The most frequent value in the data is known as
- Amean
- ✓mode
- Call the three
- Dmedian
Answer: B.
View full solution →Question types
MODEL PAPER 5 (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 5 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is the probability that a leap year has 52 Mondays?
- ✓$\frac{5}{7}$
- B$\frac{6}{7}$
- C$\frac{2}{7}$
- D$\frac{4}{7}$
Answer: A.
View full solution →A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not a king is
- A$\frac{9}{13}$
- ✓$\frac{12}{13}$
- C$\frac{1}{13}$
- D$\frac{4}{13}$
Answer: B.
View full solution →if the perimeter of a sector of a circle of radius $6.5 \ cm$ is $29 \ cm,$ then its area is
- A$56 \ cm^2$
- B$58 \ cm^2$
- ✓$52 \ cm^2$
- D$25 \ cm^2$
Answer: C.
View full solution →The minute hand of a clock is $10 \ cm$ long. Find the area of the face of the clock described by the minute hand between $8\ am$ and $8.25\ am.$
- A$120 \ cm^2$
- B$125.5 \ cm^2$
- ✓$130.95 \ cm^2$
- D$100 \ cm^2$
Answer: C.
View full solution →Assertion (A): The sum of the series with the $n$th term. $t_n=(9-5 n)$ is (465), when no. of terms $n=15$.
Reason (R): Given series is in A.P. and sum of n terms of an A.P. is $S _{ n }=\frac{n}{2}[2 a+(n-1) d]$
Reason (R): Given series is in A.P. and sum of n terms of an A.P. is $S _{ n }=\frac{n}{2}[2 a+(n-1) d]$
- 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.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
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 $300 cm^2$.
Reason (R): Total surface area of a cuboid is $2( lb + bh + lh )$
Reason (R): Total surface area of a cuboid is $2( lb + bh + lh )$
- 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.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →The short and long hands of a clock are $4 \ cm $ and $6 \ cm$ long respectively. Find the sum of distances travelled by their tips in $2$ days.$ [$Take $\pi=3.14.]$
View full solution →If $3 \tan \theta=4$, evaluate $\frac{3 \sin \theta+2 \cos \theta}{3 \sin \theta-2 \cos \theta}$.
View full solution →
Prove the trigonometric identity: $\frac{1+\cos \theta-\sin ^2 \theta}{\sin \theta(1+\cos \theta)}=\cot \theta$
View full solution →From a point $P, $ the length of the tangent to a circle is $15 \ cm$ and distance of $P$ from the centre of the circle is $17 \ cm.$ Then what is the radius of the circle?
View full solution →Prove that the tangents drawn at the ends of a chord of a circle make equal angles with chord.
In the figure below $\text{ABCDE}$ is a pentagon with $BE \| CD$ and $BC \| DE. BC$ is perpendicular to $CD$. If the perimeter
of $\text{ABCDE}$ is $21 \ cm,$ find the Values of $x$ and $y$.
View full solution →of $\text{ABCDE}$ is $21 \ cm,$ find the Values of $x$ and $y$.
Find the median of the following data.
| Class Interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | Total |
| Frequency | 8 | 16 | 36 | 34 | 6 | 100 |
Prove the following identity : $\frac{\sin \theta}{1-\cos \theta}+\frac{\tan \theta}{1+\cos \theta}=\sec \theta \cdot \operatorname{cosec} \theta+\cot \theta$
View full solution →In Fig. $1$ and $m$ are two parallel tangents at $A$ and $B$ . The tangent at $C$ makes an intercept $DE$ between $l$ and $m$ . Prove that $\angle D F E=90^{\circ}$.
View full solution →In Figure, from a solid cube of side 7 cm , a cylinder of radius 2.1 cm and height 7 cm is scooped out. Find the total surface area of the remaining solid.
The sum of ages of a father and his son is $45$ years. Five years ago, the product of their ages $($in years$)$ was $124 $. Determine their present ages.
View full solution →The median of the following data is $16.$ Find the missing frequencies $a$ and $b$ if the total of frequencies is $70$
View full solution →| Class | $0 - 5$ | $5 - 10$ | $10 - 15$ | $15 - 20$ | $20 - 25$ | $25 - 30$ | $30 - 35$ | $35 - 40$ |
| Frequency | $12$ | $a$ | $12$ | $15$ | $b$ | $6$ | $6$ | $4$ |
A well, whose diameter is $7 m ,$ has been dug $22.5 m$ deep and the earth dugout is used to form an embankment around it. If the height of the embankment is $1.5 m$ , find the width of the embankment.
View full solution →In the given figure, $\text{DEFG}$ is a square and $\angle B A C=90^{\circ}$. Prove that
$i. \triangle A G F \sim \triangle D B G$
$ii. \triangle A G F \sim \triangle E F C$
$iii. \triangle D B G \sim \triangle E F C$
$iv. D E^2=B D \times E C$
View full solution →$i. \triangle A G F \sim \triangle D B G$
$ii. \triangle A G F \sim \triangle E F C$
$iii. \triangle D B G \sim \triangle E F C$
$iv. D E^2=B D \times E C$
Read the text carefully and answer the questions:
The houses of Ajay and Sooraj are at $100 m$ distance and the height of their houses is the same as approx $150 m$ . One big tower was situated near their house.
Once both friends decided to measure the height of the tower.
They measure the angle of elevation of the top of the tower from the roof of their houses.
The angle of elevation of ajay's house to the tower and sooraj's house to the tower are $45^{\circ}$ and $30^{\circ}$ respectively as shown in the figure.
$(a)$ Find the height of the tower.
$(b)$ What is the distance between the tower and the house of Sooraj?
OR
Find the distance between top of tower and top of Ajay's house?
$(c)$ Find the distance between top of the tower and top of Sooraj's house?
View full solution →The houses of Ajay and Sooraj are at $100 m$ distance and the height of their houses is the same as approx $150 m$ . One big tower was situated near their house.
Once both friends decided to measure the height of the tower.
They measure the angle of elevation of the top of the tower from the roof of their houses.
The angle of elevation of ajay's house to the tower and sooraj's house to the tower are $45^{\circ}$ and $30^{\circ}$ respectively as shown in the figure.
$(a)$ Find the height of the tower.
$(b)$ What is the distance between the tower and the house of Sooraj?
OR
Find the distance between top of tower and top of Ajay's house?
$(c)$ Find the distance between top of the tower and top of Sooraj's house?
Read the text carefully and answer the questions:
The students of a school decided to beautify the school on an annual day by fixing colourful flags on the straight passage of the school.They have $27$ flags to be fixed at intervals of every $2$ metre. The flags are stored at the position of the middlemost flag.Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time.
$(a)$ How much distance did she cover in pacing $6$ flags on either side of center point?
$(b)$ Represent above information in Arithmetic progression
OR
How much distance did she cover in completing this job and returning to collect her books?
$(c)$ What is the maximum distance she travelled carrying a flag?
View full solution →The students of a school decided to beautify the school on an annual day by fixing colourful flags on the straight passage of the school.They have $27$ flags to be fixed at intervals of every $2$ metre. The flags are stored at the position of the middlemost flag.Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time.
$(a)$ How much distance did she cover in pacing $6$ flags on either side of center point?
$(b)$ Represent above information in Arithmetic progression
OR
How much distance did she cover in completing this job and returning to collect her books?
$(c)$ What is the maximum distance she travelled carrying a flag?
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