Which one of the following is a polynomial?
- A$\frac{x-1}{x+1}$
- B$\sqrt{2 x}-1$
- ✓$x^2+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
- D$\frac{x^2}{2}-\frac{2}{x^2}$
Answer: C.
View full solution →Question types
Model Paper 5 question types
43 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
43
Questions
6
Question groups
5
Question types
01
M.C.Q
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
7 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 5 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
How many lines pass through two points?
- Amany
- Bthree
- Ctwo
- Donly one
Which of the following points lies on the line $y = 2x + 3$?
- A$(2,8)$
- B$(5,15)$
- ✓$(3,9)$
- D$(4,12)$
Answer: C.
View full solution →In Fig. $\ce{ABCD}$ is a cyclic quadrilateral. If $\angle BAC=50^{\circ}$ and $\angle DBC=60^{\circ}$ then find $\angle BCD$.
- A$50^{\circ}$
- B$60^{\circ}$
- ✓$70^{\circ}$
- D$55^{\circ}$
Answer: C.
View full solution →If $\frac{5-\sqrt{3}}{2+\sqrt{3}}=x+y \sqrt{3}$, then
- A$x=-13, y=-7$
- B$x=13, y=-7$
- ✓$x=-13, y=7$
- D$x=13, y=7$
Answer: C.
View full solution →Assertion (A): Three rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ are $\frac{9}{20}, \frac{10}{20}$ and $\frac{11}{20}$
Reason (B): A rational number between two rational numbers p and q is $\frac{1}{2}(p+q)$
Reason (B): A rational number between two rational numbers p and q is $\frac{1}{2}(p+q)$
- 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.
- DA is false but R is true.
Assertion (A): In $\Delta ABC$, median AD is produced to X such that $AD = DX$. Then ABXC is a parallelogram.
Reason (R): Diagonals AX and BC bisect each other at right angles.
Reason (R): Diagonals AX and BC bisect each other at right angles.
- 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.
- DA is false but R is true.
A team of $10$ interns and $1$ professor from zoological department visited a forest, where they set up a conical tent for their accommodation. There they perform activities like planting saplings, yoga, cleaning lakes, testing the water for contaminants and pollutant levels and desilt the lake bed and also using the silt to strengthen bunds. Find the radius and height of the tent if the base area of tent is $154 \ cm^2$ and curved surface area of the tent is $396 \ cm ^2$.
View full solution →If the volume of a right circular cone of height $9 \ cm$ is $48 \pi \ cm^3$, find the diameter of its base.
View full solution →Express $0.35 \overline{7}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
View full solution →Prove that: $\frac{a+b+c}{a^{-1} b^{-1}+b^{-1} c^{-1}+c^{-1} a^{-1}}= abc$
View full solution →In Fig., if $\text{ABC}$ and $\text{ABD}$ are equilateral triangles then find the coordinates of $C$ and $D.$
View full solution →The polynomials ax $x^3+3 x^2-3$ and $2 x^3-5 x+$ a when divided by $(x-4)$ leave the remainders $R_1$ and $R_2$ respectively. Find the values of a if $R_1+R_2=0$
View full solution →Draw a frequency polygon for the following distribution:
| Marks obtained | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| No. of students | 7 | 10 | 6 | 8 | 12 | 3 | 2 | 2 |
Following are the marks of a group of 92 students in a test of reading ability :
Construct a frequency polygon for the above data.
| Marks | 50-52 | 47-49 | 44-46 | 41-43 | 38-40 | 35-37 | 32-34 | Total |
| Number of Stores : | 4 | 10 | 15 | 18 | 20 | 12 | 13 | 92 |
Write linear equation $3 x+2 y=18$ in the form of $a x+b y+c=0$. Also write the values of $a, b$ and $c$. Are $(4,3)$ and $(1,2)$ solution of this equation?
View full solution →$\text{ABC}$ is a triangle right angled at $C. A$ line through the mid $-$ point $M$ of hypotenuse $AB$ and parallel to $BC$ intersects $AC$ at $D$. Show that
$i. D$ is the mid $-$ point of $AC$
$ii. MD \perp AC$
$iii. CM = MA =\frac{1}{2} AB$
View full solution →$i. D$ is the mid $-$ point of $AC$
$ii. MD \perp AC$
$iii. CM = MA =\frac{1}{2} AB$
Find the integral roots of the polynomial $f(x)=x^3+6 x^2+11 x+6$.
View full solution →The sides of a triangle are in the ratio $5 : 12 : 13$ and its perimeter is $150 m.$ Find the area of the triangle.
View full solution →Find the percentage increase in the area of a triangle if its each side is doubled.
An iron pillar consists of a cylindrical portion $2.8\ m$ high and $20 \ cm$ in diameter and a cone $42 \ cm$ high is surmounting it. Find the weight of the pillar, given that $1 \ cm^3$ of iron weighs $7.5\ g.$
View full solution →In the given figure, $AB \| CD$ and $\angle A O C=x^{\circ}$. If $\angle O A B=104^{\circ}$ and $\angle O C D=116^{\circ}$, find the value of $x.$
View full solution →
Read the following text carefully and answer the questions that follow:
In the middle of the city, there was a park $\text{ABCD}$ in the form of a parallelogram form so that $\ce{AB=CD, AB \| CD}$ and $\ce{AD = BC , AD \| BC}$.
Municipality converted this park into a rectangular form by adding land in the form of $\Delta APD$ and $\Delta BCQ$. Both the triangular shape of land were covered by planting flower plants.
$i.$ Show that $\Delta APD$ and $\Delta BQC$ are congruent.
$ii. PD$ is equal to which side?
$iii.$ Show that $\Delta ABC$ and $\Delta CDA$ are congruent.
OR
What is the value of $\angle m ?$
View full solution →In the middle of the city, there was a park $\text{ABCD}$ in the form of a parallelogram form so that $\ce{AB=CD, AB \| CD}$ and $\ce{AD = BC , AD \| BC}$.
Municipality converted this park into a rectangular form by adding land in the form of $\Delta APD$ and $\Delta BCQ$. Both the triangular shape of land were covered by planting flower plants.
$i.$ Show that $\Delta APD$ and $\Delta BQC$ are congruent.
$ii. PD$ is equal to which side?
$iii.$ Show that $\Delta ABC$ and $\Delta CDA$ are congruent.
OR
What is the value of $\angle m ?$
Read the following text carefully and answer the questions that follow:
Ajay lives in Delhi, The city of Ajay's father in laws residence is at Jaipur is $600 \ km$ from Delhi.
Ajay used to travel this $600 \ km$ partly by train and partly by car.
He used to buy cheap items from Delhi and sale at Jaipur and also buying cheap items from Jaipur and sale at Delhi.
Once From Delhi to Jaipur in forward journey he covered $2x \ km$ by train and the rest $y \ km$ by taxi.
But, while returning he did not get a reservation from Jaipur in the train.
So first $2y \ km$ he had to travel by taxi and the rest $x \ km$ by Train.
From Delhi to Jaipur he took $8 hrs$ but in returning it took $10\ hrs.$
$i.$ Write the above information in terms of equation.
$ii.$ Find the value of $x$ and $y$?
$iii.$ Find the speed of Taxi?
OR
Find the speed of Train?
View full solution →Ajay lives in Delhi, The city of Ajay's father in laws residence is at Jaipur is $600 \ km$ from Delhi.
Ajay used to travel this $600 \ km$ partly by train and partly by car.
He used to buy cheap items from Delhi and sale at Jaipur and also buying cheap items from Jaipur and sale at Delhi.
Once From Delhi to Jaipur in forward journey he covered $2x \ km$ by train and the rest $y \ km$ by taxi.
But, while returning he did not get a reservation from Jaipur in the train.
So first $2y \ km$ he had to travel by taxi and the rest $x \ km$ by Train.
From Delhi to Jaipur he took $8 hrs$ but in returning it took $10\ hrs.$
$i.$ Write the above information in terms of equation.
$ii.$ Find the value of $x$ and $y$?
$iii.$ Find the speed of Taxi?
OR
Find the speed of Train?
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