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Model Paper 6 Maths - Model Paper 6

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 44 questions in this chapter.

Question types

Model Paper 6 question types

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

44
Questions
6
Question groups
5
Question types
Sample Questions

Model Paper 6 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.Q1 Mark
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. The volume of the solid is
  • ✓
    $\pi \ cm ^3$
  • B
    $4 \pi \ cm^3$
  • C
    $2 \pi \ cm^3$
  • D
    $3 \pi \ cm^3$

Answer: A.

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Q 2M.C.Q1 Mark
The value of $\frac{(0.013)^3+(0.007)^3}{(0.013)^2-0.013 \times 0.007+(0.007)^2}$ , is
  • A
    $0.0091$
  • ✓
    $0.02$
  • C
    $0.006$
  • D
    $0.00185$

Answer: B.

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Q 3M.C.Q1 Mark
In $\triangle P Q R, \angle R=\angle P$ and $Q R=4 cm$ and $P R=5 cm$. Then the length of $P Q$ is
  • A
    2.5 cm
  • B
    4 cm
  • C
    5 cm
  • D
    2 cm
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Q 5M.C.Q1 Mark
The value of $\sqrt[4]{(64)^{-2}}$ is
  • A
    $\frac{1}{2}$
  • ✓
    $\frac{1}{8}$
  • C
    $\frac{1}{16}$
  • D
    $\frac{1}{4}$

Answer: B.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): The equation of 2x + 5 = 0 and 3x + y = 5 both have degree 1.
Reason (R): The degree of a linear equation in two variables is 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.
  • D
    A is false but R is true.
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion $(A):$ The sides of a triangle are in the ratio of $25: 14: 12$ and its perimeter is $510 \ cm .$ Then the area of the triangle is $4449.08 \ cm^2$.
Reason $(R):$ Perimeter of a triangle $=a+b+c$, where $a, b, c$ are sides of a triangle.
  • ✓
    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
    $R$ is not the correct explanation of $A.$
  • D
    $A$ is false but $R$ is true.

Answer: A.

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Q 122 Marks Questions2 Marks
Two circles intersect at two points $B$ and $C.$ Through $B,$ two line segments $\ce{ABD}$ and $\ce{PBQ}$ are drawn to intersect the circles at $\ce{A, D, P, Q}$ respectively $($see figure$).$ Prove that $\ce{ACP=QCD}$.
Image
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Q 143 Marks Question3 Marks
$\text{BE}$ and $\text{CF}$ are two equal altitudes of a triangle $\text{ABC.}$ Using $\text{RHS}$ congruence rule, prove that the triangle $\text{ABC}$ is isosceles.
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Q 163 Marks Question3 Marks
The internal and external diameters of a hollow hemispherical vessel are $20 \ cm$ and $28 \ cm$ respectively. Find the cost of painting the vessel all over at $35$ paise per $cm ^2$.
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Q 23Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Harish makes a poster in the shape of a parallelogram on the topic $\text{SAVE ELECTRICITY}$ for an inter$-$school competition as shown in the follow figure.
Image
$i.$ If $\angle A =(4 x +3)^{\circ}$ and $\angle D =(5 x -3)^{\circ}$, then find the measure of $\angle B$.
$ii.$ If $\angle B =(2 y )^{\circ}$ and $\angle D =(3 y -6)^{\circ}$, then find the value of $y.$
$iii.$ If $\angle A=(2 x-3)^{\circ}$ and $\angle C=(4 y+2)^{\circ}$, then find how $x$ and $y$ relate.
OR
If $A B=(2 y-3)$ and $C D=5 \ cm$ then what is the value of $y$ ?
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Q 24Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Peter, Kevin James, Reeta and Veena were students of Class $9^{th} B$ at Govt Sr Sec School, Sector $5,$ Gurgaon.
Once the teacher told Peter to think a number $x$ and to Kevin to think another number $y$.
so that the difference of the numbers is $10(x > y).$
Now the teacher asked James to add double of Peter's number and that three times of Kevin's number, the total was found $120.$
Reeta just entered in the class, she did not know any number.
The teacher said Reeta to form the $1^{st}$ equation with two variables $x$ and $y.$
Now Veena just entered the class so the teacher told her to form $2^{nd}$ equation with two variables $x$ and $y.$
Now teacher Told Reeta to find the values of $x$ and $y.$
Peter and kelvin were told to verify the numbers $x$ and $y.$
Image
$i.$ What are the equation formed by Reeta and Veena?
$ii.$ What was the equation formed by Veena?
$iii.$ Which number did Peter think?
OR
Which number did Kelvin think? 
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Q 25Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Once upon a time in Ghaziabad was a corn cob seller. During the lockdown period in the year $2020$, his business was almost lost.
So, he started selling corn grains online through Amazon and Flipcart. Just to understand how many grains he will have from one corn cob, he started counting them.
Being a student of mathematics let's calculate it mathematically. Let's assume that one corn cob $($see Fig.$),$ shaped somewhat like a cone, has the radius of its broadest end as $2.1 \ cm$ and length as $20 \ cm.$
Image
$i.$ Find the curved surface area of the corn cub.
$ii.$ What is the volume of the corn cub?
$iii.$ If each $1 \ cm^2 $ of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob?
OR
How many such cubs can be stored in a cartoon of size $20 \ cm \times 25 \ cm \times 20 \ cm$.
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