Let $f ( x )$ be a polynomial such that $f\left(-\frac{1}{2}\right)=0$, then a factor of $f ( x )$ is
- A$X+1$
- B$2 x+1$
- C$X -1$
- D$X -1$
Question types
Model Paper 7 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 7 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$(2,3)$
The co-ordinates of two points A and B are (4, 3) and (4, -5) respectively. The co-ordinates of the point at which the line segment AB meets the x-axis are
- A$(-5,0)$
- B$(3,0)$
- C$(0,4)$
- D$(4,0)$
In the given figure, equilateral $\triangle A B C$ is inscribed in a circle and $\ce{ABCD}$ is a quadrilateral, as shown. Then, $\angle BDC =$ ?
- ✓$120^{\circ}$
- B$60^{\circ}$
- C$150^{\circ}$
- D$90^{\circ}$
Answer: A.
View full solution →If $\frac{3^{5 x} \times 81^2 \times 6561}{2^{2 x}}=3^7$, then $x=$
- A$-\frac{1}{3}$
- B$3$
- ✓$-3$
- D$\frac{1}{3}$
Answer: C.
View full solution →Assertion (A): 0.271 is a terminating decimal and we can express this number as $\frac{271}{1000}$ which is of the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$.
Reason (R): A terminating or non-terminating decimal expansion can be expressed as rational number.
Reason (R): A terminating or non-terminating decimal expansion can be expressed as rational 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): ABCD is a square. AC and BD intersect at O . The measure of $\angle AOB =90^{\circ}$.
Reason (R): Diagonals of a square bisect each other at right angles.
Reason (R): Diagonals of a square 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 hemispherical tank is made up of an iron sheet $1 \ cm$ thick. If the inner radius is $1 m,$ then find the volume of the iron used to make the tank.
View full solution →The surface areas of two spheres are in the ratio $1 : 4.$ Find the ratio of their volumes.
View full solution →Evaluate: $(32)^{\frac{1}{5}}+(-7)^0+(64)^{\frac{1}{2}}$.
View full solution →Insert five rational numbers between $-\frac{2}{3}$ and $\frac{3}{4}$.
View full solution →Seema has a $10 m \times 10 m$ kitchen garden attached to her kitchen. She divides it into a $10 \times 10$ grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sows a green chilly plant at $A,$ a coriander plant at $B$ and a tomato plant at $C.$
Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions :
$i.$ Write the coordinates of the points $A, B,$ and $C$ taking the $10 \times 10$ grid as coordinate axes.
$ii.$ By distance formula or some other formula, check whether the points are collinear.
View full solution →Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions :
$i.$ Write the coordinates of the points $A, B,$ and $C$ taking the $10 \times 10$ grid as coordinate axes.
$ii.$ By distance formula or some other formula, check whether the points are collinear.
Factorise: $2 x^3-3 x^2-17 x+30$
View full solution →In given figure, $\text{AD}$ and $\text{BE}$ are respectively altitudes of a triangle $\text{ABC}$ such that $\text{AE = BD}$. Prove that $\text{AD = BE}$.
View full solution →In the given figure, ABC and DBC are two triangles on the same base BC such that $AB = AC$ and $DB = DC$. Prove that $\angle ABD =\angle ACD$,
View full solution →Find four solutions for the following equation $:12x + 5y = 0$
View full solution →$\text{ABC}$ is a triangle. $D$ is a point on $\text{AB}$ such that $AD =\frac{1}{4} AB$ and $E$ is a point of $AC$ such that $AE =\frac{1}{4} AC$. Prove that $DE =\frac{1}{4} BC$.
View full solution →The polynomial $p(x)=x^4-2 x^3+3 x^2-a x+3 a-7$ when divided by $x+1$ leave remainder $19 .$ Find the remainder when $p(x)$ is divided by $x +2$.
View full solution →If each side of a triangle is doubled, then find the ratio of area of new triangle thus formed and the given triangle.
The difference between the sides at right angles in a right$-$angled triangle is $14 \ cm .$ The area of the triangle is $120 \ cm^2$. Calculate the perimeter of the triangle.
View full solution →The diagonals of a quadrilateral $\text{ABCD}$ are perpendicular. Show that the quadrilateral, formed by joining the mid$-$points of its sides, is a rectangle.
View full solution →In each of the figures given below, $A B \| C D$. Find the value of $x^{\circ}$
View full solution →Read the following text carefully and answer the questions that follow:
A Ferris wheel $($or a big wheel in the United Kingdom$)$ is an amusement ride consisting of a rotating upright wheel with multiple passenger$-$carrying components $($commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods$)$ attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.
$i.$ Find $\angle R O Q$.
$ii.$ Find $\angle RQP$.
$iii.$ Find $\angle RSQ$.
OR
Find $\angle ORP$.
View full solution →A Ferris wheel $($or a big wheel in the United Kingdom$)$ is an amusement ride consisting of a rotating upright wheel with multiple passenger$-$carrying components $($commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods$)$ attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.
$i.$ Find $\angle R O Q$.
$ii.$ Find $\angle RQP$.
$iii.$ Find $\angle RSQ$.
OR
Find $\angle ORP$.
Read the following text carefully and answer the questions that follow:
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop student's knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one-to-one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in 2015, the following distribution of ages (in years) of primary school teachers in a district was collected to evaluate the teacher on the above-mentioned criterion.
i. What is the total no of teachers?
ii. Find the class mark of class 15 - 20, 25 - 30 and 45 - 50?
iii. What is the no of teachers of age range 25 - 40 years?
OR
Which classes are having same no. of teachers?
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop student's knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one-to-one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in 2015, the following distribution of ages (in years) of primary school teachers in a district was collected to evaluate the teacher on the above-mentioned criterion.
i. What is the total no of teachers?
ii. Find the class mark of class 15 - 20, 25 - 30 and 45 - 50?
iii. What is the no of teachers of age range 25 - 40 years?
OR
Which classes are having same no. of teachers?
Read the following text carefully and answer the questions that follow:
The front compound wall of a house is decorated by wooden spheres of diameter $21 \ cm,$ placed on small supports as shown in figure. $25$ such spheres are used for this purpose and are to be painted silver. Each support is a cylinder and is to be painted black.
$i.$ what will be the total surface area of the spheres all around the wall?
$ii$. Find the cost of orange paint required if this paint costs $20$ paise per $\ cm^2$.
$iii.$ How much orange paint in liters is required for painting the supports if the paint required is $3 ml$ per $\ cm^2$ ?
OR
What will be the volume of total spheres all around the wall?
View full solution →The front compound wall of a house is decorated by wooden spheres of diameter $21 \ cm,$ placed on small supports as shown in figure. $25$ such spheres are used for this purpose and are to be painted silver. Each support is a cylinder and is to be painted black.
$i.$ what will be the total surface area of the spheres all around the wall?
$ii$. Find the cost of orange paint required if this paint costs $20$ paise per $\ cm^2$.
$iii.$ How much orange paint in liters is required for painting the supports if the paint required is $3 ml$ per $\ cm^2$ ?
OR
What will be the volume of total spheres all around the wall?
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