If the difference of mode and median of a data is $24,$ then the difference of median and mean of the same data is:
- A$8$
- ✓$12$
- C$34$
- D$24$
Answer: B.
View full solution →Question types
MODEL PAPER 10 (STANDARD) 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 10 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A number is chosen from the numbers $1, 2, 3$ and denoted as $x,$ and a number is chosen from the numbers $1, 4, 9$ and denoted as $y.$ Then $P(xy < 9)$ is:
- A$\frac{7}{9}$
- ✓$\frac{5}{9}$
- C$\frac{3}{9}$
- D$\frac{1}{9}$
Answer: B.
View full solution →A bag contains $100$ cards numbered $1$ to $100.$ A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube?
- A$\frac{1}{20}$
- ✓$\frac{1}{25}$
- C$\frac{7}{100}$
- D$\frac{3}{50}$
Answer: B.
View full solution →Pankaj has a motorcycle with wheels of diameter 91 cm. There are 22 spokes in the wheel. Find the length of arc between two adjoining spokes.
- ✓13 cm
- B26 cm
- C15 cm
- D18 cm
Answer: A.
View full solution →The area of the sector of a circle with radius $6 \ cm$ which subtends an angle of $60^{\circ}$ at the centre of the circle is:
- A$\frac{152}{7} \ cm^2$
- ✓$\frac{132}{7} \ cm^2$
- C$\frac{142}{7} \ cm^2$
- D$\frac{122}{7} \ cm^2$
Answer: B.
View full solution →Assertion (A): The 11th term of an AP is 7, 9, 11, 13 is 67.
Reason (R): If $s_n$ is the sum of first $n$ terms of an AP then its $n$th term an is given by a $n=s_n+s_{n-1}$.
Reason (R): If $s_n$ is the sum of first $n$ terms of an AP then its $n$th term an is given by a $n=s_n+s_{n-1}$.
- 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.
- ✓A is true but R is false.
- DA is false but R is true.
Answer: C.
View full solution →Assertion (A): A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm . By measuring the amount of water is holds, a child finds its volume to be $345 cm^3$.
Reason (R): To calculate the volume of vessel the expression used here is $v =\pi r ^2 h+\frac{4}{3} \pi r^3$.
Reason (R): To calculate the volume of vessel the expression used here is $v =\pi r ^2 h+\frac{4}{3} \pi r^3$.
- ✓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 →If a $\cos \theta+ b \sin \theta= m$ and $a \sin \theta- b \cos \theta= n$, prove that $a ^2+ b ^2= m ^2+ n ^2$
View full solution →What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters $10 \ cm$ and $24 \ cm.$
View full solution →Find the area of a quadrant of a circle whose circumference is $22 \ cm.$
View full solution →Find the value of : $\sin 30^{\circ} \cdot \cos 60^{\circ}+\cos 30^{\circ} \cdot \sin 60^{\circ}$. Is it equal to $\sin 90^{\circ}$ or $\cos 90^{\circ}$ ?
View full solution →In Fig., there are two concentric circles with centre $O$. If $\text{ARC}$ and $\text{AQB}$ are tangents to the smaller circle from the point A lying on the larger circle, find the length of $AC$, if $AQ = 5 cm.$
View full solution →Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$ . Prove that $\angle PTQ =2 \angle OPQ$.
View full solution →The sum of $5^{\text {th }}$ and $9^{\text {th }}$ terms of an $A.P.$ is $72$ and the sum of $7^{th}$ and $12^{th}$ terms is $97$ .Find the $A.P.$
View full solution →If the median of the following frequency distribution is $32.5 $. Find the values of $f_1$ and $f_2$.
View full solution →| Class | $0 - 10$ | $10 - 20$ | $20 - 30$ | $30 - 40$ | $40 - 50$ | $50 - 60$ | $60 - 70$ | Total |
| Frequency | $f _1$ | $5$ | $9$ | $12$ | $f _2$ | $63$ | $2$ | $40$ |
Prove that $\left(\frac{1+\tan ^2 A}{1+\cot ^2 A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^2=\tan ^2 A$
View full solution →In the given figure, $O$ is the centre of the circle and $TP$ is the tangent to the circle from an external point $T$ . If $\angle P B T=30^{\circ}$, prove that $BA : AT =2: 1$.
View full solution →If $(-5)$ is a root of the quadratic equation $2 x ^2+ px +15=0$ and the quadratic equation $p \left( x ^2+ x \right)+ k =0$ has equal roots, then find the values of $p$ and $k .$
View full solution →A tent is in the shape of a right circular cylinder up to a height of 3 m and then a right circular cone, with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of ₹ 2 per square metre, if the radius of the base is 14 m.
A survey regarding the heights $($in $cm)$ of $50$ girls of $X$ of a school was conducted and the following data was obtained:
Find the mean and mode of the above data
View full solution →| Height $($in $cm)$ | $120 - 130$ | $130 - 140$ | $140 - 150$ | $150 - 160$ | $160 - 170$ | Total |
| Number of girls | $2$ | $8$ | $12$ | $20$ | $8$ | $50$ |
A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $7 \ cm$ and the height of the cone is equal to its diameter. Find the volume of the solid.
View full solution →A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{\circ},$ which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{\circ}$. Find the further time taken by the car to reach the foot of the tower from this point.
View full solution →Read the following text carefully and answer the questions that follow:
Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.
The left $-$ right $($horizontal$)$ direction is commonly called $X-$ axis.
The up $-$ down $($vertical$)$ direction is commonly called $Y-$ axis.
When we include negative values, the $x$ and $y$ axes divide the space up into $4$ pieces.
Read the information given above and below:
Two friends Veena and Arun work in the same office in Delhi. In the Christmas vacations, both decided to go
their hometowns represented by Town $A$ and Town $B$ respectively in the figure given below. Town A and Town $B$ are connected by trains from the same station $C\ ($in the given figure$)$ in Delhi.
$i$. Who will travel more distance to reach their home? $(1)$
$ii.$ Find the location of the station. $(1)$
$iii$. Find in which ratio $Y-$ axis divide Town $B$ and Station. $(2)$
OR
Find the distance between Town $A$ and Town $B. (2)$
View full solution →Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.
The left $-$ right $($horizontal$)$ direction is commonly called $X-$ axis.
The up $-$ down $($vertical$)$ direction is commonly called $Y-$ axis.
When we include negative values, the $x$ and $y$ axes divide the space up into $4$ pieces.
Read the information given above and below:
Two friends Veena and Arun work in the same office in Delhi. In the Christmas vacations, both decided to go
their hometowns represented by Town $A$ and Town $B$ respectively in the figure given below. Town A and Town $B$ are connected by trains from the same station $C\ ($in the given figure$)$ in Delhi.
$i$. Who will travel more distance to reach their home? $(1)$
$ii.$ Find the location of the station. $(1)$
$iii$. Find in which ratio $Y-$ axis divide Town $B$ and Station. $(2)$
OR
Find the distance between Town $A$ and Town $B. (2)$
Read the following text carefully and answer the questions that follow:
The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti$-$clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, $AB$ is one such tangent to a circle of radius $75 \ cm$ . Point $O$ is centre of the circle and $\angle ABO$
$=30^{\circ} . PQ$ is parallel to $OA.$
i. find the length of $AB. (1)$
ii. find the length of $OB. (1)$
iii. find the length of $AP. (2)$
OR
find the length of $PQ. (2)$
View full solution →The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti$-$clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, $AB$ is one such tangent to a circle of radius $75 \ cm$ . Point $O$ is centre of the circle and $\angle ABO$
$=30^{\circ} . PQ$ is parallel to $OA.$
i. find the length of $AB. (1)$
ii. find the length of $OB. (1)$
iii. find the length of $AP. (2)$
OR
find the length of $PQ. (2)$
Read the following text carefully and answer the questions that follow:
Two schools $P$ and $Q$ decided to award prizes to their students for two games of Hockey $₹ x$ per student and Cricket $₹ y$ per student. School $P$ decided to award a total of $₹ 9,500$ for the two games to $5$ and $4$ students respectively; while school $Q$ decided to award $₹ 7,370$ for the two games to $4 $ and $3$ students respectively.
$i$. Represent the following information algebraically $($in terms of $x$ and $y). (1)$
$ii$. What is the prize amount for hockey? $(1)$
$iii.$ Prize amount on which game is more and by how much? $(2)$
OR
What will be the total prize amount if there are $2$ students each from two games? $(2)$
View full solution →Two schools $P$ and $Q$ decided to award prizes to their students for two games of Hockey $₹ x$ per student and Cricket $₹ y$ per student. School $P$ decided to award a total of $₹ 9,500$ for the two games to $5$ and $4$ students respectively; while school $Q$ decided to award $₹ 7,370$ for the two games to $4 $ and $3$ students respectively.
$i$. Represent the following information algebraically $($in terms of $x$ and $y). (1)$
$ii$. What is the prize amount for hockey? $(1)$
$iii.$ Prize amount on which game is more and by how much? $(2)$
OR
What will be the total prize amount if there are $2$ students each from two games? $(2)$
Generate a MODEL PAPER 10 (STANDARD) paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.