The mean and median of a statistical data are $21$ and $23$ respectively. The mode of the data is:
- ✓$27$
- B$23$
- C$22$
- D$17$
Answer: A.
View full solution →Question types
MODEL PAPER 6 (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 6 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A card is drawn at random from a pack of 52 cards. The probability that the card is drawn is a black king.
- A$\frac{11}{13}$
- B$\frac{3}{13}$
- ✓$\frac{1}{26}$
- D$\frac{1}{52}$
Answer: C.
View full solution →A coin is tossed thrice. The probability of getting at least two tails is
- A$\frac{4}{5}$
- B$\frac{2}{3}$
- C$\frac{1}{4}$
- ✓$\frac{1}{2}$
Answer: D.
View full solution →If the area of a sector of a circle is $\frac{7}{20}$ of the area of the circle, then the angle at the centre is equal to
- A$110^{\circ}$
- B$100^{\circ}$
- C$130^{\circ}$
- ✓$126^{\circ}$
Answer: D.
View full solution →A piece of wire $20 \ cm$ long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. The radius of the circle is
- A$\frac{20}{6+\pi} cm$
- B$\frac{30}{6+\pi} cm$
- ✓$\frac{60}{\pi} cm$
- D$\frac{15}{6+\pi} cm$
Answer: C.
View full solution →Assertion (A): Arithmetic mean between 8 and 12 is 10 .
Reason (R): Arithmetic mean between two numbers a and b is given as $\frac{a+b}{2}$.
Reason (R): Arithmetic mean between two numbers a and b is given as $\frac{a+b}{2}$.
- ✓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): A sphere of radius 7 cm is mounted on the solid cone of radius 6 cm and height 8 cm . The volume of the combined solid is $1737.97 cm^3$.
Reason (R): Volume of sphere is $\frac{4}{3} \pi r^3$.
Reason (R): Volume of sphere is $\frac{4}{3} \pi r^3$.
- ✓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 →From a circular piece of carboard of radius $3 \ cm$ two sectors of $90^\circ$ have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters. $($Take $\pi=22 / 7 ).$
View full solution →Prove that: $\tan ^2 \theta-\sin ^2 \theta=\tan ^2 \theta \sin ^2 \theta$
View full solution →Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii $4 \ cm$ and $3 \ cm.$
View full solution →Prove the trigonometric identity: $\frac{1}{1-\sin \theta}+\frac{1}{1+\sin \theta}=2 \sec ^2 \theta$
View full solution →The tangent at a point $A$ of a circle with centre $O$ intersects the diameter $PQ$ of the circle$($when extended$)$ at the point $B.$ If $\angle \text{BAQ}=105^{\circ}$, find $\text{APQ}$.
View full solution →Tangents $PA$ and $PB$ are drawn from an external point $P$ to two concentric circles with centre $O$ and radii $8 \ cm$ and $5 \ cm$ respectively, as shown in the figure. If $AP = 15 \ cm$ then find the length of $BP$.
View full solution →If we add $1$ to the numerator and subtract $1$ from the denominator, a fraction reduces to $1$ . It becomes $\frac{1}{2}$ if we only add $1$ to the denominator. What is the fraction? Solve the pair of the linear equation obtained by the elimination method.
View full solution →Find the median of the following frequency distribution:
View full solution →| Weekly wages $($in $₹)$ | $60-69$ | $70-79$ | $80-89$ | $90-99$ | $100-109$ | $110-119$ |
| No. of days | $5$ | $15$ | $20$ | $30$ | $20$ | $8$ |
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 →In the given figure, a triangle $\text{ABC}$ is drawn to circumscribe a circle of radius $3 \ cm ,$ such that the segments $BD$ and $D C$ into which $B C$ is divided by the point of contact $D$ are of lengths $6 \ cm$ and $8 \ cm$ respectively. Find the side $A B$, if the area of $\triangle A B C$ is $63 \ cm^2$
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View full solution →<A toy is in the form of a cone mounted on a hemisphere of radius $3.5 \ cm .$ The total height of the toy is $15.5 \ cm ;$ find the total surface area and volume of the toy.
View full solution →A train travels at a certain average speed for a distance of $54 \ km$ and then travels a distance of $63 \ km$ at an average speed of $6 \ km/h$ more than the first speed. If it takes $3$ hours to complete the total journey, what was its first average speed?
View full solution →The monthly income of $100$ families are given as below:
Calculate the modal income.
View full solution →| Income in $($in $₹.)$ | Number of families |
| $0-5000$ | $8$ |
| $5000-10000$ | $26$ |
| $10000-15000$ | $41$ |
| $15000-20000$ | $16$ |
| $20000-25000$ | $3$ |
| $25000-30000$ | $3$ |
| $30000-35000$ | $2$ |
| $35000-40000$ | $1$ |
A solid is in the shape of a right$-$circular cone surmounted on a hemisphere, the radius of each of them is being $3.5 \ cm$ and the total height of solid is $9.5 \ cm.$ Find the volume of the solid.
View full solution →In figure $AB \| PQ \| CD , AB = x$ units, $CD = y$ units and $PQ = z$ units, prove that $\frac{1}{x}+\frac{1}{y}=\frac{1}{z}$
View full solution →Read the following text carefully and answer the questions that follow:
Vijay lives in a flat in a multi-story building. Initially, his driving was rough so his father keeps eye on his driving. Once he drives from his house to Faridabad. His father was standing on the top of the building at point A as shown in the figure. At point $C$, the angle of depression of a car from the building was $60^{\circ}$. After accelerating $20 m$ from point $C ,$ Vijay stops at point $D$ to buy ice cream and the angle of depression changed to $30^{\circ}$
$i.$ Find the value of $x. (1)$
$ii.$ Find the height of the building $AB. (1)$
$iii.$ Find the distance between top of the building and a car at position $D$ ? $(2)$
OR
Find the distance between top of the building and a car at position $C$? $(2)$
View full solution →Vijay lives in a flat in a multi-story building. Initially, his driving was rough so his father keeps eye on his driving. Once he drives from his house to Faridabad. His father was standing on the top of the building at point A as shown in the figure. At point $C$, the angle of depression of a car from the building was $60^{\circ}$. After accelerating $20 m$ from point $C ,$ Vijay stops at point $D$ to buy ice cream and the angle of depression changed to $30^{\circ}$
$i.$ Find the value of $x. (1)$
$ii.$ Find the height of the building $AB. (1)$
$iii.$ Find the distance between top of the building and a car at position $D$ ? $(2)$
OR
Find the distance between top of the building and a car at position $C$? $(2)$
Read the following text carefully and answer the questions that follow:
Your friend Varun wants to participate in a $200\ m$ race. He can currently run that distance in $51$ seconds and with each day of practice it takes him $2$ seconds less. He wants to do in $31$ seconds.
$i.$ Write first four terms are in $AP$ for the given situations. $(1)$
$ii$. What is the minimum number of days he needs to practice till his goal is achieved? $(1)$
$iii$. How many second takes after $5^{th}$ days? $(2)$
$OR$
Out of $41, 30, 37$ and $39$ which term is not in the $AP$ of the above given situation? $(2)$
View full solution →Your friend Varun wants to participate in a $200\ m$ race. He can currently run that distance in $51$ seconds and with each day of practice it takes him $2$ seconds less. He wants to do in $31$ seconds.
$i.$ Write first four terms are in $AP$ for the given situations. $(1)$
$ii$. What is the minimum number of days he needs to practice till his goal is achieved? $(1)$
$iii$. How many second takes after $5^{th}$ days? $(2)$
$OR$
Out of $41, 30, 37$ and $39$ which term is not in the $AP$ of the above given situation? $(2)$
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