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Model Paper 4 Applied Maths - Model Paper 4

CBSE - STD 11 Science - Applied Maths (CBSE - English Medium). 44 questions in this chapter.

Question types

Model Paper 4 question types

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

44
Questions
6
Question groups
5
Question types
Sample Questions

Model Paper 4 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
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by a car or bus is
  • ✓
    60 percent
  • B
    80 percent
  • C
    70 percent
  • D
    40 percent

Answer: A.

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Q 3MCQ1 Mark
A man borrows ₹ 21000 at $10 \%$ per annum compound interest. How much he has to pay to the end of each year to clear his debt in two years?
  • ✓
    ₹ 12100
  • B
    ₹ 12000
  • C
    ₹ 10500
  • D
    ₹ 11000

Answer: A.

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Q 4MCQ1 Mark
Suppose A and B are two events. Event B has occurred and it is known that $\mathrm{P}(\mathrm{B})<1$. What is $\mathrm{P}\left(\mathrm{A} / \mathrm{B}^{\prime}\right)$ equal to?
  • A
    $\frac{P(A)-P(B)}{1-P(B)}$
  • B
    $\frac{P(A)+P\left(B^{\prime}\right)}{1-P(B)}$
  • ✓
    $\frac{P(A)-P(A B)}{1-P(B)}$
  • D
    $\frac{P(A)+P\left(A B^{\prime}\right)}{1-P(B)}$

Answer: C.

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Q 5MCQ1 Mark
Simplified from of $\log 12-\log 2-\log 3$ is
  • A
    $\log 4$
  • ✓
    $\log 2$
  • C
    $\log 6$
  • D
    $\log 1$

Answer: B.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): The Total no. words with letters of the word civilization (all taken at a time) is 19958393.
Reason (R): The number of permutation of $n$ distincts objects ($r$ taken at a time) is ${ }^{n} \mathrm{p}_{\mathrm{r}}$.
  • 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
A man $P$ speaks truth with probability $p$ and an other man $Q$ speaks truth with probability $2 p$.
Assertion (A): If $P$ and $Q$ contradict each other with probability $\frac{1}{2}$, then there are two values of $p$.
Reason (R): A quadratic equation with real coefficients has two real roots.
  • 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 .
  • ✓
    $A$ is true but $R$ is false.
  • D
    A is false but $R$ is true.

Answer: C.

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Q 82 Marks Questions2 Marks
If $A$ and $B$ are two events associated with a random experiment such that $P(A)=0.25, P(B)=0.4$ and $P(A$ or $B)$$=0.5$, find the values of
i. P(A and B)
ii. P(A and $\bar{B})$
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Q 133 Marks Question3 Marks
In a survey of 60 people, it was found that 25 people read Newspaper H, 26 read Newspaper T, 26 read Newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all the three Newspapers. Find
i. the number of people who read at least one of the three Newspapers.
ii. the number of people who read exactly one Newspaper.
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Q 143 Marks Question3 Marks
A man borrowed ₹5000 for 4 years under the following terms: $4 \%$ simple interest for the first $2 \frac{1}{2}$ years, $4 \%$ compound interest for the rest of the period on the amount due after $2 \frac{1}{2}$ years, the interest being compounded semi-annually. How much should he pay to settle the account?
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Q 153 Marks Question3 Marks
For an industrial connection monthly consumption of water is 40 Kl , calculate the Water bill. Tariff rates can be considered as the table given below:
Monthly Consumption (in Kilolitre)Service Charge (in ₹)Volumetric Charge (Per Kl in ₹)
Upto 20146.415.27
20-30219.62*26.36
> 30292.8243.93
Plus Sewer Maintenance Charges: $60\%$ of water volumetric charge
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Q 173 Marks Question3 Marks
Find the values of the letter and give a reason for the steps involved.
$\begin{array}{r}B 345 \\ +C 9 B A \\ \hline 8 B A 2 \\ \hline\end{array}$
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Q 185 Marks Questions5 Marks
An air conditioner manufacturer allows a discount of $10 \%$ on marked price to dealer and the dealer sells the air conditioner to a consumer at a discount of $4\%$ on marked price. If the marked price is ₹ $50,000$ and the sales are intra-state sales with GST at $18\%.$ Find:
i. the total amount paid by the consumer to the dealer.
ii. the GST paid by the consumer to the dealer.
iii. the GST paid by the dealer to the central and state governments.
iv. the GST paid by the manufacturer to the central and state governments.
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Q 215 Marks Questions5 Marks
Consider the real function $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}: \mathrm{f}(\mathrm{x})=\mathrm{x}+5$ for all $\mathrm{x} \in \mathrm{R}$. Find its domain and range. Draw the graph of this function.
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Q 23Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
Image
Depending upon the parents, the chances of having a left handed child are as follows:
A. When both father and mother are left handed:
Chances of left handed child is $24 \%$.
B. When father is right handed and mother is left handed:
Chances of left handed child is $22 \%$.
C. When father is left handed and mother is right handed:
Chances of left handed child is $17 \%$.
D. When both father and mother are right handed:
Chances of left handed child is $9\%.$
Assuming that $P(A)=P(B)=P(C)=P(D)=\frac{1}{4}$ and $L$ denotes the event that child is left handed.
(a) Find $P\left(\frac{L}{C}\right)$
(b) Find $\mathrm{P}\left(\frac{\overline{\mathrm{L}}}{\mathrm{A}}\right)$
(c) Find $P\left(\frac{A}{L}\right)$
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Q 24Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
In a game a girl rolls a die, if she gets an even number she will toss a coin if she gets head in coin, she will win ₹ 10 if she gets tail in coin she will win ₹ 5 . If she gets odd number in die she has to pay ₹ 20 to organiser.
(a) Find the total number of sample points in sample space?
(b) Find the probability that girl will win ₹ 10 ?
(c) Find the probability that girl will win ₹ 5 ?
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Q 26Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
During function lots of charts and displays are made with different colours, one such display is of concentric circles.
A circle is drawn whose equation is $x^{2}+y^{2}-4 x-6 y-12=0$ and based on this other consecutive circles are drawn.
(a) Find the centre of given circle?
(b) Find the radius of given circle?
(c) Find the point which lies in the interior of circle?
OR
Find the Equation of a circle concentric with given circle, whose radius is double the radius of given circle?
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