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Model Paper 1 Maths - Model Paper 1

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 43 questions in this chapter.

Question types

Model Paper 1 question types

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

43
Questions
6
Question groups
5
Question types
Sample Questions

Model Paper 1 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
The value of $\frac{\left(a^2-b^2\right)^3+\left(b^2-c^2\right)^3+\left(c^2-a^2\right)^3}{(a-b)^3+(b-c)^3+(c-a)^3}$ is
  • A
    $3(a - b)(b - c)(c - a)$
  • ✓
    $(a + b)(b + c)(c + a)$
  • C
    $3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)$
  • D
    $2(a - b)(b - c)(c - a)$

Answer: B.

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Q 2M.C.Q1 Mark
If $(-2, 5)$ is a solution of $2x + my = 11,$ then the value of $'m\ ’$ is
  • A
    $-2$
  • B
    $2$
  • ✓
    $3$
  • D
    $-3$

Answer: C.

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Q 4M.C.Q1 Mark
In the given figure, $O$ is the centre of a circle and chords $AC$ and $BD $intersect at $E.$ If $\angle \text{AEB} =110^{\circ}$ and $\angle \text{CBE}=30^{\circ}$, then $\angle \text{ADB} =$ ?
Image
  • ✓
    $80^{\circ}$
  • B
    $60^{\circ}$
  • C
    $90^{\circ}$
  • D
    $70^{\circ}$

Answer: A.

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Q 5M.C.Q1 Mark
After rationalising the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}}$, we get the denominator as
  • A
    $5$
  • B
    $35$
  • ✓
    $19$
  • D
    $13$

Answer: C.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): $2+\sqrt{6}$ is an irrational number.
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
  • 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): If the diagonals of a parallelogram ABCD are equal, then $\angle ABC =90^{\circ}$
Reason (R): If the diagonals of a parallelogram are equal, it becomes a rectangle.
  • 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 82 Marks Questions2 Marks
A hollow spherical shell is made of a metal of density $4.5\ g\ per\ cm ^3$. If its internal and external radii are $8 \ cm$ and $9 \ cm$ respectively, find the weight of the shell.
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Q 173 Marks Question3 Marks
In Fig. X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogram ABCD. Also, BX and DY intersect AC at P and Q, respectively. Show that AP = PQ = QC.
Image
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Q 205 Marks Questions5 Marks
The length of the sides of a triangle are in the ratio $3 : 4 : 5$ and its perimeter is $144 \ cm.$ Find the area of the triangle and the height corresponding to the longest side
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Q 215 Marks Questions5 Marks
What length of tarpaulin $3 m$ wide will be required to make conical tent of height $8 m$ and base radius $6 m?$
Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20 \ cm . ($Use $\pi=3.14$ )
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Q 23Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Rohan draws a circle of radius $10 \ cm$ with the help of a compass and scale. He also draws two chords, $AB$ and $CD$ in such a way that the perpendicular distance from the center to $AB$ and $CD$ are $6 \ cm$ and $8 \ cm$ respectively. Now, he has some doubts that are given below.
Image

$i.$ Show that the perpendicular drawn from the Centre of a circle to a chord bisects the chord.
$ii.$ What is the length of $CD?$
$iii.$ What is the length of $AB?$
OR
How many circles can be drawn from given three noncollinear points?
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Q 24Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
A children's park is in the shape of isosceles triangle said $\text{PQR}$ with $\text{PQ = PR, S}$ and $T$ are points on $\text{QR}$ such that $\text{QT = RS}$.
Image
$i.$ Which rule is applied to prove that congruency of $\ce{\triangle PQS}$ and $\ce{\triangle PRT}$.
$ii.$ Name the type of $\ce{\triangle PST.}$
$iii.$ If $\ce{PQ=6 \ cm}$ and $\ce{QR=7 \ cm}$, then find perimeter of $\ce{\triangle PQR}$.
OR
If $\ce{\angle QPR =80^{\circ}}$ find $\ce{\angle PQR}$ ?
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Q 25Case 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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