The maximum number of zeroes that a polynomial of degree 3 can have is
- AZero
- BOne
- CTwo
- DThree
Question types
Model Paper 4 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 4 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form:
- Ax + y = 0
- B-2x + y = 0
- Cx – y = 0
- D-x + 2y = 0
A point of the form $(0, b)$ lies on:
- Ax - axis
- Bquadrant I
- Cquadrant III
- Dy - axis
$\text{AOB}$ is the diameter of the circle. If $\angle A O E=150^{\circ}$, then the measure of $\angle C B E$ is
- A$115^{\circ}$
- B$125^{\circ}$
- C$120^{\circ}$
- ✓$105^{\circ}$
Answer: D.
View full solution →If $x=\sqrt{5}+2$, then $x-\frac{1}{x}$ equals
- A$2$
- ✓$4$
- C$2 \sqrt{5}$
- D$\sqrt{5}$
Answer: B.
View full solution →Assertion (A): $5-\sqrt{2}=5-1.414=3.586$ is an irrational number.
Reason (R): The difference of a rational number and an irrational number is an irrational number.
Reason (R): The difference of a rational number and an irrational number is an irrational number.
- 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 $\Delta ABC , E$ and $F$ are the midpoints of AC and AB respectively. The altitude AP at BC intersects $F E$ at $Q$ . Then, $AQ = QP$.
Reason (R): Q is the midpoint of AP.
Reason (R): Q is the midpoint of AP.
- 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.
If the radius and slant height of a cone are in the ratio $7: 13$ and its curved surface area is $286 \ cm^2,$ find its radius.
View full solution →Curved surface area of a cone is $308 \ cm^2$ and its slant height is $14 \ cm$. Find the radius of the base.
View full solution →Express the decimal $0 . \overline{235}$ in the form $\frac{p}{q}$, where $p,q$ are integers and $q \neq 0$.
View full solution →Find two rational and two irrrational numbers between $0.5$ and $0.55.$
View full solution →Name the quadrant in which the point lies :(i) A(1, 1) (ii) (–2, –4) (iii) C(1, –2).
If $x+y+z=0$, show that $x^3+y^3+z^3=3xyz$.
View full solution →$\text{ABC}$ is an isosceles triangle in which $\text{AB = AC. BE}$ and $\text{CF}$ are its two medians. Show that $\text{BE = CF.}$
View full solution →$AB$ is a line segment and $P$ is the mid$-$point. $D$ and $E$ are points on the same side of $AB$ such that $\angle BAD =\angle ABE $ and $\angle EPA =\angle DPB$. Show that:
$i. \Delta DAP \cong \Delta EBP$
$ii. AD = BE ($See figure$)$
View full solution →$i. \Delta DAP \cong \Delta EBP$
$ii. AD = BE ($See figure$)$
Find at least $3$ solutions for the linear equation $2x – 3y + 7 = 0.$
View full solution →
Factorize: $x^3-2 x^2-x+2$
View full solution →The perimeter of a right triangle is $24 \ cm.$ If its hypotenuse is $10 \ cm,$ find the other two sides. Find its area by using the formula area of a right triangle. Verify your result by using Heron's formula.
View full solution →The perimeter of a triangular field is $420 m$ and its sides are in the ratio $6 : 7 : 8.$ Find the area of the triangular field.
View full solution →Prove that the line joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half of the difference of these sides.
In figure, $\angle ABC =65^{\circ}, \angle BCE =30^{\circ}, \angle DCE =35^{\circ}$ and $\angle CFE =145^{\circ}$. Prove that $AB \| EF$.
View full solution →Read the following text carefully and answer the questions that follow:
Sanjay and his mother visited in a mall. He observes that three shops are situated at $P, Q, R$ as shown in the figure from where they have to purchase things according to their need. Distance between shop $P$ and $Q$ is $8 m$ and between shop $P$ and $R$ is $6 m$.
Considering $O$ as the center of the circles.
$i$. Find the Measure of $\angle QPR$.
$ii$. Find the radius of the circle.
$iii$. Find the Measure of $\angle QSR$.
OR
Find the area of $\Delta PQR$.
View full solution →Sanjay and his mother visited in a mall. He observes that three shops are situated at $P, Q, R$ as shown in the figure from where they have to purchase things according to their need. Distance between shop $P$ and $Q$ is $8 m$ and between shop $P$ and $R$ is $6 m$.
Considering $O$ as the center of the circles.
$i$. Find the Measure of $\angle QPR$.
$ii$. Find the radius of the circle.
$iii$. Find the Measure of $\angle QSR$.
OR
Find the area of $\Delta PQR$.
Read the following text carefully and answer the questions that follow:
Ladli Scheme was launched by the Delhi Government in the year $2008$. This scheme helps to make women strong and will empower a girl child. This scheme was started in $2008$.
The expenses for the scheme are plotted in the following bar chart.
$i$. What are the total expenses from $2009$ to $2011$?
$ii$. What is the percentage of no of expenses in $2009-10$ over the expenses in $2010-11$?
$iii$. What is the percentage of minimum expenses over the maximum expenses in the period $2007-201$1?
OR
What is the difference of expenses in $2010-11$ and the expenses in $2006-09$?
View full solution →Ladli Scheme was launched by the Delhi Government in the year $2008$. This scheme helps to make women strong and will empower a girl child. This scheme was started in $2008$.
The expenses for the scheme are plotted in the following bar chart.
$i$. What are the total expenses from $2009$ to $2011$?
$ii$. What is the percentage of no of expenses in $2009-10$ over the expenses in $2010-11$?
$iii$. What is the percentage of minimum expenses over the maximum expenses in the period $2007-201$1?
OR
What is the difference of expenses in $2010-11$ and the expenses in $2006-09$?
A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40\ cm$ and a height of $1\ m.$
$i.$ Find the curved surface area of the cone.
$ii.$ If the outer side of each of the cones is to be painted and the cost of painting is $₹ 12$ per $m^2$, what will be the cost of painting all these cones ? $($Use $\pi=3.14$ and take $\sqrt{1.04}=1.02 )$
View full solution →$i.$ Find the curved surface area of the cone.
$ii.$ If the outer side of each of the cones is to be painted and the cost of painting is $₹ 12$ per $m^2$, what will be the cost of painting all these cones ? $($Use $\pi=3.14$ and take $\sqrt{1.04}=1.02 )$
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