$\frac{\text { Upper class limit }+ \text { Lower class limit }}{2}=$
- Afrequency
- ✓class mark
- CClass interval
- Dclass size
Answer: B.
View full solution →Question types
MODEL PAPER 9 (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 9 (BASIC) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A cylindrical vessel $32 \ cm$ high and $18 \ cm$ as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \ cm ,$ the radius of its base is
- ✓$36 \ cm$
- B$24 \ cm$
- C$12 \ cm$
- D$48 \ cm$
Answer: A.
View full solution →Median $=$ ?
- A$l+\left\{h \times \frac{\left(c f-\frac{N}{2}\right)}{f}\right\}$
- B$l-\left\{h \times \frac{\left(\frac{N}{2}-c f\right)}{f}\right\}$
- ✓$l+\left\{h \times \frac{\left(\frac{N}{2}-c f\right)}{f}\right\}$
- D$l+\left\{h \times \frac{\left(\frac{N}{2}+c f\right)}{f}\right\}$
Answer: C.
View full solution →A bag contains 3 white, 4 red and 5 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white?
- ✓$\frac{1}{3}$
- B$\frac{1}{4}$
- C$\frac{1}{2}$
- D$\frac{4}{3}$
Answer: A.
View full solution →If the area of a sector of a circle bounded by an arc of length $5 \pi \ cm$ is equal to $20 \pi \ cm^2$, then find it's radius
- A$10 \ cm$
- B$16 \ cm$
- C$17 \ cm$
- ✓$8 \ cm$
Answer: D.
View full solution →Assertion (A): $\sqrt{2}(5-\sqrt{2})$ 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 A and R are true and R is the correct
- BBoth $A$ and $R$ are true but $R$ is not the explanation of A . correct explanation of A.
- ✓A is true but R is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →Assertion (A): Point $P (0,2)$ is the point of intersection of y -axis with the line $3 x +2 y =4$.
Reason (R): The distance of point $P (0,2)$ from x -axis is 2 units.
Reason (R): The distance of point $P (0,2)$ from x -axis is 2 units.
- ABoth $A$ and $R$ are true and $R$ is the correct
- BBoth $A$ and $R$ are true but $R$ is not the explanation of A . correct explanation of A.
- ✓A is true but R is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →The minute hand of a clock is $7.5 \ cm$ long. Find the area of the face of the clock described by the minute hand in $56$ minutes.
View full solution →Reeti prepares a Rakhi for her brother Ronit. The Rakhi consists of a rectangle of length $8 \ cm$ and breadth $6 \ cm$ inscribed in a circle as shown in the figure. Find the area of the shaded region. $($Use $\pi=3 \cdot 14)$
View full solution →Prove the trigonometric identity: $\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$
View full solution →In fig common tangents $PQ$ and $RS$ to two circles intersect at $A$. Prove that $PQ=RS$.
View full solution →The diagonals of a quadrilateral $A B C D$ intersect each other at the point $O$ such that $\frac{A O}{B O}=\frac{C O}{O D}$
Show that quadrilateral $A B C D$ is a trapezium.
View full solution →Show that quadrilateral $A B C D$ is a trapezium.
Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number $25$ ?
View full solution →If $\sin (A-B)=\frac{1}{2}, \cos (A+B)=\frac{1}{2}, 0^{\circ} < A+B \leqslant 90^{\circ}, A > B,$ find the values of $A$ and $B$ .
View full solution →Prove the identity: $\frac{(1+\cot A+\tan A)(\sin A-\cos A)}{\sec ^3 A-\operatorname{cosec}^3 A}=\sin ^2 A \cos ^2 A$
View full solution →In figure $P O \perp Q O$. The tangents to the circle at $P$ and $Q$ intersect at a point $T$ . Prove that $PQ$ and $OT$ are right bisectors of each other.
View full solution →A part of monthly hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for $20$ days, she has to pay $Rs.3,000$ as hostel charges whereas Mansi who takes food for $25$ days pays $Rs.3,500$ as hostel charges. Find the fixed charges and the cost of food per day.
View full solution →If the median of the distribution given below is $28.5,$ then find the values of $x$ and $y.$
View full solution →| Class Interval | frequency |
| $0-10$ | $5$ |
| $10-20$ | $X$ |
| $20-30$ | $20$ |
| $30-40$ | $15$ |
| $40-50$ | $Y$ |
| $50-60$ | $5$ |
| $\text{Total}$ | $60$ |
A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is $14 \ cm$ and the total height of the vessel is $13 \ cm .$ Find the inner surface area of the vessel. Also, find the volume of the vessel.
View full solution →A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm . If each cone has a height of 2 cm , find the volume of air contained in the model.
AD and PM are medians of triangles ABC and PQR respectively where $\triangle ABC \sim \triangle PQR$. Prove that $\frac{A B}{P Q}=$ $\frac{A D}{P M}$.
View full solution →$A$ and $B$ jointly finish a piece of work in $15$ days. When they work separately, A takes $16$ days less than the number of days taken by $B$ to finish the same piece of work. Find the number of days taken by $B$ to finish the work.
View full solution →Read the following text carefully and answer the questions that follow:
Basant Kumar is a farmer in a remote village of Rajasthan. He has a small square farm land. He wants to do fencing of the land so that stray animals may not enter his farmland. For this, he wants to get the perimeter of the land. There is a pole at one corner of this field. He wants to hang an effigy on the top of it to keep birds away. He standing in one corner of his square field and observes that the angle subtended by the pole in the corner just diagonally opposite to this corner is $60^{\circ}$. When he retires 80 m from the corner, along the same straight line, he finds the angle to be $30^{\circ}$.
$i$. Find the height of the pole too so that he can arrange a ladder accordingly to put an effigy on the pole.
$ii$. Find the length of his square field so that he can buy material to do the fencing work accordingly.
$iii$. Find the Distance from Farmer at position $C$ and top of the pole?
OR
Find the Distance from Farmer at position $D$ and top of the pole?
View full solution →Basant Kumar is a farmer in a remote village of Rajasthan. He has a small square farm land. He wants to do fencing of the land so that stray animals may not enter his farmland. For this, he wants to get the perimeter of the land. There is a pole at one corner of this field. He wants to hang an effigy on the top of it to keep birds away. He standing in one corner of his square field and observes that the angle subtended by the pole in the corner just diagonally opposite to this corner is $60^{\circ}$. When he retires 80 m from the corner, along the same straight line, he finds the angle to be $30^{\circ}$.
$i$. Find the height of the pole too so that he can arrange a ladder accordingly to put an effigy on the pole.
$ii$. Find the length of his square field so that he can buy material to do the fencing work accordingly.
$iii$. Find the Distance from Farmer at position $C$ and top of the pole?
OR
Find the Distance from Farmer at position $D$ and top of the pole?
Read the following text carefully and answer the questions that follow:
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of $TV$ sets in a factory increases uniformly by a fixed number every year. It produced $16000$ sets in 6th year and $22600$ in $9^{th}$ year.
$i.$ Find the production during first year.
$ii.$ Find the production during $8^{th}$ year.
$iii$. Find the production during first $3$ years.
OR
In which year, the production is $₹ 29,20$0.
View full solution →India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of $TV$ sets in a factory increases uniformly by a fixed number every year. It produced $16000$ sets in 6th year and $22600$ in $9^{th}$ year.
$i.$ Find the production during first year.
$ii.$ Find the production during $8^{th}$ year.
$iii$. Find the production during first $3$ years.
OR
In which year, the production is $₹ 29,20$0.
Generate a MODEL PAPER 9 (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.