Using empirical relationship, the mode of a distribution whose mean is 7.2 and the median 7.1, is:
- A6.5
- ✓6.9
- C6.2
- D6.3
Answer: B.
View full solution →Question types
MODEL PAPER 4 (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 4 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following numbers cannot be the probability of an event?
- A5%
- B0.5
- ✓$\frac{1}{0.5}$
- D$\frac{0.5}{14}$
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 $\frac{5}{18}$ of the area of the circle, then the sector angle is equal to
- ✓$100^{\circ}$
- B$120^{\circ}$
- C$190^{\circ}$
- D$60^{\circ}$
Answer: A.
View full solution →In a circle of radius 21 cm, an arc subtends an angle of $60^0$ at the centre. The length of the arc is
- A18.16 cm
- B23.5 cm
- ✓22 cm
- D21 cm
Answer: C.
View full solution →Assertion (A): If $S_n$ is the sum of the first $n$ terms of an A.P., then its $n^{\text {th }}$ term $a_n$ is given by $a_n=S_n-S_{n-1}$
Reason (R): The $10^{\text {th }}$ term of the A.P. $5,8,11,14, \ldots$ is 35
Reason (R): The $10^{\text {th }}$ term of the A.P. $5,8,11,14, \ldots$ is 35
- 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): If we join two hemispheres of same radius along their bases, then we get a sphere.
Reason (R): A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is $3.3 m^2$.
Reason (R): A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is $3.3 m^2$.
- ABoth A and R are true and R is the correct explanation of A.
- ✓Both 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: B.
View full solution →The perimeter of a sector of a circle of radius $5.2 \ cm$ is $16.4 \ cm$. Find the area of the sector.
View full solution →Find the area of a quadrant of a circle , whose circumference is $22 \ cm $.
View full solution →If $\cot \theta=\frac{15}{8}$, then evaluate: $\frac{(2+2 \sin \theta)(1-\sin \theta)}{(1+\cos \theta)(2-2 \cos \theta)}$
View full solution →Prove that:
$\frac{1+\tan A}{2 \sin A}+\frac{1+\cot A}{2 \cos A}=\operatorname{cosec} A+\sec A$
View full solution →$\frac{1+\tan A}{2 \sin A}+\frac{1+\cot A}{2 \cos A}=\operatorname{cosec} A+\sec A$
In the given figure, $O$ is the centre of the circle. $\text{PA}$ and $\text{PB}$ are tangents. Show that $\text{AOBP}$ is a cyclic quadrilateral.
View full solution →During the $2011$ census, the records of various aspects like good health, death rate and literacy rate were recorded for all the States and Union territories of India. The Literacy rates of $40$ cities are given in the following table:
If it is given that the mean literacy rate is $63.5,$ then find the missing frequencies $x$ and $y.$
View full solution →| Literacy rate $($in $\%)$ | $35-40$ | $40-45$ | $45-50$ | $50-55$ | $55-60$ | $60-65$ | $65-70$ | $70-75$ | $75-80$ | $80-85$ | $85-90$ |
| Number of cities | $1$ | $2$ | $3$ | $x$ | $y$ | $6$ | $8$ | $4$ | $2$ | $3$ | $2$ |
Prove the trigonometric identity : $\sqrt{\sec ^2 \theta+\operatorname{cosec}^2 \theta}=\tan \theta+\cot \theta$
View full solution →In the given figure, the radii of two concentric circles are $13 \ cm$ and $8 \ cm. AB$ is a diameter of the bigger circle and $BD$ is a tangent to the smaller circle touching it at $D$. Find the length of $AD$.
View full solution →In the adjoining figure $, AB$ and $CD$ are two parallel tangents to a circle with centre $O. ST$ is the tangent segment between two parallel tangents touching the circle at $Q$. Show that $\angle SOT =90^{\circ}$.
View full solution →How many terms of the $AP : 9, 17, 25, ….$ must be taken to give a sum of $636?$
View full solution →Find the mean and the mode of the data given below:
| Weight (in kg) | Number of students |
| 40 - 45 | 5 |
| 45 - 50 | 11 |
| 50 - 55 | 20 |
| 55 - 60 | 24 |
| 60 - 65 | 28 |
| 65 - 70 | 12 |
From a solid cylinder of height $20 \ cm$ and diameter $12 \ cm,$ a conical cavity of height $8 \ cm$ and radius $6 \ cm$ is hallowed out. Find the total surface area of the remaining solid.
View full solution →A solid is in the shape of a cone standing on a hemisphere with both their diameters being equal to $1 \ cm$ and the height of the cone is equal to its radius. Find the volume of the solid. $[$Use $\pi=3.14 ]$
View full solution →A girl on a ship standing on a wooden platform, which is $50 \ m$ above water level, observes the angle of elevation of the top of a hill as $30^{\circ}$ and the angle of depression of the base of the hill as $60^{\circ}$ . Calculate the distance of the hill from the platform and the height of the hill.
View full solution →Solve for$ x: \frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}=\frac{2}{3} ; x \neq 1,2,3$
View full solution →Read the following text carefully and answer the questions that follow:
Jagdish has a field which is in the shape of a right angled triangle $\text{AQC.}$ He wants to leave a space in the form of a square $\text{PQRS}$ inside the field for growing wheat and the remaining for growing vegetables $($as shown in the figure$)$. In the field, there is a pole marked as $O.$
$i.$ Taking $O$ as origin, coordinates of $P$ are $(-200, 0)$ and of $Q$ are $(200, 0). \text{PQRS}$ being a square, what are the coordinates of $R$ and $S\ ?$
$ii.$ What is the area of square $\text{PQRS}\ ?$
$iii.$ What is the length of diagonal $\text{PR}$ in square $\text{PQRS}\ ?$
OR
If $S$ divides $\text{CA}$ in the ratio $K : 1,$ what is the value of $K,$ where point $A$ is $(200, 800)\ ?$
View full solution →Jagdish has a field which is in the shape of a right angled triangle $\text{AQC.}$ He wants to leave a space in the form of a square $\text{PQRS}$ inside the field for growing wheat and the remaining for growing vegetables $($as shown in the figure$)$. In the field, there is a pole marked as $O.$
$i.$ Taking $O$ as origin, coordinates of $P$ are $(-200, 0)$ and of $Q$ are $(200, 0). \text{PQRS}$ being a square, what are the coordinates of $R$ and $S\ ?$
$ii.$ What is the area of square $\text{PQRS}\ ?$
$iii.$ What is the length of diagonal $\text{PR}$ in square $\text{PQRS}\ ?$
OR
If $S$ divides $\text{CA}$ in the ratio $K : 1,$ what is the value of $K,$ where point $A$ is $(200, 800)\ ?$
Read the following text carefully and answer the questions that follow:
Ashok wanted to determine the height of a tree on the corner of his block. He knew that a certain fence by the tree was $4$ feet tall. At $3 PM,$ he measured the shadow of the fence to be $2.5$ feet tall. Then he measured the tree’s shadow to be $11.3$ feet.
$i$. What is the height of the tree?
$ii$. What will be length of shadow of tree at $12:00 \ pm$ ?
$iii$. Write the name triangle formed for this situation.
OR
What will be the length of wall at $12:00\ pm$ ?
View full solution →Ashok wanted to determine the height of a tree on the corner of his block. He knew that a certain fence by the tree was $4$ feet tall. At $3 PM,$ he measured the shadow of the fence to be $2.5$ feet tall. Then he measured the tree’s shadow to be $11.3$ feet.
$i$. What is the height of the tree?
$ii$. What will be length of shadow of tree at $12:00 \ pm$ ?
$iii$. Write the name triangle formed for this situation.
OR
What will be the length of wall at $12:00\ pm$ ?
Read the following text carefully and answer the questions that follow:
$\text{TOWER OF PISA}$ : To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. An object dropped off the top of Leaning Tower of Pisa falls vertically with constant acceleration. If $s $ is the distance of the object above the ground $($in feet$) \ t$ seconds after its release, then $s$ and $t$ are related by an equation of the form $s=a+b t^2$ where $a$ and $b$ are constants. Suppose the object is $180$ feet above the ground $1$ second after its release and $132$ feet above the ground $2$ seconds after its release.
$i$. Find the constants $a$ and $b$.
$ii$. How high is the Leaning Tower of Pisa?
$iii$. How long does the object fall?
OR
At $t = 2 \sec,$ the object is at what height?
View full solution →$\text{TOWER OF PISA}$ : To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. An object dropped off the top of Leaning Tower of Pisa falls vertically with constant acceleration. If $s $ is the distance of the object above the ground $($in feet$) \ t$ seconds after its release, then $s$ and $t$ are related by an equation of the form $s=a+b t^2$ where $a$ and $b$ are constants. Suppose the object is $180$ feet above the ground $1$ second after its release and $132$ feet above the ground $2$ seconds after its release.
$i$. Find the constants $a$ and $b$.
$ii$. How high is the Leaning Tower of Pisa?
$iii$. How long does the object fall?
OR
At $t = 2 \sec,$ the object is at what height?
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