If $p(x)= x ^3- x ^2+ x +1$, then the value of $\frac{p(-1)+p(1)}{2}$ is
- A$2$
- B$3$
- ✓$0$
- D$1$
Answer: C.
View full solution →Question types
Model Paper 9 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 9 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The graph of $x + y = 6$ intersect coordinate axes at
- ABoth $(0,6)$ and $(6,0)$
- B$(6,0)$
- C$(0,6)$
- D$(2,3)$
If $P (3,9)$ and $Q (-3,-4)$, then (abscissa of P ) - (ordinate of Q ) is
- A1
- B7
- C$-1$
- D$-7$
In the given figure, $O$ is the centre of a circle in which $\angle OAB =20^{\circ}$ and $\angle OCB =50^{\circ}$. Then, $\angle AOC =$ ?
- A$20^{\circ}$
- B$70^{\circ}$
- ✓$60^{\circ}$
- D$50^{\circ}$
Answer: C.
View full solution →The simplest rationalising factor of $\sqrt{3}+\sqrt{5}$, is
- A$\sqrt{3}+\sqrt{5}$
- B$\sqrt{3}-\sqrt{5}$
- C$\sqrt{3}-5$
- D$3-\sqrt{5}$
Assertion (A): Rational number lying between two rational numbers a and b is $\frac{a+b}{2}$.
Reason (R): There is one rational number lying between any two rational numbers.
Reason (R): There is one rational number lying between any two rational numbers.
- 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): Two opposite angles of a parallelogram are $(3 x-2)^{\circ}$ and $(50-x)^{\circ}$. The measure of one of the angle is $37^{\circ}$.
Reason (R): Opposite angles of a parallelogram are equal.
Reason (R): Opposite angles of a parallelogram are equal.
- 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.
The radius and slant height of a cone are in the ratio $4: 7$. If its curved surface area is $792 \ cm^2$, find its radius. $($Use $\left.\pi=\frac{22}{7}\right)$.
View full solution →The largest sphere is carved out of a solid cube of side $21 \ cm$. Find the volume of the sphere.
View full solution →Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^3\right]^{\frac{1}{4}}$
View full solution →Simplify: $\left(\frac{5^{-1} \times 7^2}{5^2 \times 7^{-4}}\right)^{7 / 2} \times\left(\frac{5^{-2} \times 7^3}{5^3 \times 7^{-6}}\right)^{-5 / 2}$
View full solution →In which quadrant will the point lie, if:
(i) The y-coordinate is 3 and the x-coordinate is -4?
(ii) The x-coordinate is -5 and the y-coordinate is-3?
(iii) The y-coordinate is 4 and the x-coordinate is 5?
(iv) The y-coordinate is 4 and the x-coordinate is -4?
(i) The y-coordinate is 3 and the x-coordinate is -4?
(ii) The x-coordinate is -5 and the y-coordinate is-3?
(iii) The y-coordinate is 4 and the x-coordinate is 5?
(iv) The y-coordinate is 4 and the x-coordinate is -4?
Factorise: $(2 x-3 y)^3+(3 y-4 z)^3+(4 z-2 x)^3$
View full solution →Construct a histogram for the following data:
| Monthly School fee (in ₹): | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 | 210-240 |
| No of Schools | 5 | 12 | 14 | 18 | 10 | 9 | 4 |
Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:
Draw histogram and frequency polygon representing the data above.
| Class interval (km/h) | Frequency |
| 30-40 | 3 |
| 40-50 | 6 |
| 50-60 | 25 |
| 60-70 | 65 |
| 70-80 | 50 |
| 80-90 | 28 |
| 90-100 | 14 |
Find solutions of the form $x=a, y=0$ and $x=0, y=b$ for the following pairs of equations. Do they have any common such solution?
$3 x+2 y=6$ and $5 x+2 y=10$
View full solution →$3 x+2 y=6$ and $5 x+2 y=10$
$\text{ABC}$ is a triangle right angled at $C$. A line through the mid $-$ point $M$ of hypotenuse $AB$ and parallel to $BC$ intersects $AC$ at $D$. Then prove that,
$i. D$ is the midpoint $AC$
$ii. MD$ is perpendicular to $AC$
$iii. CM = AM =\frac{1}{2} AB$
View full solution →$i. D$ is the midpoint $AC$
$ii. MD$ is perpendicular to $AC$
$iii. CM = AM =\frac{1}{2} AB$
If $x-3$ and $x-\frac{1}{3}$ are both factors of $p x^2+5 x+r$, then show that $p=r$
View full solution →Find the area of a triangular field whose sides are $91 m, 98 m$ and $105 m$ in length. Find the height corresponding to the longest side.
View full solution →Find the area of the triangle whose sides are $42 \ cm, 34 \ cm$ and $20 \ cm$ in length. Hence, find the height corresponding to the longest side.
View full solution →A cloth having an area of $165 m^2$ is shaped into the form of a conical tent of radius $5 m .$
$i.$ How many students can sit in the tent if a student on an average, occupies $\frac{5}{7} m^2$ on the ground?
$ii.$ Find the volume of the cone.
View full solution →$i.$ How many students can sit in the tent if a student on an average, occupies $\frac{5}{7} m^2$ on the ground?
$ii.$ Find the volume of the cone.
If is given that $\angle X Y Z=64^{\circ}$ and XY is produced to point P . Draw a figure from the given information. If ray YQ bisects $\angle ZYP$, find $\angle XYQ$ and reflex $\angle QYP$.
View full solution →Read the following text carefully and answer the questions that follow:
There was a circular park in Defence colony at Delhi. For fencing purpose poles $A, B, C$ and $D$ were installed at the circumference of the park.Ram tied wires From $A$ to $B , B$ to $C$ and $C$ to $D , $ and he managed to measure the $\angle A =100^{\circ}$ and $\angle D =80^{\circ}$
Point $O$ in the middle of the park is the center of the circle.
$i.$ Name the quadrilateral $\text{ABCD} .$
$ii$. What is the value of $\angle C$ ?
$iii$. What is the value of $\angle B$.
OR
Write any three properties of cyclic quadrilateral?
View full solution →There was a circular park in Defence colony at Delhi. For fencing purpose poles $A, B, C$ and $D$ were installed at the circumference of the park.Ram tied wires From $A$ to $B , B$ to $C$ and $C$ to $D , $ and he managed to measure the $\angle A =100^{\circ}$ and $\angle D =80^{\circ}$
Point $O$ in the middle of the park is the center of the circle.
$i.$ Name the quadrilateral $\text{ABCD} .$
$ii$. What is the value of $\angle C$ ?
$iii$. What is the value of $\angle B$.
OR
Write any three properties of cyclic quadrilateral?
Read the following text carefully and answer the questions that follow:
In a forest, a big tree got broken due to heavy rain and wind. Due to this rain the big branches $AB$ and $AC$ with lengths $5 m$ fell down on the ground. Branch $AC$ makes an angle of $30^{\circ}$ with the main tree $AP$. The distance of Point $B$ from $P$ is $4 m$ . You can observe that $\triangle ABP$ is congruent to $\triangle ACP$.
$i.$ Show that $\triangle ACP$ and $\triangle ABP$ are congruent.
$ii$. Find the value of $\angle ACP$ ?
$iii$. Find the value of $\angle BAP$ ?
OR
What is the total height of the tree?
View full solution →In a forest, a big tree got broken due to heavy rain and wind. Due to this rain the big branches $AB$ and $AC$ with lengths $5 m$ fell down on the ground. Branch $AC$ makes an angle of $30^{\circ}$ with the main tree $AP$. The distance of Point $B$ from $P$ is $4 m$ . You can observe that $\triangle ABP$ is congruent to $\triangle ACP$.
$i.$ Show that $\triangle ACP$ and $\triangle ABP$ are congruent.
$ii$. Find the value of $\angle ACP$ ?
$iii$. Find the value of $\angle BAP$ ?
OR
What is the total height of the tree?
Read the following text carefully and answer the questions that follow:
Ajay is writing a test which consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while $1 / 4$ mark is deducted for every wrong answer. Ajay knew answers to some of the questions. Rest of the questions he attempted by guessing.
i. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he answer correctly?
ii. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he guess?
iii. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?
OR
If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?
View full solution →Ajay is writing a test which consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while $1 / 4$ mark is deducted for every wrong answer. Ajay knew answers to some of the questions. Rest of the questions he attempted by guessing.
i. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he answer correctly?
ii. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he guess?
iii. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?
OR
If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?
Generate a Model Paper 9 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.