The marks obtained by $9$ students in Mathematics are $59, 46, 30, 23, 27, 40, 52, 35$ and $29.$ The median of the data is
- A$29$
- ✓$35$
- C$40$
- D$30$
Answer: B.
View full solution →Question types
MODEL PAPER 7 (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 7 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two dice are rolled together. What is the probability of getting a sum greater than 10?
- A$\frac{5}{18}$
- B$\frac{1}{9}$
- C$\frac{1}{6}$
- ✓$\frac{1}{12}$
Answer: D.
View full solution →In a family of 3 children, the probability of having at least one boy is
- A$\frac{1}{8}$
- ✓$\frac{7}{8}$
- C$\frac{3}{4}$
- D$\frac{5}{8}$
Answer: B.
View full solution →A piece of paper in the shape of a sector of a circle (see figure 1) is rolled up to form a right-circular cone (see figure 2). The value of angle $\theta$ is:
- A$\frac{5 \pi}{13}$
- B$\frac{6 \pi}{13}$
- C$\frac{10 \pi}{13}$
- D$\frac{9 \pi}{13}$
A chord of a circle of radius $10 \ cm$ subtends a right angle at the centre. The area of the minor segments $($given, $\pi=3.14 )$ is
- A$32.5 \ cm^2$
- B$34.5 \ cm^2$
- C$30.5 \ cm^2$
- ✓$28.5 \ cm^2$
Answer: D.
View full solution →Assertion (A): The sum of series with the nth term $t_n=(9-5 n)$ is 220 when no. of terms $n=6$.
Reason (R): Sum of first $n$ terms in an A.P. is given by the formula: $S n=2 n \times[2 a+(n-1) d]$
Reason (R): Sum of first $n$ terms in an A.P. is given by the formula: $S n=2 n \times[2 a+(n-1) d]$
- ✓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 $(A):$ Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $10 a^2.$
Reason $(R):$ The total surface area of a cube having side $a = 6 a^2.$
Reason $(R):$ The total surface area of a cube having side $a = 6 a^2.$
- ✓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 $A$.
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →What is the angle subtended at the centre of a circle of radius $6 \ cm$ by an arc of length $6 \ \pi cm$ ?
View full solution →In Figure, OACB is a quadrant of a circle with centre O and radius 7 cm . If $OD =3 cm$, then find the area of the shaded region.
View full solution →If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=1,0^{\circ}<(A+B)<90^{\circ}$ and $A>B$ then find $A$ and $B$.
View full solution →If $\sin \theta+\cos \theta=\sqrt{3}$, then find the value of $\sin \theta \cdot \cos \theta$.
View full solution →A circle touches all the four sides of a quadrilateral $\text{ABCD}$. Prove that $A B+C D=B C+D A$.
View full solution →The pilot of an aircraft flying horizontally at a speed of $1200 \ km/h$r. observes that the angle of depression of a point on the ground changes from $30^\circ$ to $45^\circ$ in $15$ seconds. Find the height at which the aircraft is flying.
View full solution →Prove that: $\frac{1}{\operatorname{cosec} A-\cot A}-\frac{1}{\sin A}=\frac{1}{\sin A}-\frac{1}{\operatorname{cosec} A+\cot A}$.
View full solution →If $\text{ABC}$ is isosceles with $AB = AC,$ prove that the tangent at $A$ to the circumcircle of $\text{ABC}$ is parallel to $BC$.
View full solution →The tangent at a point $C$ of a circle and a diameter $AB$ when extended intersect at $P$ . If $\angle PCA =110^{\circ}$, find $\angle C B A$.
$[$Hint: Join $C$ with centre $O]$.
If $\text{ABC}$ is isosceles with $AB = AC,$ prove that the tangent at $A$ to the circumcircle of $\text{ABC}$ is parallel to $BC$.
View full solution →$[$Hint: Join $C$ with centre $O]$.
If $\text{ABC}$ is isosceles with $AB = AC,$ prove that the tangent at $A$ to the circumcircle of $\text{ABC}$ is parallel to $BC$.
The hypotenuse of a grassy land in the shape of a right triangle is $1$ metre more than twice the shortest side. If the third side is $7$ metres more than the shortest side, find the sides of the grassy land.
View full solution →The sum of the first $9$ terms of an $AP$ is $81$ and that of its first $20$ terms is $400.$ Find the first term and the common difference of the $AP.$
View full solution →A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of cone is $4 \ cm$ and the diameter of the base is $8 \ cm.$ Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy.
View full solution →A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is $3.5 \ cm$ and the height of the cone is $4 \ cm.$ The solid is placed in a cylindrical tub, full of water, in such a way that the whole solid is submerged in water. If the radius of the cylinder is $5 \ cm$ and its height is $10.5 \ cm,$ find the volume of water left in the cylindrical tub. $\left(\right.$ Use $\left.\pi=\frac{22}{7}\right)$
View full solution →The base $\text{BC}$ of an equilateral triangle $\text{ABC}$ lies on $y-$axis. The co$-$ordinates of point $C$ are $(0,3).$ The origin is the mid$-$point of the base. Find the co$-$ordinates of the point $A$ and $B.$ Also find the co$-$ordinates of another point $D$ such that $\text{BACD}$ is a rhombus.
View full solution →A man travels $370 \ km,$ partly by train and partly by car. If he covers $250 \ km$ by train and the rest by car, it takes him $4$ hours. But, if he travels $130 \ km$ by train and the rest by car, he takes $18$ minutes longer. Find the speed of the train and that of the car.
View full solution →Read the following text carefully and answer the questions that follow:
Statue of a Pineapple: The Big Pineapple is a heritage $-$ listed tourist attraction at Nambour Connection Road, Woombye, Sunshine Coast Region, Queensland, Australia. It was designed by Peddle Thorp and Harvey, Paul Luff, and Gary Smallcombe and Associates. It is also known as Sunshine Plantation. It was added to the Queensland Heritage Register on $6$ March $2009$.
Kavita last year visited Nambour and wanted to find the height of a statue of a pineapple. She measured the pineapple's shadow and her own shadow. Her height is $156 \ cm$ and casts a shadow of $39 \ cm$. The length of shadow of pineapple is $4 \ m$.
$i$. What is the height of the pineapple?
$ii$. What is the height Kavita in metres?
$iii.$ Write the type of triangles used to solve this problem.
OR
Which similarity criterion of triangle is used?
View full solution →Statue of a Pineapple: The Big Pineapple is a heritage $-$ listed tourist attraction at Nambour Connection Road, Woombye, Sunshine Coast Region, Queensland, Australia. It was designed by Peddle Thorp and Harvey, Paul Luff, and Gary Smallcombe and Associates. It is also known as Sunshine Plantation. It was added to the Queensland Heritage Register on $6$ March $2009$.
Kavita last year visited Nambour and wanted to find the height of a statue of a pineapple. She measured the pineapple's shadow and her own shadow. Her height is $156 \ cm$ and casts a shadow of $39 \ cm$. The length of shadow of pineapple is $4 \ m$.
$i$. What is the height of the pineapple?
$ii$. What is the height Kavita in metres?
$iii.$ Write the type of triangles used to solve this problem.
OR
Which similarity criterion of triangle is used?
Read the following text carefully and answer the questions that follow:
India meteorological department observes seasonal and annual rainfall every year in different sub$-$divisions of our country
I
t helps them to compare and analyse the results. The table given below shows sub$-$division wise seasonal $($monsoon$)$ rainfall $($mm$)$ in $2018:$
$i.$ Write the modal class.
$ii.$ Find the median of the given data.
$iii.$ If sub$-$division having at least $1000$ mm rainfall during monsoon season$,$ is considered good rainfall sub$-$ division, then how many subdivisions had good rainfall?
$OR$
Find the mean rainfall in this season.
View full solution →India meteorological department observes seasonal and annual rainfall every year in different sub$-$divisions of our country
It helps them to compare and analyse the results. The table given below shows sub$-$division wise seasonal $($monsoon$)$ rainfall $($mm$)$ in $2018:$
| Rainfall (mm) | Number of Sub-divisions |
| $200-400$ | $2$ |
| $400-600$ | $4$ |
| $600-800$ | $7$ |
| $800-1000$ | $4$ |
| $1000-1200$ | $2$ |
| $1200-1400$ | $3$ |
| $1400-1600$ | $1$ |
| $1600-1800$ | $1$ |
$ii.$ Find the median of the given data.
$iii.$ If sub$-$division having at least $1000$ mm rainfall during monsoon season$,$ is considered good rainfall sub$-$ division, then how many subdivisions had good rainfall?
$OR$
Find the mean rainfall in this season.
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