Mean and median of some data are $32$ and $30$ respectively. Using empirical relation, mode of the data is:
- A$36$
- B$30$
- C$20$
- ✓$26$
Answer: D.
View full solution →Question types
MODEL PAPER 8 (BASIC) 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 (1 Marks)
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 8 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If three coins are tossed simultaneously, what is the probability of getting at most one tail?
- A$\frac{3}{8}$
- ✓$\frac{5}{8}$
- C$\frac{7}{8}$
- D$\frac{4}{8}$
Answer: B.
View full solution →A die is thrown once. Find the probability of getting a number less than 7.
- A$\frac{1}{6}$
- B$0$
- C$\frac{5}{6}$
- ✓1
Answer: D.
View full solution →The area of the sector of a circle of radius $10.5 \ cm$ is $69.3 \ cm^2$. Find the central angle of the sector.
- A$85^\circ$
- ✓$72^\circ$
- C$70^\circ$
- D$26^\circ$
Answer: B.
View full solution →The area of a sector of angle a (in degrees) of a circle with radius R is:
- A$\frac{\alpha}{180} \times 2 \pi R$
- B$\frac{\alpha}{180} \times \pi R^2$
- C$\frac{\alpha}{360} \times 2 \pi R$
- ✓$\frac{\alpha}{360} \times \pi R^2$
Answer: D.
View full solution →Assertion (A): The constant difference between any two terms of an AP is commonly known as common difference.
Reason (R): The common difference of 2, 4, 6, 8 this A.P. is 2.
Reason (R): The common difference of 2, 4, 6, 8 this A.P. is 2.
- ✓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): In the given figure, a sphere circumscribes a right cylinder whose height is 8 cm and radius of the base is 3 cm. The ratio of the surface area of the sphere and the cylinder is 6: 11
Reason (R): Ratio of their surface area $=\frac{\text { Sur face area of sphere }}{\text { Surface area of cylinder }}$
Reason (R): Ratio of their surface area $=\frac{\text { Sur face area of sphere }}{\text { Surface area of cylinder }}$
- ✓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 →Find the area of the minor and the major sectors of a circle with radius $6 \ cm ,$ if the angle subtended by the minor arc at the centre is $60^{\circ}. ($Use $\pi=3.14 )$
View full solution →A chord of a circle of radius $10 \ cm$ subtends a right angle at the centre. Find the area of the minor segment. $[$Use $\pi=3.14].$
View full solution →Prove that $(\sin \theta+\cos \theta)(\tan \theta+\cot \theta)=\sec \theta+\operatorname{cosec} \theta$.
View full solution →In $\triangle \text{ABC}$, right$-$angled at $\text{B , AB} =5 \ cm$ and $\angle \text{ACB} =30^{\circ}$. Determine the lengths of sides $\text{BC}$ and $\text{AC}.$
View full solution →From a point $P, 10 \ cm$ away from the centre of a circle, a tangent $PT$ of length $8 \ cm$ is drawn. Find the radius of the circle.
View full solution →Weekly income of $600$ families is given below:
Find the median.yuj
View full solution →| Income $($in $Rs)$ | $0-1000$ | $1000-2000$ | $2000-3000$ | $3000-4000$ | $4000-5000$ | $5000-6000$ |
| No. of Families | $250$ | $190$ | $100$ | $40$ | $15$ | $5$ |
If $\operatorname{cosec} A+\cot A=m$. show that $\frac{m^2-1}{m^2+1}=\cos A$.
View full solution →In the figure, $X Y$ and $M N$ are two parallel tangents to a circle with centre $O$ and another tangent $A B$ with point of contact $C$ intersecting $XY$ at $A$ and $MN$ at $B$ . Prove that $\angle AOB =90^{\circ}$.
View full solution →Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line$-$segment joining the points of contact at the centre.
View full solution →If the $m ^{\text {th }}$ term of an $A.P$. is $\frac{1}{n}$ and $n ^{\text {th }}$ term be $\frac{1}{m},$ then show that its $( mn )^{\text {th }}$ term is $1$ .
View full solution →The following table gives the marks obtained by $50$ students in a class test:
Calculate the mean and median for the above data.
View full solution →| Marks | $11-15$ | $16-20$ | $21-25$ | $26-30$ | $31-35$ | $36-40$ | $41-45$ | $46-50$ |
| Number of students | $2$ | $3$ | $6$ | $7$ | $14$ | $12$ | $4$ | $2$ |
Calculate the mean and median for the above data.
An ice$-$cream filled cone having radius $5 \ cm$ and height $10 \ cm$ is as shown in the figure. Find the volume of the ice$-$cream in $7$ such cones.
View full solution →A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure. If the height of the cylinder is $10 \ cm$ and its base is of radius $3.5 \ cm ,$ find the total surface area of the article.
View full solution →From a point $P$ on the ground, the angle of elevation of the top of a 10 m tall building is $30^{\circ}$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point $P$. (use $\sqrt{3}=1.73$ )
View full solution →Two pipes together can fill a tank in $\frac{15}{8}$ hours. The pipe with larger diameter takes $2$ hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.
View full solution →Read the following text carefully and answer the questions that follow:
A satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of $x$ and $y-$ axes. If we go $2 \ c$m east and $3 \ cm$ north from the house, then we reach to a Grocery store. If we go $4 \ c$m west and $6 \ cm$ south from the house, then we reach to an Electricians's shop. If we go $6 \ cm$ east and $8 \ c$m south from the house, then we reach to a food cart. If we go $6 \ cm$ west and $8 \ cm$ north from the house, then we reach a bus stand.
Scale:
$x-$ axis: $1 \ cm = 1$ unit
$y -$ axis: $1 \ cm = 1$ unit
$i.$ What is the distance between the grocery store and food cart?
$ii$. What is the distance of the bus stand from the house?
$iii$. If the grocery store and electricians shop lie on a line, then what will be the ratio of distance of house from grocery store to that from electrician's shop?
OR
What are the ratio of distances of the house from bus stand to food cart?
View full solution →A satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of $x$ and $y-$ axes. If we go $2 \ c$m east and $3 \ cm$ north from the house, then we reach to a Grocery store. If we go $4 \ c$m west and $6 \ cm$ south from the house, then we reach to an Electricians's shop. If we go $6 \ cm$ east and $8 \ c$m south from the house, then we reach to a food cart. If we go $6 \ cm$ west and $8 \ cm$ north from the house, then we reach a bus stand.
Scale:
$x-$ axis: $1 \ cm = 1$ unit
$y -$ axis: $1 \ cm = 1$ unit
$i.$ What is the distance between the grocery store and food cart?
$ii$. What is the distance of the bus stand from the house?
$iii$. If the grocery store and electricians shop lie on a line, then what will be the ratio of distance of house from grocery store to that from electrician's shop?
OR
What are the ratio of distances of the house from bus stand to food cart?
Read the following text carefully and answer the questions that follow:
Observe the figures given below carefully and answer the questions:
$i$. Name the figure $(s)$ where in two figures are similar.
$ii$. Name the figure $(s)$ wherein the figures are congruent.
$iii$. Prove that congruent triangles are also similar but not the converse.
OR
What more is least needed for two similar triangles to be congruent?
View full solution →Observe the figures given below carefully and answer the questions:
$i$. Name the figure $(s)$ where in two figures are similar.
$ii$. Name the figure $(s)$ wherein the figures are congruent.
$iii$. Prove that congruent triangles are also similar but not the converse.
OR
What more is least needed for two similar triangles to be congruent?
Read the following text carefully and answer the questions that follow:
Architect: An architect is a skilled professional who plans and designs buildings and generally plays a key role in their construction. Architects are highly trained in the art and science of building design. Since they bear responsibility for the safety of their buildings' occupants, architects must be professionally licensed.Vishu is a licensed architect and design very innovative house. She has made a house layout for her client which is given below. In the layout, the design and measurements has been made such that area of two bedrooms and kitchen together is $95$ sq. m.
$i.$ Which pair of linear equations does describe this situation?
$ii.$ What is the length of the outer boundary of the layout?
$iii.$ What is the area of the bedroom $1?$
OR
What is the area of living room in the layout?
View full solution →Architect: An architect is a skilled professional who plans and designs buildings and generally plays a key role in their construction. Architects are highly trained in the art and science of building design. Since they bear responsibility for the safety of their buildings' occupants, architects must be professionally licensed.Vishu is a licensed architect and design very innovative house. She has made a house layout for her client which is given below. In the layout, the design and measurements has been made such that area of two bedrooms and kitchen together is $95$ sq. m.
$i.$ Which pair of linear equations does describe this situation?
$ii.$ What is the length of the outer boundary of the layout?
$iii.$ What is the area of the bedroom $1?$
OR
What is the area of living room in the layout?
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