An icecream cone has hemispherical top. If the height of the cone is $9 \ cm$ and base radius is $2.5 \ cm,$ then the volume of icecream is
- ✓$91.67 \ cm^3$
- B$96.67 \ cm^3$
- C$90.67 \ cm^3$
- D$91.76 \ cm^3$
Answer: A.
View full solution →Question types
Model Paper 2 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
01
M.C.Q
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
8 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\sqrt{3}$ is a polynomial of degree.
- A$0$
- B2
- C$\frac{1}{2}$
- D1
In a $\ce{\triangle ABC}$, if $\angle A-\angle B=42^{\circ}$ and $\angle B-\angle C=21^{\circ}$ then $\angle B= ?$
- A$95^{\circ}$
- B$63^{\circ}$
- ✓$53^{\circ}$
- D$32^{\circ}$
Answer: C.
View full solution →The line represented by the equation x + y = 16 passes through (2, 14). How many more lines pass through the point (2, 14)
- A10
- B2
- Cmany
- D100
If $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$, then the value of $\frac{1}{\sqrt{3}-\sqrt{2}}$ is
- ✓$3.146$
- B$\frac{1}{3.146}$
- C$0.318$
- D$\frac{1}{\sqrt{1.732}-\sqrt{1.414}}$
Answer: A.
View full solution →Assertion (A): The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.
Reason (R): (0, 3) satisfies the equation 3x + 4y = 12.
Reason (R): (0, 3) satisfies the equation 3x + 4y = 12.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Assertion $(A):$ The height of the triangle is $18 \ cm$ and its area is $72 \ cm^2$. Its base is $8 \ cm.$
Reason $(R):$ Area of a triangle $=\frac{1}{2} \times$ base $\times$ height
Reason $(R):$ Area of a triangle $=\frac{1}{2} \times$ base $\times$ height
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ 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.
Answer: A.
View full solution →Cost of pen is two half times the cost of a pencil. Express this situation as a linear equation in two variable.
The following values of x and y are thought to satisfy a linear equation :
| X | 1 | 2 |
| y | 1 | 3 |
In the given figure, $O$ is the centre of the circle and $\ce{\angle AOB=70^{\circ}}$. Calculate the values of $\ce{(i) \angle OCA, (ii) \angle OAC}$.
View full solution →
Draw the graphs of y = x and y = -x in the same graph. Also find the co-ordinates of the point where the two lines intersect.
$\ce{\triangle ABC}$ is an isosceles triangle in which $\ce{AB = AC}$. Side $BA$ is produced to $D$ such that $\ce{AD = AB}$. Show that $\ce{\angle BCD}$ is a right angle.
View full solution →A heap of wheat is in the form of a cone whose diameter is $10.5 m$ and height is $3 m.$ Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
View full solution →The sides of a triangular plot are in the ratio of $3 : 5 : 7$ and its perimeter is $300 m.$ Find its area.
View full solution →The following table shows the average daily earnings of 40 general stores in a market, during a certain week:
Draw a histogram to represent the above data.
| Daily earning (in rupees) | 700-750 | 750-800 | 800-850 | 850-900 | 900-950 | 950-1000 |
| Number of stores | 6 | 9 | 2 | 7 | 11 | 5 |
In each of the figures given below, $AB \| CD$. Find the value of $x^{\circ}$ in each case.
View full solution →In the given figure, $AB \| CD \| EF , \angle D B G=x, \angle E D H=y, \angle A E B=z, \angle E A B=90^{\circ}$ and $\angle B E F=65^{\circ}$. Find the values of $x , y$ and z .
View full solution →i. AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.
ii. BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
ii. BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
If x is a positive real number and exponents are rational numbers, simplify $\left(\frac{x^b}{x^c}\right)^{b+c-a} \cdot\left(\frac{x^c}{x^a}\right)^{c+a-b} \cdot\left(\frac{x^a}{x^b}\right)^{a+b-c}$.
View full solution →Read the following text carefully and answer the questions that follow:
Modern curricula include several problem$-$solving strategies. Teachers model the process, and students work independently to copy it. Sheela Maths teacher of class $9^{th}$ wants to explain the properties of parallelograms in a creative way, so she gave students colored paper in the shape of a quadrilateral and then ask the students to make a parallelogram from it by using paper folding.
$i.$ How can a parallelogram be formed by using paper folding?
$ii.$ If $\angle RSP =30^{\circ}$, then find $\angle RQP$.
$iii.$ If $\angle RSP =50^{\circ}$, then find $\angle SPQ$ ?
OR
If $SP =3 cm$, Find the $RQ.$
View full solution →Modern curricula include several problem$-$solving strategies. Teachers model the process, and students work independently to copy it. Sheela Maths teacher of class $9^{th}$ wants to explain the properties of parallelograms in a creative way, so she gave students colored paper in the shape of a quadrilateral and then ask the students to make a parallelogram from it by using paper folding.
$i.$ How can a parallelogram be formed by using paper folding?
$ii.$ If $\angle RSP =30^{\circ}$, then find $\angle RQP$.
$iii.$ If $\angle RSP =50^{\circ}$, then find $\angle SPQ$ ?
OR
If $SP =3 cm$, Find the $RQ.$
Read the following text carefully and answer the questions that follow:
Reeta was studying in the class $9^{th} C$ of St. Surya Public school, Mehrauli, New Delhi$-110030$
Once Ranjeet and his daughter Reeta were returning after attending teachers' parent meeting at Reeta's school.
As the home of Ranjeet was close to the school so they were coming by walking.
Reeta asked her father, "Daddy how old are you?"
Ranjeet said, "Sum of ages of both of us is $55$ years, After $10$ years my age will be double of you.
$i.$ What is the second equation formed?
$ii.$ What is the present age of Reeta in years?
$iii.$ What is the present age of Ranjeet in years?
OR
If the ratio of age of Reeta and her mother is $3 : 7$ then what is the age of Reeta's mother in years?
View full solution →Reeta was studying in the class $9^{th} C$ of St. Surya Public school, Mehrauli, New Delhi$-110030$
Once Ranjeet and his daughter Reeta were returning after attending teachers' parent meeting at Reeta's school.
As the home of Ranjeet was close to the school so they were coming by walking.
Reeta asked her father, "Daddy how old are you?"
Ranjeet said, "Sum of ages of both of us is $55$ years, After $10$ years my age will be double of you.
$i.$ What is the second equation formed?
$ii.$ What is the present age of Reeta in years?
$iii.$ What is the present age of Ranjeet in years?
OR
If the ratio of age of Reeta and her mother is $3 : 7$ then what is the age of Reeta's mother in years?
Read the following text carefully and answer the questions that follow:
$11 \ 950-1000 5$ Vinod and Basant have an adventure tourism business in Rishikesh. They have a resort in Rishikesh but now they are planning to build some tent houses too.
The newly built tent house will have all the basic amenities and it will attract the young tourists coming for adventure. Their conical tent is $9 m$ high and the radius of its base is $12 m.$
$i.$ What is the cost of the canvas required to make it, if $1 m^2$ canvas costs $₹ 10$?
$ii.$ How many persons can be accommodated in the tent, if each person requires $2 m^2$ on the ground?
$iii.$ How many persons can be accommodated in the tent, if each person requires $15 m^3$ of space to breathe in?
OR
If each person requires $20 m^3$ of space to breathe in and $100$ person can be accommodated then what should be height of tent?
View full solution →$11 \ 950-1000 5$ Vinod and Basant have an adventure tourism business in Rishikesh. They have a resort in Rishikesh but now they are planning to build some tent houses too.
The newly built tent house will have all the basic amenities and it will attract the young tourists coming for adventure. Their conical tent is $9 m$ high and the radius of its base is $12 m.$
$i.$ What is the cost of the canvas required to make it, if $1 m^2$ canvas costs $₹ 10$?
$ii.$ How many persons can be accommodated in the tent, if each person requires $2 m^2$ on the ground?
$iii.$ How many persons can be accommodated in the tent, if each person requires $15 m^3$ of space to breathe in?
OR
If each person requires $20 m^3$ of space to breathe in and $100$ person can be accommodated then what should be height of tent?
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