Download App

Model Paper 4 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 44 Marks
Question
A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
Image
How many words, with or without meaning can be made from the letters of the word, $\text{MONDAY,}$ assuming that no letter is repeated if 
$(i) 4$ letters are used at a time
$(ii)$ all letters are used at a time
✓

Answer

Total number of letters in word $\text{MONDAY} = 6$
Number of vowels in word $\text{MONDAY} = 2$
$(i)$ Number of letters used $= 4$
$\therefore$ Number of permutations $={ }^6 P_4=\frac{6!}{(6-4)!}$
$=\frac{6!}{2!}=\frac{6 \times 5 \times 4 \times 3 \times 2!}{2!}=360$
$(ii)$ Number of letters used $= 6$
$\therefore$ Number of permutations $={ }^6 P_6$
$=\frac{6!}{0!}$
$=6 \times 5 \times 4 \times 3 \times 2 \times 1$
$=720$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Case study (4 Marks)" from Model Paper 4→Model Paper 4 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A class teacher Mamta Sharma of class $XI$ write three sets $A, B$ and Care such that $A = \{1, 3, 5, 7, 9\}, B = \{2, 4, 6, 8\}$ and $C = \{2, 3, 5, 7, 11\}.$
Answer the following questions which are based on above sets.
  1. Find $\text{A}\cap\text{B}.$
  1. $\{3, 5, 7\}$
  2. $\phi$
  3. $\{1, 5, 7\}$
  4. $\{2, 5, 7\}$
  1. Find $\text{A}\cap\text{C}.$
  1. $\{3, 5, 7\}$
  2. $\{1, 5, 7\}$
  3. $\phi$
  4. $\{3, 4, 7\}$
  1. Which of the following is correct for two sets $A$ and $B$ to be disjoint?
  1. $\text{A}\cap\text{B}=\phi$
  2. $\text{A}\cap\text{B}\neq\phi$
  3. $\text{A}\cup\text{B}=\phi$
  4. $\text{A}\cup\text{B}\neq\phi$
  1. Which of the following is correct for two sets $A$ and $C$ to be intersecting?
  1. $\text{A}\cap\text{C}=\phi$
  2. $\text{A}\cap\text{C}\neq\phi$
  3. $\text{A}\cup\text{C}=\phi$
  4. $\text{A}\cup\text{C}\neq\phi$
  1. Write the $n[P(B)].$
  1. $8$
  2. $4$
  3. $16$
  4. $12$
→
Two complex numbers $Z _1= a + ib$ and $Z _2= c + id$ are said to be equal, if $a = c$ and $b = d$.
$i.$ If $(x+i y)(2-3 i)=4+i$ then find the value of $(x, y)$.
$ii.$ If $\frac{(1+i)^2}{2-i}=x+i y$, then find the value of $x+y. (1)$
$iii.$ If $\left(\frac{1-i}{1+i}\right)^{100}=a+i b$, then find the values of $a$ and $b. (2)$
$OR$
If $(a-2,2 b+1)=(b-1, a+2)$, then find the real values of $a$ and $b. (2)$
→
Republic day is a national holiday of India. It honours the date on which the constitution of India came into effect on 26 January 1950 replacing the Government of India Act (1935) as the governing document of India and thus, turning the nation into a newly formed republic.

Answer the following question, which are based on the word "REPUBLIC".

(i) Find the number of arrangements of the letters of the word 'REPUBLIC'.
(a) 40300     (b) 30420    (c) 40320     (d) 40400

(ii) How many arrangements start with a vowel?
(a) 12015     (b) 15120     (c) 12018     (d) 15100

(iii) Which concept is used for finding the arrangements start with a vowel?
(a) Permutation     (b) FPM     (c) Combination     (d) FPA

(iv) If the number of arrangements of the letters of the word 'REPUBLIC' is abcde, the (a + b + $\mathbf{c}+\mathbf{d}+\mathbf{e})$ is
(a) 10     (b) 9     (c) 8     (d) 15

(v) If the number of arrangements start with a vowel is abcde, then $(\mathbf{a}+\mathbf{b})-(\mathbf{d}+\mathbf{e})$ is
(a) 2     (b) 3     (c) 4     (d) 5
→
We have, $i=\sqrt{-1}$. So, we can write the higher powers of $i$ as follows
(i) $i^2=-1$
(ii) $i^3=i^2 \cdot i=(-1) \cdot i=-i$
(iii) $i^4=\left(i^2\right)^2=(-1)^2=1$
(iv) $i^5=i^{4+1}=i^4 \cdot i=1 \cdot i=i$
(v) $i^6=i^{4+2}=i^4 \cdot i^2=1 \cdot i^2=-1$

In order to compute $i^n$ for $n>4$, write $i^n=i^{4 q+r}$ for some $q, r \in N$ and $0 \leq r \leq 3$. Then, $i^n=$ $i^{4 q} \cdot i^r=\left(i^4\right)^q \cdot i^r=(1)^q \cdot i^r=i^r$.
In general, for any integer $k, i^{4 k}=1, i^{4 k+1}=i, i^{4 k+2}=-1$ and $i^{4 k+3}=-i$.

On the basis of above information, answer the following questions.

(i) The value of $i^{37}$ is equal to
    (a) $i$     (b) $-i$     (c) 1     (d) -1

(ii) The value of $i^{-30}$ is equal to
    (a) $i$     (b) 1     (c) -1     (d) $-i$

(iii) If $z=i^9+i^{19}$, then $z$ is equal to
    (a) $0+0 i$     (b) $1+0 i$     (c) $0+i$     (d) $1+2 i$

(iv) The value of $\left[i^{19}+\left(\frac{1}{i}\right)^{25}\right]^2$ is equal to
    (a) -4     (b) 4     (c) $\mathrm{i}$     (d) 1

(v) If $z=i^{-39}$, then simplest form of $z$ is equal to
    (a) $1+0 i$     (b) $0+i$     (c) $0+0 i$     (d) $1+i$
→
For a group of $200 $ candidates, the mean and the standard deviation of scores were found to be $40$ and $15 ,$ respectively. Later on it was discovered that the scores of $43$ and $35$ were misread as $34$ and $53,$ respectively.
Student English Hindi S.st Science Maths
Ramu $39$ $59$ $84$ $80$ $41$
Rajitha $79$ $92$ $68$ $38$ $75$
Komala $41$ $60$ $38$ $71$ $82$
Patil $77$ $77$ $87$ $75$ $42$
Pursi $72$ $65$ $69$ $83$ $67$
Gayathri $46$ $96$ $53$ $71$ $39$
$i.$ Find the correct variance. $(1)$
$ii$. What is the formula of variance. $(1)$
$iii.$  Find the correct mean. $(2)$​​​​​​​
OR
Find the sum of correct scores.$ (2)$
→
The girder of a railway bridge is a parabola with its vertex at the highest point, $10\ m$ above the ends. Its span is $100 \ m$. 
Image
$i$. Find the coordinates of the focus of the parabola. $(1)$
$ii$. Find the equation of girder of bridge and find the length of latus rectum of girder of bridge.$ (1)$
$iii$. Find the height of the bridge at $20\ m$ from the mid $-$ point. $(2)$
OR
Find the radius of circle with centre at focus of the parabola and passes through the vertex of parabola. $(2)$
 
→
Four friends Dinesh, Yuvraj, Sonu, and Rajeev are playing cards. Dinesh, shuffling a cards and told to Rajeev choose any four cards. 
Image
$i$. What is the probability that Rajeev getting all face card. $(1)$
$ii$. What is the probability that Rajeev getting two red cards and two black card. $(1)$
$iii$. What is the probability that Rajeev getting one card from each suit. $(2)$
OR
What is the probability that Rajeev getting two king and two Jack cards. $(2)$
→
Method to Find the Sets When Cartesian Product is Given
For finding these two sets, we write first element of each ordered pair in first set say $A$ and corresponding second element in second set $B\ ($say$)$.
Number of Elements in Cartesian Product of Two Sets
If there are $p$ elements in set $A$ and $q$ elements in set $B$, then there will be pq elements in $A \times B$ i.e. if $n(A)=p$ and $n(B)=q$, then $n(A \times B)=p q$.
$i$. The Cartesian product $A \times A$ has $9$ elements among which are found $(-1,0)$ and $(0,1)$. Find the set $A$ and the remaining elements of $A \times A. (1)$
$ii. A$ and $B$ are two sets given in such a way that $A \times B$ contains $6$ elements. If three elements of $A \times B$ are $(1, 3 ), (2,5)$ and $(3, 3),$ then find the remaining elements of $A \times B. (1)$
$iii$. If the set $A$ has $3$ elements and set $B$ has $4$ elements, then find the number of elements in $A \times B$. $(2)$
OR
If $A \times B=\{(a, 1),(b, 3),(a, 3),(b, 1),(a, 2),(b, 2)\}$. Find $A$ and $B .(2)$
→
Indian track and field athlete Neeraj Chopra, who competes in the Javelin throw, won a gold medal at Tokyo Olympics. He is the first track and field athlete to win a gold medal for India at the Olympics.
Image

Image

$i$. Name the shape of path followed by a javelin. If equation of such a curve is given by $x^2=-16 y,$ then find the coordinates of foci. $(1)$
$ii.$ Find the equation of directrix and length of latus rectum of parabola $x^2=-16 y. (1)$
$iii.$ Find the equation of parabola with Vertex $(0,0)$, passing through $(5,2)$ and symmetric with respect to $y-$ axis and also find equation of directrix.$ (2)$
OR
Find the equation of the parabola with focus $(2,0)$ and directrix $x=-2$ and also length of latus rectum. $(2)$
→
A company produces 500 computers in the third year and 600 computers in the seventh year. Assuming that the production increases uniformly by a constant number every year.
Image
Based on the above information, answer the following questions.

(i) The value of the fixed number by which production is increasing every year is
    (a) 25     (b) 20     (c) 10     (d) 30

(ii) The production in first year is
    (a) 400     (b) 250     (c) 450     (d) 300

(iii) The total production in 10 years is
    (a) 5625     (b) 5265     (c) 2655     (d) 6525

(iv) The number of computers produced in 21 st year is
    (a) 650     (b) 700     (c) 850     (d) 950

(v) The difference in number of computers produced in 10th year and 8th year is
    (a) 25     (b) 50     (c) 100     (d) 75
→