q 102 Marks Questions2 Marks
If $A=\left[\begin{array}{rr}2 & -1 \\ 3 & 2\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 4 \\ -1 & 7\end{array}\right]$, find $3 A^2-2 B+I$
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Q 122 Marks Questions2 Marks
Jyoti buys a car for which she makes down payment of ₹3,50,000 and the balance is to be paid in 3 years by monthly installments of ₹34,000 each. If the financer charges interest at the rate of 12% per annum and uses flat rate method, find the actual price of the car.
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Q 133 Marks Question3 Marks
A random sample of 17 values from a normal population has a mean of 105 cm and the sum of the squares of deviations from this mean is $1225 cm^2$. Is the assumption of a mean of 110 cm for the normal population reasonable? Test under 5% and 1% levels of significance. Also, obtain the 95% and 99% confidence limits. (Given $t _{16}(0.05)=2.12$ and $\left.t _{16}(0.01)=2.921\right)$
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Q 143 Marks Question3 Marks
Given below are the consumer price index numbers (CPI) of the industrial workers.
 Year 2014 2015 2016 2017 2018 2019 2020
 Index number 145 140 150 190 200 220 230

Find the best fitted trend line by the method of least squares and tabulate the trend values.
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Q 153 Marks Question3 Marks
In a binomial distribution the sum and product of the mean and the variance are $\frac{25}{3}$ and $\frac{50}{3}$ respectively. Find the distribution.
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Q 163 Marks Question3 Marks
The income of a group of 10,000 persons was found to be normally distributed with mean ₹ 750 p.m. and standard deviation ₹ 50. Show that of this group about 95% had income exceeding ₹ 668 and only 5% had income exceeding ₹ 832. What was the lowest income among the richest 100?
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Q 173 Marks Question3 Marks
A company suffers a loss of ₹1,000 if its product does not sell at all. Marginal revenue and Marginal cost functions for the product are given by MR = 50 - 4x and MC = -10 + x respectively. Determine the total profit function, break-even points and the profit maximization level of output
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Q 185 Marks Questions5 Marks
A loan of ₹ 400000 at the interest rate of 6.75 % p.a. compounded monthly is to be amortized by equal payments at the end of each month for 10 years. Find
i. the size of each monthly payment.
ii. the principal outstanding at the beginning of 61st month.
iii. the interest paid in 61st payment.
iv. the principal contained in 61st payment.
v. total interest paid.
Given $\left.(1.005625)^{120}=1.9603,(1.005625)^{60}=1.4001\right)$
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Q 195 Marks Questions5 Marks
A random variable X has the following probability distribution:
X01234567
P(X)0k2 k2 k3 kk22k27k2+k
Find each of the following:
i. k
ii. $P ( X <6)$
iii. $P(X \geq 6)$
iv. $P (0< X <5)$
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Q 205 Marks Questions5 Marks
Find the probability distribution of the number of green balls drawn when 3 balls are awn, one by one, without replacement from a bag containing 3 green and 5 white balls.
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Q 225 Marks Questions5 Marks
A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. In view of the need to ensure certain nutrient constituents (call them X, Y and Z), it is necessary to buy two additional products, say, A and B. One unit of product A contains 36 units of X, 3 units of Y, and 20 units of Z. One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirement of X, Y and Z is 108 units, 36 units and 100 units respectively. Product A costs ₹ 20 per unit and product B costs ₹ 40 per unit. Formulate the above as a linear programming problem to minimize the total cost, and solve the problem by using graphical method.
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Q 26Case study (4 Marks)4 Marks
An equated monthly installment (EMI) is a set monthly payment provided by a borrower to a creditor on a set day, each month. EMIs apply to both interest and principal each month, and the loan is paid off in full over some years.
How is EMI calculated?
There are two ways in which EMI can be calculated. These methods are:
•The flat rate method: When the loan amount is progressively being repaid, each interest charge is computed using the original principal amount in the flat rate method.
•The reducing balance method: The reducing balance technique, compared to the flat rate method, determines the interest payment according to the outstanding principal.
Example:
A loan of ₹250000 at the interest rate of 6% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 5 years.
$\left(\right.$ Given $\left.(1.005)^{60}=1.3489,(1.005)^{21}=1.1104\right)$
(a) Find the size of each monthly payment.
(b) Find the principal outstanding at beginning of 40th month.
(c) Find interest paid in 40th payment.
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