A quadratic polynomial whose zeroes are $\frac{2}{5}$ and $\frac{-1}{5}$is
- A$25 x^2+5 x-2$
- B$5 x^2-2 x+1$
- C$5 x^2+2 x-1$
- ✓$25 x^2-5 x-2$
Answer: D.
View full solution →Question types
MODEL PAPER 2025 (BASIC) 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 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The following distribution shows the marks distribution of 80 students.
The median class is
| Marks | Below 10 | Below 20 | Below 30 | Below 40 | Below 50 | Below 60 |
| No. of students | 2 | 12 | 28 | 56 | 76 | 80 |
- A20-30
- B40-50
- ✓30-40
- D10-20
Answer: C.
View full solution →The roots of quadratic equation $3 x^2-4 \sqrt{3} x+4=0$ are
- Anot real
- ✓real and equal
- Crational and distinct
- Dirrational and distinct
Answer: B.
View full solution →Which of the following cannot be the probability of an event?
- A0.4
- B0.04
- C0.0004
- ✓4
Answer: D.
View full solution →The total surface area of solid hemisphere of radius r is
- A$\pi r^2$
- B$2\pi r^2$
- ✓$3\pi r^2$
- D$4\pi r^2$
Answer: C.
View full solution →Assertion(A): $(2+\sqrt{3}) \sqrt{3}$ is an irrational number.
Reason(R): Product of two irrational numbers is always irrational.
Reason(R): Product of two irrational numbers is always irrational.
- 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)
- ✓Assertion (A) is true but reason (R) is false.
- DAssertion (A) is false but reason (R) is true.
Answer: C.
View full solution →Assertion(A): The sequence −1, −1 − 1, . . . , −1 is an AP.
Reason(R): In an AP, $a_n-a_{n-1}$ is constant where $n \geq 2$ and $n \in N$
Reason(R): In an AP, $a_n-a_{n-1}$ is constant where $n \geq 2$ and $n \in N$
- 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)
- ✓Assertion (A) is true but reason (R) is false.
- DAssertion (A) is false but reason (R) is true.
Answer: C.
View full solution →Calculate mode of the following distribution:
| Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |
| Frequency | 5 | 6 | 15 | 10 | 5 | 4 |
If $\sin (A-B)=\frac{1}{2}$ and $\cos (A+B)=\frac{1}{2}, 0^{\circ} < A + B < 90^{\circ}$ and $A > B,$ then find the values of $A$ and $B.$
View full solution →The sum of first 𝑛 terms of an A.P. is represented by $S_n=6 n-n^2$. Find the common difference.
View full solution →The sum of the first $12$ terms of an $A.P.$ is $900.$ If its first term is $20$ then find the common difference and $12^{\text {th }}$ term.
View full solution →In two concentric circles, a chord of length $8 \ cm$ of the larger circle touches the smaller circle. If the radius of the larger circle is $5 \ cm,$ then find the radius of the smaller circle.
View full solution →The sum of a two-digit number and the number obtained by reversing the order of its digits is 99. If ten’s digit is 3 more than the unit’s digit, then find the number.
Prove that the lengths of tangents drawn from an external point to a circle are equal.
In the given figure, PA and PB are tangents to a circle centred at O. Prove that (i) OP bisects $\angle A P B$ (ii) OP is the right bisector of AB.
View full solution →Find the mean using the step deviation method.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 6 | 10 | 15 | 9 | 10 |
Prove that: $(\operatorname{cosec} A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$.
View full solution →As observed from the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$ If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships (Use $\sqrt{3}=1.732)$
View full solution →From the top of a 9 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and angle of depression of its foot is $45^{\circ}$. Determine the height of the tower and distance between building and tower. $($ Use $\sqrt{3}=1.732)$
View full solution →The perimeter of sector OACB of the circle centred at O and of radius 24, is 73.12 cm.
(i) Find the central angle $\angle A O B$.
(ii) Find the area of the minor segment ACB. (Use $\pi=3.14$ and $\sqrt{3}=1.73$ )
View full solution →(i) Find the central angle $\angle A O B$.
(ii) Find the area of the minor segment ACB. (Use $\pi=3.14$ and $\sqrt{3}=1.73$ )
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
A train travels at a certain average speed for a distance of 132 km and then travels a distance of 140 km at an average speed of 4 km/h more than the initial speed. If it takes 4 hours to complete the whole journey, what was the initial average speed? Determine the time taken by train to cover the distances separately.
Rinku was very happy to receive a fancy jumbo pencil from his best friend Rohan on his birthday. Pencil is a basic writing tool, when sharpened its shape is a combination of cylinder & cone as given in the picture.
Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are made up of wood & plastic but we should promote pencils made up of eco-friendly material (many options available in the market these days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i) Find the slant height of the sharpened part.
(ii) Find curved surface area of sharpened part (in terms of $\pi$).
(iii)(A) Find the total surface area of the pencil (in terms of $\pi$).
OR
(B)The pencil’s total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of $\pi$)?
View full solution →Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are made up of wood & plastic but we should promote pencils made up of eco-friendly material (many options available in the market these days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i) Find the slant height of the sharpened part.
(ii) Find curved surface area of sharpened part (in terms of $\pi$).
(iii)(A) Find the total surface area of the pencil (in terms of $\pi$).
OR
(B)The pencil’s total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of $\pi$)?
A group of students conducted a survey to find out about the preferred mode of transportation to school among their classmates. They surveyed 200 students from their school. The results of the survey are as follows:
120 students preferred to walk to school.
25% of the students preferred to use bicycles.
10% of the students preferred to take the bus.
Remaining students preferred to be dropped off by car.
Based on the above information, answer the following questions:
(i) What is the probability that a randomly selected student does not prefer to walk to school?
(ii) Find the probability of a randomly selected student who prefers to walk or use a bicycle.
(iii)(A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?
OR
(B) What is the probability that a randomly selected student prefers to be dropped off by car?
120 students preferred to walk to school.
25% of the students preferred to use bicycles.
10% of the students preferred to take the bus.
Remaining students preferred to be dropped off by car.
Based on the above information, answer the following questions:
(i) What is the probability that a randomly selected student does not prefer to walk to school?
(ii) Find the probability of a randomly selected student who prefers to walk or use a bicycle.
(iii)(A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?
OR
(B) What is the probability that a randomly selected student prefers to be dropped off by car?
Generate a MODEL PAPER 2025 (BASIC) 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.