If the arithmetic mean of $x, x+3, x+6, x+9$ and $x+12$ is $10 ,$ then $x=$
- A$2$
- B$1$
- C$6$
- ✓$4$
Answer: D.
View full solution →Question types
MODEL PAPER 10 (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 10 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If a digit is chosen at random from the digits $1,2,3,4,5,6,7,8,9$, then the probability that it is odd and is a multiple of 3 is
- A$\frac{1}{9}$
- ✓$\frac{2}{9}$
- C$\frac{2}{3}$
- D$\frac{1}{3}$
Answer: B.
View full solution →The probability of guessing the correct answer to a certain test questions is $\frac{x}{12}$. If the probability of not guessing the correct answer to this question is $\frac{2}{3}$, then $x =$
- A$6$
- ✓$4$
- C$2$
- D$3$
Answer: B.
View full solution →If the perimeter of a sector of a circle of radius $5.2 \ cm$ is $16.4 \ cm ,$ then the area of the sector is.
- A$15.5 \ cm^2$
- ✓$15.6 \ cm^2$
- C$15.9 \ cm^2$
- D$15.1 \ cm^2$
Answer: B.
View full solution →Three horses are tethered with 7-meter-long ropes at the three corners of a triangular field having sides $20 m, 34$ m , and 42 m . The area of the plot which can be grazed by the horses is
- ✓$77 m^2$
- B$80 m^2$
- C$100 m^2$
- D$30 m^2$
Answer: A.
View full solution →Assertion (A): Sum of natural number from 1 to 100 is 5050.
Reason (R): Sum of n natural number is $\frac{n(n+1)}{2}$.
Reason (R): Sum of n natural number is $\frac{n(n+1)}{2}$.
- ✓Both A and R are true and R is the correct
- BBoth $A$ and $R$ are true but $R$ is not the explanation of A . 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): In a solid hemisphere of radius 10 cm , a right cone of same radius is removed out. The volume of the remaining solid is $523.33 cm^3$ [Take $\pi=3.14$ and $\sqrt{2}=1.4$ ]
Reason (R): Expression used here to calculate volume of remaining solid = Volume of hemisphere - Volume of cone
Reason (R): Expression used here to calculate volume of remaining solid = Volume of hemisphere - Volume of cone
- ABoth A and R are true and R is the correct
- BBoth $A$ and $R$ are true but $R$ is not the explanation of A . correct explanation of A.
- CA is true but $R$ is false.
- ✓A is false but $R$ is true.
Answer: D.
View full solution →Find the area of the segment shown in Fig., if radius of the circle is $21 \ cm$ and $\angle A O B=120^{\circ}$ $($Use $\pi=\frac{22}{7} )$
View full solution →In Figure, two concentric circles with centre $O$, have radii $21 \ cm$ and $42 \ cm .$ If $\angle AOB=60^{\circ},$ find the area of the shaded region.
View full solution →Prove the trigonometric identity: $\frac{\tan \theta}{\left(1+\tan ^2 \theta\right)^2}+\frac{\cot \theta}{\left(1+\cot ^2 \theta\right)^2}=\sin \theta \cos \theta$
View full solution →If $\sin \theta+\sin ^2 \theta=1$, find the value of $\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2 \cos ^4 \theta+2 \cos ^2 \theta-2$
View full solution →In Fig., PQ is a chord of length 8 cm of a circle of radius 5 cm and centre $O$. The tangents at $P$ and $Q$ intersect at point T. Find the length of TP.
View full solution →From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$. If the bridge is at a height of $8 m$ from the banks, then find the width of the river.
View full solution →Prove the trigonometric identity: $\frac{\cot ^2 \theta(\sec \theta-1)}{(1+\sin \theta)}+\frac{\sec ^2 \theta(\sin \theta-1)}{(1+\sec \theta)}=0$
View full solution →Find the length of a tangent drawn to a circle with radius $5 \ cm ,$ from a point $13 \ cm$ from the centre of the circle.
View full solution →A point $P$ is at a distance of $29 \ cm$ from the centre of a circle of radius $20 \ cm .$ Find the length of the tangent drawn from $P$ to the circle.
View full solution →A 2-digit number is four times the sum of its digits and twice the product of its digits. Find the number.
Let there be an $A.P.$ with first term $'a\ ',$ common difference $'d\ '.$ If $a_n$ denotes its $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find. $n$ and $S _{ n } ,$ if $a =5, d=3$ and $a _{ n }=50.$
View full solution →A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building. Find the height of the building, if it contains $67 \frac{1}{21} m^3$ of air.
View full solution →A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
View full solution →Show that the points $A(3,1), B(0,-2), C(1,1)$ and $D(4,4)$ are the vertices of a parallelogram $A B C D$.
View full solution →Sangeeta went to a book$-$seller's shop and purchased $2$ textbook of $IX$ Mathematics and $3$ textbook of $X$ mathematics for $Rs.250.$ Her friend Meenu also bought $4$ textbooks of $IX$ Mathematics and $6$ textbooks of $X$ maths of same kind for $Rs.500.$ Represents this situation algebraically and graphically.
View full solution →Read the following text carefully and answer the questions that follow:
Swimmer in Distress: A lifeguard located $20$ metre from the water spots a swimmer in distress. The swimmer is $30$ metre from shore and $100$ metre east of the lifeguard. Suppose the lifeguard runs and then swims to the swimmer in a direct line, as shown in the figure.
$i$. How far east from his original position will he enter the water? $($Hint: Find the value of $x$ in the sketch$)$.
$ii$. Which similarity criterion of triangle is used?
$iii$. What is the distance of swimmer from the shore?
OR
What is the length of $AD$?
View full solution →Swimmer in Distress: A lifeguard located $20$ metre from the water spots a swimmer in distress. The swimmer is $30$ metre from shore and $100$ metre east of the lifeguard. Suppose the lifeguard runs and then swims to the swimmer in a direct line, as shown in the figure.
$i$. How far east from his original position will he enter the water? $($Hint: Find the value of $x$ in the sketch$)$.
$ii$. Which similarity criterion of triangle is used?
$iii$. What is the distance of swimmer from the shore?
OR
What is the length of $AD$?
Read the following text carefully and answer the questions that follow:
Heart Rate : The heart rate is one of the 'vital signs' of health in the human body. It measures the number of times per minute that the heart contracts or beats. While a normal heart rate does not guarantee that a person is free of health problems, it is a useful benchmark for identifying a range of health issues.
Thirty women were examined by doctors of $\text{AIIMS}$ and the number of heart beats per minute were recorded and summarized as follows:
Based on the above information, answer the following questions:
$i$. How many women are having heart beat in the range $68 - 77$ ?
$ii$. What is the median class of heart beats per minute for these women?
$iii$. a. Find the modal value of heart beats per minute for these women.
OR
Find the median value of heart beats per minute for these women.
View full solution →Heart Rate : The heart rate is one of the 'vital signs' of health in the human body. It measures the number of times per minute that the heart contracts or beats. While a normal heart rate does not guarantee that a person is free of health problems, it is a useful benchmark for identifying a range of health issues.
Thirty women were examined by doctors of $\text{AIIMS}$ and the number of heart beats per minute were recorded and summarized as follows:
| Number of heart beats per minute | Number of Women |
| $65-68$ | $2$ |
| $68-71$ | $4$ |
| $71-74$ | $3$ |
| $74-77$ | $8$ |
| $77-80$ | $7$ |
| $80-83$ | $4$ |
| $83-86$ | $2$ |
$i$. How many women are having heart beat in the range $68 - 77$ ?
$ii$. What is the median class of heart beats per minute for these women?
$iii$. a. Find the modal value of heart beats per minute for these women.
OR
Find the median value of heart beats per minute for these women.
Read the following text carefully and answer the questions that follow:
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
$i.$ In the standard form of quadratic polynomial, $a x^2+b x+c$, what are $a, b$ and $c$ ?
$ii.$ If the roots of the quadratic polynomial are equal, what is the discriminant $D$ ?
$iii.$ If $\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the quadratic polynomial are $2 x ^2- x +8 k$, then find the value of $k\ ?$
OR
What is the relation between zeros and coefficient for a quadratic polynomial?
View full solution →The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
$i.$ In the standard form of quadratic polynomial, $a x^2+b x+c$, what are $a, b$ and $c$ ?
$ii.$ If the roots of the quadratic polynomial are equal, what is the discriminant $D$ ?
$iii.$ If $\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the quadratic polynomial are $2 x ^2- x +8 k$, then find the value of $k\ ?$
OR
What is the relation between zeros and coefficient for a quadratic polynomial?
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