If the mode of the data: $64, 60, 48, x, 43, 48, 43, 34$ is $43,$ then $x + 3 =$
- A$45$
- B$48$
- C$44$
- ✓$46$
Answer: D.
View full solution →Question types
MODEL PAPER 2 (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 2 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two dice are rolled together. What is the probability of getting a sum greater than 10?
- A$\frac{5}{18}$
- B$\frac{1}{9}$
- C$\frac{1}{6}$
- ✓$\frac{1}{12}$
Answer: D.
View full solution →A dice is thrown once. The probability of getting an odd number is
- ✓$\frac{1}{2}$
- B1
- C$\frac{2}{6}$
- D$\frac{4}{6}$
Answer: A.
View full solution →Area of a sector of angle $p ($in degrees$)$ of a circle with radius $R$ is
- A$\frac{p}{360} \times 2 \pi R$
- B$\frac{ p }{180} \times \pi R ^2$
- C$\frac{p}{180} \times 2 \pi R$
- ✓$\frac{p}{720} \times 2 \pi R^2$
Answer: D.
View full solution →In a circle of radius $21 \ cm ,$ an $arc$ subtends an angle of $60^{\circ}$ at the centre. The area of the sector formed by the $arc$ is:
- ✓$231 \ cm^2$
- B$250 \ cm^2$
- C$220 \ cm^2$
- D$200 \ cm^2$
Answer: A.
View full solution →Assertion (A): Let the positive numbers a, b, c be in A.P., then $\frac{1}{b c}, \frac{1}{a c}, \frac{1}{a b}$ are also in A.P.
Reason (R): If each term of an A.P. is divided by a b c, then the resulting sequence is also in A.P.
Reason (R): If each term of an A.P. is divided by a b c, then the resulting sequence is also in A.P.
- ✓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 m ounted on the solid cone of radius 6 cm and height 8 cm . the volume of the combined solid is $1737.47 cm^3$. [Take $\pi=3.14$ ]
Reason (R): Volume of sphere and surface area of cone is given by $\frac{4}{3} \pi r^3$ and $\frac{1}{3} \pi r^2 h$ respectively.
Reason (R): Volume of sphere and surface area of cone is given by $\frac{4}{3} \pi r^3$ and $\frac{1}{3} \pi r^2 h$ respectively.
- 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 →A sector of a circle of radius $4 \ cm$ contains an angle of $30^{\circ}$. Find the area of the sector.
View full solution →Verify that if $\tan ^2 \theta+\sin \theta=\cos ^2 \theta$ is an identity or not.
View full solution →Four cows are tethered at the four corners of a square field of side $50 m$ such that each can graze the maximum unshared area. What area will be left ungrazed? $[$Take $\pi=3.14].$
View full solution →If $\sin X+\sin ^2 X=1,$ prove that $\cos ^2 X+\cos ^4 X=1$.
View full solution →In figure, $\triangle ABC$ is circumscribing a circle. Find the length of $BC$ .
View full solution →In the given figure, a quadrilateral $\text{ABCD}$ is drawn to circumscribe a circle such that its sides $AB, BC, CD$ and $AD$ touch the circle at $P, Q, R $ and $S$ respectively. If $AB = x \ cm, BC = 7 \ cm, CR = 3 \ cm$ and $AS = 5 \ cm,$ find $x$.
View full solution →A man has only $20$ paisa coins and $25$ paisa coins in his purse. If he has $50$ coins in all totalling to $₹ 11.25, $ how many coins of each kind $38196$ does he have?
View full solution →Five coins were simultaneously tossed $1000$ times and at each toss the number of heads were observed. The number of tosses during which $0,1,2,3,4$ and $5$ heads were obtained are shown in the table below. Find the mean number of heads per toss.
View full solution →| No. of heads per toss | No. of tosses |
| $0$ | $38$ |
| $1$ | $144$ |
| $2$ | $342$ |
| $3$ | $287$ |
| $4$ | $164$ |
| $5$ | $25$ |
| $\text{Total}$ | $1000$ |
Prove that $\sec \theta(1-\sin \theta)(\sec \theta+\tan \theta)=1$
View full solution →Out of the two concentric circles, the radius of the outer circle is $5 \ cm$ and the chord $AC$ of length $8 \ cm$ is a tangent to the inner circle. Find the radius of the inner circle.
View full solution →A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure. If the height of the cylinder is $10 \ cm$ and its base is of radius $3.5 \ cm,$ find the total surface area of the article.
View full solution →The product of Tanay's age $($in years$)$ five years ago and his age ten years later is $16.$ Determine Tanay's present age.
View full solution →Find the mean of the following frequency distribution:
View full solution →| Class | $5 - 15$ | $15 - 25$ | $25 - 35$ | $35 - 45$ | $45 - 55$ | $55 - 65$ |
| Frequency | $6$ | $11$ | $21$ | $23$ | $14$ | $5$ |
A conical vessel of radius $6 \ cm$ and height $8 \ cm$ is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in Figure. What fraction of water over flows?
View full solution →If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Read the text carefully and answer the questions:
Totem poles are made from large trees. These poles are carved with symbols or figures and mostly found in western Canada and northwestern United States.
In the given picture, two such poles of equal heights are standing $28 m$ apart. From a point somewhere between them in the same line, the angles of elevation of the top of the two poles are $60^{\circ}$ and $30^{\circ}$ respectively.
$(a)$ Draw a neat labelled diagram.
$(b)$ Find the height of the poles.
OR
Find the location of the point of observation.
$(c)$ If the distances of the top of the poles from the point of observation are taken as $p$ and $q,$ then find a relation between $p$ and $q$ .
View full solution →Totem poles are made from large trees. These poles are carved with symbols or figures and mostly found in western Canada and northwestern United States.
In the given picture, two such poles of equal heights are standing $28 m$ apart. From a point somewhere between them in the same line, the angles of elevation of the top of the two poles are $60^{\circ}$ and $30^{\circ}$ respectively.
$(a)$ Draw a neat labelled diagram.
$(b)$ Find the height of the poles.
OR
Find the location of the point of observation.
$(c)$ If the distances of the top of the poles from the point of observation are taken as $p$ and $q,$ then find a relation between $p$ and $q$ .
Read the text carefully and answer the questions:
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 $O$.
$(a)$ 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 $S$ ?
$(b)$ What is the area of square $\text{PQRS}$?
OR
If $S$ divides $CA$ in the ratio $K : 1,$ what is the value of $K,$ where point $A$ is $(200, 800)$?
$(c)$ What is the length of diagonal $PR$ in square $\text{PQRS}$?
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 $O$.
$(a)$ 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 $S$ ?
$(b)$ What is the area of square $\text{PQRS}$?
OR
If $S$ divides $CA$ in the ratio $K : 1,$ what is the value of $K,$ where point $A$ is $(200, 800)$?
$(c)$ What is the length of diagonal $PR$ in square $\text{PQRS}$?
Read the text carefully and answer the questions:
Akshat's father is planning some construction work in his terrace area.
He ordered $360$ bricks and instructed the supplier to keep the bricks in such as way that the bottom row has $30$ bricks and next is one less than that and so on.
The supplier stacked these $360$ bricks in the following manner, $30$ bricks in the bottom row, $29$ bricks in the next row, $28$ bricks in the row next to it, and so on.
$(a)$ In how many rows, $360$ bricks are placed?
$(b)$ How many bricks are there in the top row?
OR
If which row 26 bricks are there?
$(c)$ How many bricks are there in $10^{\text {th }}$ row?
View full solution →Akshat's father is planning some construction work in his terrace area.
He ordered $360$ bricks and instructed the supplier to keep the bricks in such as way that the bottom row has $30$ bricks and next is one less than that and so on.
The supplier stacked these $360$ bricks in the following manner, $30$ bricks in the bottom row, $29$ bricks in the next row, $28$ bricks in the row next to it, and so on.
$(a)$ In how many rows, $360$ bricks are placed?
$(b)$ How many bricks are there in the top row?
OR
If which row 26 bricks are there?
$(c)$ How many bricks are there in $10^{\text {th }}$ row?
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