If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data:
- Adecreases by 1
- Bremains unchanged
- ✓decreases by 2
- Ddecreases by 2n
Answer: C.
View full solution →Question types
MODEL PAPER 5 (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 5 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a 6?
- ✓$\frac{1}{13}$
- B$\frac{3}{26}$
- C$\frac{1}{52}$
- D$\frac{4}{52}$
Answer: A.
View full solution →An event is unlikely to happen. Its probability is closest to
- ✓
- B0.0001
- C0.1
- D1
Answer: A.
View full solution →A car has two wipers which do not overlap. Each wiper has a blade of length 42 cm sweeping through an angle of $120^{\circ}$. Find the total area cleaned at each sweep of the blades.
- A$5544 cm^2$
- ✓$3696 cm^2$
- C$4224 cm^2$
- D$1848 cm^2$
Answer: B.
View full solution →A horse is grazing in a field. It is tied to a pole with a rope of length $6 m.$ The horse moves from point $A$ to point $B$ making an arch with an angle of $70^\circ .$ Find the area of the sector grazed by the horse.
- A$22.99 m$
- B$20.99 m$
- ✓$21.99 m$
- D$21 m$
Answer: C.
View full solution →Assertion (A): Common difference of the AP -5, -1, 3, 7, ... is 4.
Reason (R): Common difference of the AP a, a + d, a + 2d, ... is given by d = 2nd term - 1st term.
Reason (R): Common difference of the AP a, a + d, a + 2d, ... is given by d = 2nd term - 1st term.
- ✓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 5 cm are joined end to end. The total surface area of the resulting cuboid is 350 $cm ^2$.
Reason (R): Total surface area of a cuboid is 2(lb + bh + hl)
Reason (R): Total surface area of a cuboid is 2(lb + bh + hl)
- 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 →If a chord of a circle of radius $10 \ cm$ subtends an angle of $60^{\circ}$ at the centre of the circle, find the area of the corresponding minor segment of the circle. $($Use $\pi=3.14$ and $\sqrt{3}=1.73 )$
View full solution →In a circle of radius $21 \ cm,$ an arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the sector formed by the arc. Also, find the length of the arc.
View full solution →If $m \sin A+n \cos A=p$ and $m \cos A-n \sin A=q$, prove that $m^2+n^2=p^2+q^2$
View full solution →Prove that: $\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A$
View full solution →In figure $, PQ$ is a tangent from an external point $P$ to a circle with centre $O$ and $OP$ cuts the circle at $T$ and $\text{QOR}$ is a diameter. If $\angle POR =130^{\circ}$ and $S$ is a point on the circle, find $\angle 1+\angle 2$.
View full solution →The weights $($in $kg)$ of $50$ wild animals of a National Park were recorded and the following data was obtained:
Find the mean weight $($in $kg)$ of animals, using assumed mean method.
View full solution →| Weight $($in $kg)$ | Number of animals |
| $100 - 110$ | $4$ |
| $110 - 120$ | $12$ |
| $120 - 130$ | $23$ |
| $130 - 140$ | $8$ |
| $140 - 150$ | $3$ |
If $\tan \theta+\frac{1}{\tan \theta}=2$, find the value of $\tan ^2 \theta+\frac{1}{\tan ^2 \theta}$
View full solution →Equal circles with centres $O$ and $O\ '$ touch each other at $X. OO\ '$ produced to meet a circle with centre $O\ ', $ at $A. AC$ is a tangent to the circle whose centre is $O. O\ ' \ D$ is perpendicular to $AC$. Find the value of $\frac{ DO ^{\prime}}{ CO }$
View full solution →In two concentric circles, a chord of length $8 \ cm$ of the larger circle touches the smaller circle. If the radius of the larger circle is $5 \ cm$ then find the radius of the smaller circle.
View full solution →The ratio of the sums of first m and first $n$ terms of an $A.P.$ is $m^2: n^2$. Show that the ratio of its $m ^{\text {th }}$ and $n ^{\text {th }}$ terms is $(2m - 1):(2n -1 ).$
View full solution →Find the mode, median and mean for the following data:
View full solution →| Marks Obtained | $25-35$ | $35-45$ | $45-55$ | $55-65$ | $65-75$ | $75-85$ |
| Number of students | $7$ | $31$ | $33$ | $17$ | $11$ | $1$ |
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends. Length of the cylindrical part is $7 \ m$ and radius of cylindrical part is $\frac{7}{2}m$.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
View full solution →Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
A spherical glass vessel has a cylindrical neck $8 \ cm$ long and $1 \ cm$ in radius. The radius of the spherical part is $9 \ cm.$ Find the amount of water $($in litres$)$ it can hold, when filled completely.
View full solution →A $1.2 \ m$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2\ m$ from the ground.The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time, the angle of elevation reduces to $30^{\circ}$. Find the distance travelled by the balloon during the interval.
View full solution →A train travels at a certain average speed for a distance $63 \ km$ and then travels a distance of $72 \ km$ at an average speed of $6 \ km / hr$ more than the original speed. If it takes $3$ hours to complete total journey, what is its original average speed?
View full solution →
Read the following text carefully and answer the questions that follow:
The centroid is the centre point of the object. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle separates the median in the ratio of $2: 1$. It can be found by taking the average of $x$ coordinate points and $y-$ coordinate points of all the vertices of the triangle. See the figure given below
Here $D, E$ and $F$ are mid points of sides $BC , AC$ and $AB$ in same order. $G$ is centroid, the centroid divides the median in the ratio $2: 1$ with the larger part towards the vertex. Thus $AG : GD =2: 1$
On the basis of above information read the question below. If $G$ is Centroid of $\triangle A B C$ with height $h$ and $J$ is Centroid of $\triangle ADE$. Line $DE$ parallel to $BC ,$ cuts the $\triangle ABC$ at a height $\frac{h}{4}$ from $BC . HF =\frac{h}{4}$
$i$. What is the length of $AH$ ?
$ii$. What is the distance of point $A$ from point $G$ ?
$iii$. What is the distance of point $A$ from point $J$ ?
OR
What is the distance $GJ$?
View full solution →The centroid is the centre point of the object. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle separates the median in the ratio of $2: 1$. It can be found by taking the average of $x$ coordinate points and $y-$ coordinate points of all the vertices of the triangle. See the figure given below
Here $D, E$ and $F$ are mid points of sides $BC , AC$ and $AB$ in same order. $G$ is centroid, the centroid divides the median in the ratio $2: 1$ with the larger part towards the vertex. Thus $AG : GD =2: 1$
On the basis of above information read the question below. If $G$ is Centroid of $\triangle A B C$ with height $h$ and $J$ is Centroid of $\triangle ADE$. Line $DE$ parallel to $BC ,$ cuts the $\triangle ABC$ at a height $\frac{h}{4}$ from $BC . HF =\frac{h}{4}$
$i$. What is the length of $AH$ ?
$ii$. What is the distance of point $A$ from point $G$ ?
$iii$. What is the distance of point $A$ from point $J$ ?
OR
What is the distance $GJ$?
Read the following text carefully and answer the questions that follow: A coaching institute of Mathematics conducts classes in two batches $I$ and $II$ and fees for rich and poor children are different. In batch $I,$ there are $20$ poor and $5$ rich children, whereas in batch $II,$ there are $5$ poor and $25$ rich children. The total monthly collection of fees from batch $I $ is $₹ 9000$ and from batch II is $₹ 26,000$ . Assume that each poor child pays $₹ x$ per month and each rich child pays $₹ y$ per month.
$i$. Represent the information given above in terms $x$ and $y$ .
$ii$. Find the monthly fee paid by a poor child.
$iii$. Find the difference in the monthly fee paid by a poor child and a rich child.
OR
If there are $10$ poor and $20$ rich children in batch $II,$ what is the total monthly collection of fees from batch II?
View full solution →$i$. Represent the information given above in terms $x$ and $y$ .
$ii$. Find the monthly fee paid by a poor child.
$iii$. Find the difference in the monthly fee paid by a poor child and a rich child.
OR
If there are $10$ poor and $20$ rich children in batch $II,$ what is the total monthly collection of fees from batch II?
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