Model Paper 7 - Rajasthan Board (RBSE) STD 11 Science MATHS Questions - Vidyadip

Question types

Model Paper 7 question types

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

45

Questions

6

Question groups

5

Question types

M.C.Q (1 Marks)

2 Marks Questions

3 Marks Question

5 Marks Questions

Assertion (A) & Reason (B) MCQ

Case study (4 Marks)

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 1M.C.Q (1 Marks)1 Mark

If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then

A
Re(z)=0
B
$\left.\operatorname{Re}( z )>0, I _{ m } z \right)>$
C
$\operatorname{Re}( z )>0, I _{ rs }( z )<0$
D
$I _{ m }( z )=0$

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Q 2M.C.Q (1 Marks)1 Mark

$\frac{\sin 3 x-\sin x}{\cos x-\cos 3 x}$ is equal to

A
$\cot 2 x$
B
$-\cot 2 x$
C
$-\tan 2 x$
D
$\tan 2 x$

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Q 3M.C.Q (1 Marks)1 Mark

Solve the system of inequalities: $\frac{x+7}{x-8}>2, \frac{2 x+1}{7 x-1}>5$

A
(4, 8)
B
(3, 6)
C
no solution
D
(2, 5)

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Q 4M.C.Q (1 Marks)1 Mark

The total number of 9 digit numbers which have all different digits is

A
91
B
$10 \times 10!$
C
10!
D
$9 \times 9$ !

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Q 5M.C.Q (1 Marks)1 Mark

If $y=\frac{\sin x+\cos x}{\sin x-\cos x}$, then $\frac{d y}{d x}$ at $x =0$ is equal to

A
$0$
B
-2
C
$\frac{1}{2}$
D
Does not exist

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Q 62 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 72 Marks Questions2 Marks

Find the coordinates of the point which divides the join of A(-5, 11) and B(4, -7) in the ratio 2 : 7.

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Q 82 Marks Questions2 Marks

Is $A =\{ x : x \in N , 1< x \leq 2\}$ null set?

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Q 92 Marks Questions2 Marks

Evaluate: $\lim _{\theta \rightarrow 0} \frac{1-\cos 4 \theta}{1-\cos 6 \theta}$.

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Q 102 Marks Questions2 Marks

Two dice are thrown simultaneously. Find the probability of getting a total of at least 10.

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Q 113 Marks Question3 Marks

The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.

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Q 123 Marks Question3 Marks

Prove that: ${ }^{2 n} C_n=\frac{2^n[1 \cdot 3 \cdot 5 \ldots \ldots(2 n-1)]}{n!}$.

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Q 133 Marks Question3 Marks

Out of 25 members in a family, 12 like to take tea, 15 like to take coffee and 7 like to take coffee and tea both. How many like
i. at least one of the two drinks
ii. only tea but not coffee
iii. only coffee but not tea
iv. neither tea nor coffee

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Q 143 Marks Question3 Marks

The sum of first three terms of a G.P. is $\frac{39}{10}$ and their product is 1 . Find the common ratio and the terms.

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Q 153 Marks Question3 Marks

Differentiate the function: $3^{ x -5}$

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Q 165 Marks Questions5 Marks

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{x^2}{100}+\frac{y^2}{400}=1$

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Q 175 Marks Questions5 Marks

Prove that: $\cos 36^{\circ} \cos 42^{\circ} \cos 60^{\circ} \cos 78^{\circ}=\frac{1}{16}$.

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Q 185 Marks Questions5 Marks

If $\sin x=\frac{\sqrt{5}}{3}$ and $x$ lies in the 2nd quadrant, find the values of $\cos \frac{x}{2}, \sin \frac{x}{2}$ and $\tan \frac{x}{2}$.

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Q 195 Marks Questions5 Marks

Find the mean and standard deviation for the following data:

Class interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	2	4	6	5	5	5	2	8	5

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Q 205 Marks Questions5 Marks

Find the lengths major and minor axes, coordinates of the vertices, coordinates of the foci, eccentricity, and length of the latus rectum of the ellipse $9 x^2+y^2=36$

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Q 21Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A): A sequence is said to definite if it has finite no of terms.
Reason (R): The sequence whose $n^{\text {th }}$ term if $\frac{2^n}{n}$ if $2,2, \frac{8}{3}, 4 \ldots$

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.
D
A is false but R is true.

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Q 22Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A): Let $A =\{ a , b \}$ and $B =\{ a , b , c \}$. Then, $A \not \subset B$.
Reason (R): If $A \subset B$, then $A \cup B=B$.

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.
D
A is false but R is true.

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Q 23Case study (4 Marks)4 Marks

The conjugate of a complex number $z$, is the complex number, obtained by changing the
sign of imaginary part of z . It is denoted by $\bar{z}$.
The modulus (or absolute value) of a complex number, z = a + ib is defined as the non
negative real number
$\sqrt{a^2+b^2}$. It is denoted by |z|. i.e.
$|z|=\sqrt{a^2+b^2}$
Multiplicative inverse of z is $\frac{\bar{z}}{|z|^2}$. It is also called reciprocal of z .
$z \bar{z}=|z|^2$
i. If $f(z)=\frac{7-z}{1-z^2}$, where $z=1+2 i$, then find $|f(z)|$. ( 1 )
ii. Find the value of $(z+3)(\bar{z}+3)$. (1)
iii. If ( $x-i y)(3+5 i)$ is the conjugate of $-6-24 i$, then find the value of $x+y$. (2)
OR
If $z=3+4 i$, then find $\bar{z}$. (2)

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Q 24Case study (4 Marks)4 Marks

Two students Ankit and Vinod appeared in an examination. The probability that Ankit will qualify the examination is 0.05 and that Vinod will qualify is 0.10. The probability that both will qualify is 0.02.
i. Find the probability that atleast one of them will qualify the exam. (1)
ii. Find the probability that atleast one of them will not qualify the exam. (1)
iii. Find the probability that both Ankit and Vinod will not qualify the exam. (2)
OR
Find the probability that only one of them will qualify the exam. (2)

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Q 25Case study (4 Marks)4 Marks

Representation of a Relation
A relation can be represented algebraically by roster form or by set-builder form and visually it can be represented by an arrow diagram which are given below
i. Roster form In this form, we represent the relation by the set of all ordered pairs belongs to R.
ii. Set-builder form In this form, we represent the relation $R$ from set $A$ to set $B$ as $R=\{(a, b)$ : $a \in A, b \in B$ and the rule which relate the elements of A and B ).
iii. Arrow diagram To represent a relation by an arrow diagram, we draw arrows from first element to second element of all ordered pairs belonging to relation R.
Questions:
i. If n(A) = 3 and B = {2, 3, 4, 6, 7, 8} then find the number of relations from A to B. (1)
ii. If A = {a, b} and B = {2, 3}, then find the number of relations from A to B. (1)
iii. If A = {a, b} and B = {2, 3}, write the relation in set-builder form. (2)
OR
Express of R = {(a, b): 2a + b = 5; a, b ∈ W} as the set of ordered pairs (in roster form). (2)

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