The number of spherical bullets each $5\ dm$ in diameter which can be cast from a rectangular block of lead $11 m$ long, $10 m$ broad and $5$ high is
- ✓$8400$
- B$5600$
- C$6300$
- D$4200$
Answer: A.
View full solution →Question types
Model Paper 10 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 10 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
To draw a histogram to represent the following frequency distribution :
The adjusted frequency for the class 25-45 is
| Class interval | 5-10 | 10-15 | 15-25 | 25-45 | 45-75 |
| Frequency | 6 | 12 | 10 | 8 | 15 |
- A6
- B5
- ✓2
- D3
Answer: C.
View full solution →Line sgements $AB$ and $CD$ intersect at $O$ such that $AC \| DB$. If $\angle CAB =45^{\circ}$ and $\angle CDB =55^{\circ}$, then $\angle BOD =$
- A$135^{\circ}$
- ✓$80^{\circ}$
- C$100^{\circ}$
- D$90^{\circ}$
Answer: B.
View full solution →If a linear equation has solutions $(1, 2), (-1, -16)$ and $(0, -7)$, then it is of the form
- ✓$y=9 x-7$
- B$9 x-y+7=0$
- C$x-9 y=7$
- D$x=9 y-7$
Answer: A.
View full solution →The simplest rationalising factor of $\sqrt[3]{500}$, is
- A$\sqrt{3}$
- ✓$\sqrt[3]{2}$
- C$2 \sqrt{3}$
- D$\sqrt[3]{5}$
Answer: B.
View full solution →Assertion (A): The point (1, 1) is the solution of x + y = 2.
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
- ✓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.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion $(A)$ : The side of an equilateral triangle is $6 \ cm$ then the height of the triangle is $9 \ cm$.
Reason $(R)$ : The height of an equilateral triangle is $\frac{\sqrt{3}}{2} a$.
Reason $(R)$ : The height of an equilateral triangle is $\frac{\sqrt{3}}{2} a$.
- 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 $A$.
- C$A$ is true but $R$ is false.
- ✓$A$ is false but $R$ is true.
Answer: D.
View full solution →The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).
A three-wheeler scooter charges ₹ 15 for first kilometer and ₹ 8 each for every subsequent kilometer. For a distance of x km, an amount of y is paid. Write the linear equation representing the above information.
In given figure, $\angle A B C=69^{\circ}, \angle A C B=31^{\circ}$, find $\angle B D C$.
View full solution →In a given figure, $O$ is the centre of a circle and $P Q$ is a diameter. If $\angle R O S=40^{\circ}$, find $\angle R T S$.
View full solution →The surface areas of two spheres are in the ratio of $4 : 25$. Find the ratio of their volumes.
View full solution →In fig find the vertices' co-ordinates of $\triangle ABC$
View full solution →Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.
Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\triangle ABC$ as shown in Fig., Show that $BC =\frac{1}{2} QR$
View full solution →Write linear equation 3x + 2y =18 in the form of ax + by + c = 0. Also write the values of a, b and c. Are (4, 3) and (1, 2) solution of this equation?
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13 m, 14 m$ and $15 m$. The advertisements yield an earning of $Rs\ 2000$ per $m ^2$ a year. A company hired one of its walls for $6$ months. How much rent did it pay?
View full solution →Using factor theorem, factorize the polynomial: $x^3-6 x^2+3 x+10$
View full solution →In each of the figures given below, $A B \| C D$. Find the value of $x^{\circ}$ in each other 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 →In Fig, name the following:
i. Five line segments
ii. Five rays
iii. Four collinear points
iv. Two pairs of non-intersecting line segments
i. Five line segments
ii. Five rays
iii. Four collinear points
iv. Two pairs of non-intersecting line segments
If $x=2-\sqrt{3}$, find the value of $\left(x-\frac{1}{x}\right)^3$.
View full solution →Read the following text carefully and answer the questions that follow:
As shown In the village of Surya there was a big pole $PC$. This pole was tied with a strong wire of $10 m$ length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of $10 m$ so that it can reach at point $P$ on the pole and this should make $60^{\circ}$ with line $AC. $
$i.$ Show that $\triangle APC$ and $\triangle BPC$ are congruent.
$ii.$ Find the value of $\angle x$.
$iii.$ What is the value of $\angle PBC$ ?
OR
Find the value of $\angle y$.
View full solution →As shown In the village of Surya there was a big pole $PC$. This pole was tied with a strong wire of $10 m$ length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of $10 m$ so that it can reach at point $P$ on the pole and this should make $60^{\circ}$ with line $AC. $
$i.$ Show that $\triangle APC$ and $\triangle BPC$ are congruent.
$ii.$ Find the value of $\angle x$.
$iii.$ What is the value of $\angle PBC$ ?
OR
Find the value of $\angle y$.
A construction company purchased a big cylindrical vessel to keep some liquid on it. Before using this vessel, the company decided to paint it properly. It costed $₹\ 3300$ to paint the inner curved surface of this $10 \ m$ deep cylindrical vessel at the rate of $₹\ 30$ per $m^2$.
$i.$ Find the inner curved surface area of the vessel,
$ii.$ Find the inner radius of the base and capacity of the vessel.
View full solution →$i.$ Find the inner curved surface area of the vessel,
$ii.$ Find the inner radius of the base and capacity of the vessel.
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