A card is drawn from a well shuffled deck of playing cards. The probability of getting red face card is
- A$\frac{3}{13}$
- B$\frac{1}{2}$
- C$\frac{3}{52}$
- ✓$\frac{3}{26}$
Answer: D.
View full solution →Question types
MODEL PAPER 2025 (STANDARD) 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 (1 Marks)
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 2025 (STANDARD) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A point on the $x$-axis divides the line segment joining the points $A(2,-3)$ and $B(5,6)$ in the ratio 1:2. The point is
- A$(4,0)$
- B$\left(\frac{7}{2}, \frac{3}{2}\right)$
- ✓(3, 0)
- D(0,3)
Answer: C.
View full solution →Which of the following gives the middle most observation of the data?
- ✓Median
- BMean
- CRange
- DMode
Answer: A.
View full solution →The point on the x- axis nearest to the point (-4,-5) is
- A(0, 0)
- ✓(-4, 0)
- C(-5, 0)
- D$(\sqrt{41}, 0)$
Answer: B.
View full solution →In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is
- A$\frac{1}{6}$
- ✓$\frac{3}{8}$
- C$\frac{11}{24}$
- D$\frac{5}{8}$
Answer: B.
View full solution →Assertion (A) : If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same.
Reason (R) : The length of the arc subtending angle $\theta$ at the centre of a circle of radius $r$ $=\frac{\Pi r \theta}{180}$.
Reason (R) : The length of the arc subtending angle $\theta$ at the centre of a circle of radius $r$ $=\frac{\Pi r \theta}{180}$.
- ABoth assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
- BBoth assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
- CAssertion (A) is true but reason (R) is false
- ✓Assertion (A) is false but reason (R) is true.
Answer: D.
View full solution →Assertion (A): HCF of any two consecutive even natural numbers is always 2.
Reason (R): Even natural numbers are divisible by 2.
Reason (R): Even natural numbers are divisible by 2.
- ABoth assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
- ✓Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
- CAssertion (A) is true but reason (R) is false
- DAssertion (A) is false but reason (R) is true.
Answer: B.
View full solution →$(B)$ The $\text{H.C.F}$ of $85$ and $238$ is expressible in the form $85m -238.$ Find the value of $m.$
View full solution →(B)How many positive three digit integers have the hundredths digit 8 and unit’s digit 5? Find the probability of selecting one such number out of all three digit numbers.
Show that the points $A(-5,6), B(3, 0)$ and $C( 9, 8)$ are the vertices of an isosceles triangle.
View full solution →Find the point$(s)$ on the $x-$axis which is at a distance of $\sqrt{41}$ units from the point $(8,-5)$.
View full solution →Evaluate: $\frac{2 \sin ^2 60^{\circ}-\tan ^2 30^{\circ}}{\sec ^2 45^{\circ}}$
View full solution →
$(B)$ In $\triangle A B C, P$ and $Q$ are points on $A B$ and $A C$ respectively such that $P Q$ is parallel to $BC$. Prove that the median $A D$ drawn from $A$ on $B C$ bisects $P Q$.
View full solution →Prove that $\sqrt{3}$ is an irrational number.
View full solution →$(a)$ The minute hand of a wall clock is $18 \ cm$ long. Find the area of the face of the clock described by the minute hand in $35$ minutes.
View full solution →If $\cos \theta+\sin \theta=1$, then prove that $\cos \theta-\sin \theta= \pm 1$
View full solution →(B)Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?
The monthly expenditure on milk in $200$ families of a Housing Society is given below
Find the value of $x$ and also find the mean expenditure
View full solution →| Monthly Expenditure $($in$)$ |
$1000- 1500$ |
$1500- 2000$ |
$2000- 2500$ |
$2500- 3000$ |
$3000- 3500$ |
$3500- 4000$ |
$4000- 4500$ |
$4500- 5000$ |
| Number of families |
$24$ | $40$ | $33$ | $\times$ | $30$ | $22$ | $16$ | $7$ |
Find the mean and median of the following dat
| Class | 85-90 | 90-95 | 95-100 | 100-105 | 105-110 | 110-115 |
| frequency | 15 | 22 | 20 | 18 | 15 | 25 |
A boy whose eye level is $1.35 m$ from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is $60^{\circ}$. After $12$ seconds, the angle of elevation reduces to $30^{\circ}$. If the speed of the wind is $3 m / s$ then find the height of the balloon from the ground. $($Use $\sqrt{3}=1.73)$
View full solution →Prove that the lengths of tangents drawn from an external point to a circle are equal.
Using above result, find the length $B C$ of $\triangle A B C$. Given that, a circle is inscribed in $\triangle A B C$ touching the sides $A B, B C$ and $C A$ at $R, P$ and $Q$ respectively and $A B=10 cm$, $A Q=7 cm, C Q=5 cm$.
View full solution →Using above result, find the length $B C$ of $\triangle A B C$. Given that, a circle is inscribed in $\triangle A B C$ touching the sides $A B, B C$ and $C A$ at $R, P$ and $Q$ respectively and $A B=10 cm$, $A Q=7 cm, C Q=5 cm$.
Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone.
Dimensions of the conical part of a silo is as follows:
Radius of base $= 1.5 m$
Height $= 2 m$
Dimensions of the cylindrical part of a silo is as follows:
Radius $= 1.5 m$
Height $= 7 m$
On the basis of the above information answer the following questions.
$(i)$ Calculate the slant height of the conical part of one silo.
$(ii)$ Find the curved surface area of the conical part of one silo.
$(iii)(A)$ Find the cost of metal sheet used to make the curved cylindrical part of $1$ silo at the rate of $₹ 2000\ per\ m ^2$.
OR
$(iii) (B)$ Find the total capacity of one silo to store grains.
View full solution →Dimensions of the conical part of a silo is as follows:
Radius of base $= 1.5 m$
Height $= 2 m$
Dimensions of the cylindrical part of a silo is as follows:
Radius $= 1.5 m$
Height $= 7 m$
On the basis of the above information answer the following questions.
$(i)$ Calculate the slant height of the conical part of one silo.
$(ii)$ Find the curved surface area of the conical part of one silo.
$(iii)(A)$ Find the cost of metal sheet used to make the curved cylindrical part of $1$ silo at the rate of $₹ 2000\ per\ m ^2$.
OR
$(iii) (B)$ Find the total capacity of one silo to store grains.
Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer.
Here the largest triangle is represented by $\triangle A B C$ and smallest one with shelf is represented by $\triangle D E F . P Q$ is parallel to $E F$.
$(i)$ Show that $\triangle DPQ \sim \triangle DEF$.
$(ii)$ If $DP =50 cm$ and $PE =70 cm$ then find $\frac{P Q}{E F}$.
$(iii) \ (A)$ If $2 A B=5 D E$ and $\triangle A B C \sim \triangle D E F$ then show that $\frac{\text { perimeter of } \triangle A B C}{\text { perimeter of } \triangle D E F}$ is constant.
OR
$(iii) \ (B)$ If $AM$ and $DN$ are medians of triangles $A B C$ and $D E F$ respectively then prove that $\triangle ABM \sim \triangle DEN$.
Ms. Sheela visited a store near her house and found that the glass jars are arranged one above the other in a specific pattern.
On the top layer there are $3$ jars. In the next layer there are $6$ jars. In the $3^{rd}$ layer from
the top there are $9$ jars and so on till the $8^{th}$ layer.
On the basis of the above situation answer the following questions.
$(i)$ Write an $A.P$ whose terms represent the number of jars in different layers starting
from top . Also, find the common difference.
$(ii)$ Is it possible to arrange $34$ jars in a layer if this pattern is continued? Justify your
answer.
$(iii) (A)$ If there are $' n\ '$ number of rows in a layer then find the expression for finding the total number of jars in terms of $n$.
Hence find $S_8$.
OR
$(iii) (B)$ The shopkeeper added $3$ jars in each layer. How many jars are there in the $5^{th}$ layer from the top?
View full solution →On the top layer there are $3$ jars. In the next layer there are $6$ jars. In the $3^{rd}$ layer from
the top there are $9$ jars and so on till the $8^{th}$ layer.
On the basis of the above situation answer the following questions.
$(i)$ Write an $A.P$ whose terms represent the number of jars in different layers starting
from top . Also, find the common difference.
$(ii)$ Is it possible to arrange $34$ jars in a layer if this pattern is continued? Justify your
answer.
$(iii) (A)$ If there are $' n\ '$ number of rows in a layer then find the expression for finding the total number of jars in terms of $n$.
Hence find $S_8$.
OR
$(iii) (B)$ The shopkeeper added $3$ jars in each layer. How many jars are there in the $5^{th}$ layer from the top?
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