The curved surface area of a cylinder and a cone is equal. If their base radius is same, then the ratio of the slant height of the cone to the height of the cylinder is
- A$1 : 1$
- B$2 : 3$
- C$1 : 2$
- ✓$2 : 1$
Answer: D.
View full solution →Question types
Model Paper 3 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
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 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In a histogram, which of the following is proportional to the frequency of the corresponding class?
- AWidth of the rectangle
- BLength of the rectangle
- CPerimeter of the rectangle
- DArea of the rectangle
The congruence rule, by which the two triangles in the given figure are congruent is$............$
- A$\text{ASA}$
- ✓$\text{SAS}$
- C$\text{SSS}$
- D$\text{RHS}$
Answer: B.
View full solution →Which of the following point does not lie on the line y = 2x + 3?
- A$(-5,-7)$
- B$(-1,1)$
- C$(3,9)$
- D$(3,7)$
The simplest form of $0.5 \overline{7}$ is
- A$\frac{26}{45}$
- B$\frac{57}{99}$
- C$\frac{57}{100}$
- D$\frac{57}{90}$
Assertion (A): The point $(1,1)$ is the solution of $x+y=2$.
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
- 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 $(A) :$ The sides of a triangle are $3 \ cm, 4 \ cm$ and $5 \ cm$ . Its area is $6 \ cm^2$.
Reason $(R) :$ If $2 s=( a + b + c )$, where $a , b , c$ are the sides of a triangle, then area $=\sqrt{(s-a)(s-b)(s-c)}$.
Reason $(R) :$ If $2 s=( a + b + c )$, where $a , b , c$ are the sides of a triangle, then area $=\sqrt{(s-a)(s-b)(s-c)}$.
- 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 $A.$
- ✓$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →Find whether $(\sqrt{2}, 4 \sqrt{2})$ is the solution of the equation $x-2 y=4$ or not?
View full solution →Find whether the given equation have x = 2, y = 1 as a solution:x + y + 4 = 0.
If $O$ is the centre of the circle, find the value of $x$ in given figure :
View full solution →In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles. Prove that B lies on the line segment DC.
The outer diameter of a spherical shell is $10 \ cm$ and the inner diameter is $9 \ cm.$ Find the volume of the metal contained in the shell.
View full solution →In Figure, LM is a line parallel to the y-axis at a distance of 3 units.
i. What are the coordinates of the points P, R and Q?
ii. What is the difference between the abscissa of the points L and M?
i. What are the coordinates of the points P, R and Q?
ii. What is the difference between the abscissa of the points L and M?
Show that the quadrilateral formed by joining the mid-points the sides of a rhombus, taken in order, form a rectangle.
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$?\ 3x + 2y = 6$ and $5x + 2y = 10$
View full solution →The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13\ m, 14\ m$ and $15\ m$. The advertisements yield an earning of $Rs.2000$ per $m^2$ a year. A company hired one of its walls for $6$ months. How much rent did it pay?
View full solution →Find the values of $a$ and $b$ so that the polynomial $\left(x^4+a x^3-7 x^2-8 x+b\right)$ is exactly divisible by $(x+2)$ as well as $(x+3)$.
View full solution →Fig., $A B \| C D$ and $C D \| E F$. Also, $E A \perp A B$. If $\angle B E F=55^{\circ}$, find the values of $x, y$ and $z$.
View full solution →In the given figure, $\text{POQ}$ is a line. Ray $\text{OR}$ is perpendicular to line $\text{PQ. OS}$ is another ray lying between rays $\text{OP}$ and $\text{OR.}$ Prove that $\angle R O S=\frac{1}{2}(\angle Q O S-\angle P O S)$.
View full solution →
If $p=\frac{3-\sqrt{5}}{3+\sqrt{5}}$ and $q=\frac{3+\sqrt{5}}{3-\sqrt{5}}$, find the value of $p ^2+ q ^2$.
View full solution →Read the following text carefully and answer the questions that follow:
Haresh and Deep were trying to prove a theorem. For this they did the following
$i.$ Draw a triangle $ABC$
$ii. \ D$ and E are found as the mid points of $AB$ and $AC$
$iii.\ DE$ was joined and $DE$ was extended to $F$ so $DE = EF$
$iv. \ FC$ was joined.
Questions :
$i. \triangle ADE$ and $\triangle EFC$ are congruent by which criteria?
$ii.$ Show that $C F \| A B$.
$iii.$ Show that $C F=B D$.
OR
Show that $D F=B C$ and $D F \| B C$.
View full solution →Haresh and Deep were trying to prove a theorem. For this they did the following
$i.$ Draw a triangle $ABC$
$ii. \ D$ and E are found as the mid points of $AB$ and $AC$
$iii.\ DE$ was joined and $DE$ was extended to $F$ so $DE = EF$
$iv. \ FC$ was joined.
Questions :
$i. \triangle ADE$ and $\triangle EFC$ are congruent by which criteria?
$ii.$ Show that $C F \| A B$.
$iii.$ Show that $C F=B D$.
OR
Show that $D F=B C$ and $D F \| B C$.
Read the following text carefully and answer the questions that follow:
A golf ball is spherical with about $300 - 500$ dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter $4.2 \ cm$ and the surface has $315$ dimples $($hemi$-$spherical$)$ of radius $2 mm.$
$i.$ Find the surface area of one such dimple.
$ii.$ Find the volume of the material dug out to make one dimple.
$iii.$ Find the total surface area exposed to the surroundings.
OR
Find the volume of the golf ball.
View full solution →A golf ball is spherical with about $300 - 500$ dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter $4.2 \ cm$ and the surface has $315$ dimples $($hemi$-$spherical$)$ of radius $2 mm.$
$i.$ Find the surface area of one such dimple.
$ii.$ Find the volume of the material dug out to make one dimple.
$iii.$ Find the total surface area exposed to the surroundings.
OR
Find the volume of the golf ball.
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 $2007-2011?$
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 $2007-2011?$
OR
What is the difference of expenses in $2010-11$ and the expenses in $2006-09?$
Generate a Model Paper 3 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.