The marks obtained by $9$ students in Mathematics are $59, 46, 31, 23, 27, 40, 52, 35$ and $29.$ The mean of the data is
- A$30$
- B$41$
- C$23$
- ✓$38$
Answer: D.
View full solution →Question types
MODEL PAPER 7 (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 7 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If a letter of English alphabet is chosen at random, then the probability of this letter to be a consonant is:
- A$\frac{11}{13}$
- B$\frac{10}{13}$
- ✓$\frac{21}{26}$
- D$\frac{5}{26}$
Answer: C.
View full solution →In a family of two children, the probability of having at least one girl is:
- A$\frac{1}{2}$
- B$\frac{2}{5}$
- ✓$\frac{3}{4}$
- D$\frac{1}{4}$
Answer: C.
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 →Find the area of the sector of a circle having radius $6 \ cm$ and of angle $30^{\circ}$.
- A$8.42 \ cm^2$
- B$9 \ cm^2$
- ✓$9.42 \ cm^2$
- D$9.52 \ cm^2$
Answer: C.
View full solution →Assertion $(A):$ The sum of the first $n$ terms of an $A P$ is given by $S_n=3 n^2-4 n$. Then its $n$th term $a_n=6 n-7$
Reason $(R):$ nth term of an $AP,$ whose sum to $n$ terms is $S_n$, is given by $a_n=S_n-S_{n-1}$
Reason $(R):$ nth term of an $AP,$ whose sum to $n$ terms is $S_n$, is given by $a_n=S_n-S_{n-1}$
- 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 $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: B.
View full solution →Assertion (A): In a solid hemisphere of radius 10 cm , a right cone of same radius is removed out. The surface area of the remaining solid is $570.74 cm^2$ [Take $\pi=3.14$ and $\sqrt{2}=1.4$ ]
Reason (R): Expression used here to calculate Surface area of remaining solid = Curved surface area of hemisphere + Curved surface area of cone
Reason (R): Expression used here to calculate Surface area of remaining solid = Curved surface area of hemisphere + Curved surface area of cone
- 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 →Reeti prepares a Rakhi for her brother Ronit. The Rakhi consists of a rectangle of length $8 \ cm$ and breadth $6 \ cm$ inscribed in a circle as shown in the figure. Find the area of the shaded region. $($Use $\pi=3 \cdot 14 )$
View full solution →Prove the trigonometric identity: $\sec ^4 \theta-\sec ^2 \theta=\tan ^4 \theta+\tan ^2 \theta$.
View full solution →
If $\sin (A+B)=1$ and $\cos (A-B)=1$, find $A$ and $B$.
View full solution →In the given figure, common tangents $\text{AB}$ and $\text{CD}$ to the two circles with centres $O _1$ and $O _2$ intersect at $E.$ Prove that $\text{AB=CD}$.
View full solution →In the given figure, $\text{PT}$ and $\text{PS}$ are tangents to a circle with centre $O$ ,from a point $P$ , such that $\text{PT} =4 \ cm$ and $\angle \text{TPS} =60^{\circ}$ Find the length of the chord $\text{TS.}$ Also, find the radius of the circle.
View full solution →At $t$ minutes past $2\ pm$ the time needed by the minutes hand of a clock to show $3\ pm$ was found to be $3$ minutes less than $\frac{t^2}{4}$ minutes. Find $t .$
View full solution →Find the mean of the following frequency distribution:
View full solution →| $\text{Class}$ | $\text{Frequency}$ |
| $0-10$ | $12$ |
| $10-20$ | $18$ |
| $20-30$ | $27$ |
| $30-40$ | $20$ |
| $40-50$ | $17$ |
| $50-60$ | $6$ |
If $\sec \theta+\tan \theta= p$, show that $\frac{p^2-1}{p^2+1}=\sin \theta$
View full solution →If radii of the two circles are equal, prove that AB = CD where AB and CD are common tangents.
If the ratio of the sum of the first $n$ terms of two $APs$ is $(7n +1): (4n + 27)$ then find the ratio of their $9^{th}$ terms.
View full solution →Ved travels $600 \ km$ to his home partly by train and partly by car. He takes $8$ hours if he travels $120 \ km$ by train and the rest by car. He takes $20$ minutes longer if he travels $200 \ km$ by train and the rest by car. Find the speed of the train and the car.
View full solution →The following table shows the ages of the patients admitted in a hospital during a month:
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
View full solution →| $\text{Age(in years)}$ | $6 - 15$ | $16 - 25$ | $26 - 35$ | $36 - 45$ | $46 - 55$ | $56 - 65$ |
| $\text{Number of patients}$ | $6$ | $11$ | $21$ | $23$ | $14$ | $5$ |
The sum of four consecutive numbers in $A.P$. is $32$ and the ratio of the product of the first and last terms to the product of two middle terms is $7 : 15.$ Find the number.
View full solution →In a trapezium $ABCD , AB \| DC$ and $DC =2 AB . EF \| AB$, where $E$ and $F$ lie on $BC$ and $AD$ respectively such that $\frac{B E}{E C}=\frac{4}{3}$. Diagonal $DB$ intersects $EF$ at $G$ . Prove that, $7 EF =11 AB$.
View full solution →Read the following text carefully and answer the questions that follow:
Some students were asked to list their favourite colour. The measure of each colour is shown by the central angle of a pie chart given below:
$i$. If a student is chosen at random, then find the probability of his/her favourite colour being white? $(1)$
$ii$. What is the probability of his/her favourite colour being blue or green? $(1)$
$iii.$ If $15$ students liked the colour yellow, how many students participated in the survey? $(2)$
OR
What is the probability of the favourite colour being red or blue? $(2)$
View full solution →Some students were asked to list their favourite colour. The measure of each colour is shown by the central angle of a pie chart given below:
$i$. If a student is chosen at random, then find the probability of his/her favourite colour being white? $(1)$
$ii$. What is the probability of his/her favourite colour being blue or green? $(1)$
$iii.$ If $15$ students liked the colour yellow, how many students participated in the survey? $(2)$
OR
What is the probability of the favourite colour being red or blue? $(2)$
Read the following text carefully and answer the questions that follow:
Two friends Govind and Pawan decided to go for a trekking. During summer vacation, they went to Panchmarhi. While trekking they observed that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.
$i.$ What are the zeroes of the polynomial whose graph is given $?\ (1)$
$ii.$ What will be the expression of the given polynomial $p(x)\ ?\ (1)$
$iii.$ What is the product of the zeroes of the polynomial which represents the parabola $?\ (2)$
OR
In the standard form of quadratic polynomial, $a x^2+b x+c$, whar are $a, b$, and $c\ ?\ (2)$
View full solution →Two friends Govind and Pawan decided to go for a trekking. During summer vacation, they went to Panchmarhi. While trekking they observed that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.
$i.$ What are the zeroes of the polynomial whose graph is given $?\ (1)$
$ii.$ What will be the expression of the given polynomial $p(x)\ ?\ (1)$
$iii.$ What is the product of the zeroes of the polynomial which represents the parabola $?\ (2)$
OR
In the standard form of quadratic polynomial, $a x^2+b x+c$, whar are $a, b$, and $c\ ?\ (2)$
Read the following text carefully and answer the questions that follow:
Aashish and his family went for a vacation to Manali. There they had a stay in tent for a night. Aashish found that the tent in which they stayed is in the form of a cone surmounted on a cylinder. The total height of the tent is $42 m,$ diameter of the base is $42 m$ and height of the cylinder is $22 m$.
$i$. What is curved surface area of cone? $(1)$
$ii$. If each person needs $126 m^2$ of floor, then how many persons can be accommodated in the tent? $(1)$
$iii$. What is the curved surface area of cylinder? $(2)$
OR
How much canvas required to make a tent? $(2)$
View full solution →Aashish and his family went for a vacation to Manali. There they had a stay in tent for a night. Aashish found that the tent in which they stayed is in the form of a cone surmounted on a cylinder. The total height of the tent is $42 m,$ diameter of the base is $42 m$ and height of the cylinder is $22 m$.
$i$. What is curved surface area of cone? $(1)$
$ii$. If each person needs $126 m^2$ of floor, then how many persons can be accommodated in the tent? $(1)$
$iii$. What is the curved surface area of cylinder? $(2)$
OR
How much canvas required to make a tent? $(2)$
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