The median of first $8$ prime numbers is
- ✓$9$
- B$11$
- C$13$
- D$7$
Answer: A.
View full solution →Question types
MODEL PAPER 6 (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 6 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A sphere of diameter $18 \ cm$ is dropped into a cylindrical vessel of diameter $36 \ cm,$ partly filled with water. If the sphere is completely submerged then the water level rises by
- A$4 \ cm$
- B$5 \ cm$
- ✓$3 \ cm$
- D$6 \ cm$
Answer: C.
View full solution →In the formula $\bar{X}= a + h \left(\frac{1}{N} \sum f_i u_i\right)$ for finding the mean of grouped frequency distribution $u _{ i }=$
- A$\frac{x_i+a}{2 h}$
- B$h\left(x_i-a\right)$
- ✓$\frac{x_i-a}{h}$
- D$\frac{x_i+a}{h}$
Answer: C.
View full solution →In a survey, it is found that every fifh person has a vehicle. The probability of a person $\text{NOT}$ having a vehicle, is
- A$\frac{1}{5}$
- ✓$\frac{4}{5}$
- C$5 \%$
- D$95 \%$
Answer: B.
View full solution →In the figure, ABDCA represents a quadrant of a circle of radius 7 cm a with centre A. Find the area of the shaded portion.
- A$14 cm^2$
- ✓$31.5 cm^2$
- C$24.5 cm^2$
- D$38.5 cm^2$
Answer: B.
View full solution →Assertion (A): The H.C.F. of two numbers is 16 and their product is 3072. Then their L.C.M. = 162
Reason (R): If a, b are two positive integers, then H.C.F. x L.C.M. = a x b
Reason (R): If a, b are two positive integers, then H.C.F. x L.C.M. = a x b
- 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.
- ✓A is false but R is true.
Answer: D.
View full solution →Assertion (A): Image of point (5, -16) under x-axis is (-5, 16).
Reason (R): To find image of point (x, y) under x-axis change the sign of y and to find image under y-axis change sign of x.
Reason (R): To find image of point (x, y) under x-axis change the sign of y and to find image under y-axis change sign of x.
- 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.
- ✓A is false but R is true.
Answer: D.
View full solution →A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find
i. the area of that part of the field in which the horse can graze.
ii. the increase in the grazing area if the rope were 10 m long instead of 5 m (Use $\pi=3.14$ ).
View full solution →i. the area of that part of the field in which the horse can graze.
ii. the increase in the grazing area if the rope were 10 m long instead of 5 m (Use $\pi=3.14$ ).
An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm, Find the area between the two consecutive ribs of the umbrella..
Prove the trigonometric identity:
$
\frac{\sin A+\cos A}{\sin A-\cos A}+\frac{\sin A-\cos A}{\sin A+\cos A}=\frac{2}{\sin ^2 A-\cos ^2 A}=\frac{2}{2 \sin ^2 A-1}=\frac{2}{1-2 \cos ^2 A}
$
View full solution →$
\frac{\sin A+\cos A}{\sin A-\cos A}+\frac{\sin A-\cos A}{\sin A+\cos A}=\frac{2}{\sin ^2 A-\cos ^2 A}=\frac{2}{2 \sin ^2 A-1}=\frac{2}{1-2 \cos ^2 A}
$
In two concentric circles, the radii are $OA = r \ cm$ and $OQ =6 \ cm,$ as shown in the figure. Chord $CD$ of larger circle is a tangent to smaller circle at $Q . PA$ is tangent to larger circle. If $PA =16 \ cm$ and $OP =20 \ cm,$ find the length $CD.$
View full solution → In the given figure, $\angle ABC =\angle ACB$ and $\frac{B C}{B E}=\frac{B D}{A C}$.
Show that $\angle ABE \sim \angle DBC$ and $AE \| DC$.
View full solution →Show that $\angle ABE \sim \angle DBC$ and $AE \| DC$.
game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers $1,2,3, \ldots, 12$ as shown in the figure. What is the probability that it will point to.
i. 6
ii. an even number?
iii. a prime number?
iv. a number which is a multiple of 5?
View full solution →i. 6
ii. an even number?
iii. a prime number?
iv. a number which is a multiple of 5?
If $\sin \theta+\cos \theta= p$ and $\sec \theta+\operatorname{cosec} \theta= q$, show that $q \left( p ^2-1\right)=2 p$
View full solution →Prove that $\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta}$, using identity $\sec ^2 \theta=1+\tan ^2 \theta$.
View full solution →In figure $,O$ is the centre of a circle of radius $5 \ cm . \ T$ is a point such that $OT =13 \ cm$ and $OT$ intersects circle at $E$. If $A B$ is a tangent to the circle at $E,$ find the length of $A B$. where $TP$ and $TQ$ are two tangents to the circle.
View full solution →Use elimination method to find all possible solutions of the following pair of linear equations $a x+b y-a+b=0$ and $bx - ay - a - b =0$
View full solution →The median of the following data is $525.$ Find the values of $x$ and $y,$ if the total frequency is $100.$
View full solution →| Class interval | Frequency |
| $0-100$ | $2$ |
| $100-200$ | $5$ |
| $200-300$ | $X$ |
| $300-400$ | $12$ |
| $400-500$ | $17$ |
| $500-600$ | $20$ |
| $600-700$ | $y$ |
| $700-800$ | $9$ |
| $800-900$ | $7$ |
| $900-1000$ | $4$ |
An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone.The radius of the base of each of cone and cylinder is $8 \ cm.$ The cylindrical part is $240 \ cm$ high and the conical part is $36 \ cm$ high. Find the weight of the pillar if one cubic $\ cm$ of iron weighs $7.8$ grams.
View full solution →Two cubes each of volume $125 \ cm^3$ are joined end to end. Find the volume and the surface area of the resulting $[5]$ cuboid.
View full solution →$A B C D$ is a quadrilateral in which $A D=B C$. If $P, Q, R, S$ be the midpoints of $A B, A C, C D$ and $B D$ respectively, show that PQRS is a rhombus.
View full solution →If the equation $\left(1+m^2\right) x^2+2 m c x+\left(c^2-a^2\right)=0$ has equal roots, prove that $c^2=a^2\left(1+m^2\right)$
View full solution →Read the following text carefully and answer the questions that follow:
Mr. Vinod is a pilot in Air India. During the Covid $-19$ pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. He is flying from Dubai to New Delhi with these passengers. His airplane is approaching point $A$ along a straight line and at a constant altitude h. At $10:00 \ am$, the angle of elevation of the airplane is $30^\circ $ and at $10:01 am$, it is $60^\circ .$
$i.$ What is the distance d is covered by the airplane from $10:00 \ am$ to $10:01 \ am$ if the speed of the airplane is constant and equal to $600$ miles/hour?
$ii.$ What is the altitude h of the airplane? $($round answer to $2$ decimal places$)$
$iii.$ Find the distance between passenger and airplane when the angle of elevation is $30^\circ .$
OR
Find the distance between passenger and airplane when the angle of elevation is $60^\circ .$
View full solution →Mr. Vinod is a pilot in Air India. During the Covid $-19$ pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. He is flying from Dubai to New Delhi with these passengers. His airplane is approaching point $A$ along a straight line and at a constant altitude h. At $10:00 \ am$, the angle of elevation of the airplane is $30^\circ $ and at $10:01 am$, it is $60^\circ .$
$i.$ What is the distance d is covered by the airplane from $10:00 \ am$ to $10:01 \ am$ if the speed of the airplane is constant and equal to $600$ miles/hour?
$ii.$ What is the altitude h of the airplane? $($round answer to $2$ decimal places$)$
$iii.$ Find the distance between passenger and airplane when the angle of elevation is $30^\circ .$
OR
Find the distance between passenger and airplane when the angle of elevation is $60^\circ .$
Read the following text carefully and answer the questions that follow:
The Chief Minister of Delhi launched the, 'Switch Delhi', an electric vehicle mass awareness campaign in the National Capital. The government has also issued tenders for setting up $100$ charging stations across the city. Each station will have five charging points. For demo charging station is set up along a straight line and has charging points at $A\left(\frac{-7}{3}, 0\right), B\left(0, \frac{7}{4}\right), C (3,4), D (7,7)$ and $E ( x , y )$. Also, the distance between $C$ and $E$ is $10$ units.
$i$. What is the distance $DE$?
$ii$. What is the value of $x + y$?
$iii$. Points $C, D, E$ are collinear or not?
OR
What is the ratio in which $B$ divides $AC$?
View full solution →The Chief Minister of Delhi launched the, 'Switch Delhi', an electric vehicle mass awareness campaign in the National Capital. The government has also issued tenders for setting up $100$ charging stations across the city. Each station will have five charging points. For demo charging station is set up along a straight line and has charging points at $A\left(\frac{-7}{3}, 0\right), B\left(0, \frac{7}{4}\right), C (3,4), D (7,7)$ and $E ( x , y )$. Also, the distance between $C$ and $E$ is $10$ units.
$i$. What is the distance $DE$?
$ii$. What is the value of $x + y$?
$iii$. Points $C, D, E$ are collinear or not?
OR
What is the ratio in which $B$ divides $AC$?
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