If the mean of a frequency distribution is 8.1 and $\sum f _{ i } x _{ i }=132+5 k , \sum f _{ i }=20$ then k =
- A3
- B4
- C5
- ✓6
Answer: D.
View full solution →Question types
MODEL PAPER 1 (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 1 (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 tub of radius 5 cm and height 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, then find the volume of water left in the tub.(Take $\pi=\frac{22}{7}$ )
- A$716 cm^3$
- B$616 cm^3$
- C$600 cm^3$
- D$535 cm^3$
If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by:
- ✓0.5
- B1.5
- C2
- D1
Answer: A.
View full solution →Raju bought a fish from a shop for his aquarium. The shop keeper takes out one fish from a tank containing 15 male fish and 18 female fish. The probability that the fish taken out is a male fish is
- ✓$\frac{5}{11}$
- B$\frac{6}{11}$
- C$\frac{5}{12}$
- D$\frac{7}{11}$
Answer: A.
View full solution →A chord of a circle subtends an angle of $60^{\circ}$ at the centre. If the length of the chord is 100 cm, find the area of the major segment.
- A$30391.7 cm^2$
- B$30720.5 cm^2$
- C$30520.61 cm^2$
- D$31021.42 cm^2$
Assertion (A): No two positive numbers can have 18 as their H.C.F and 380 as their L.C.M.
Reason (R): L.C.M. is always completely divisible by H.C.F.
Reason (R): L.C.M. is always completely divisible by H.C.F.
- ✓Both 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.
Answer: A.
View full solution →Assertion (A): Distance between (5, 12) and origin is 13 units.
Reason (R): D = $\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
Reason (R): D = $\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
- ✓Both 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.
Answer: A.
View full solution →What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length $3 \pi$ cm?
View full solution →To warm ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.(use $\pi=3.14$ )
View full solution →If $\operatorname{cosec}^2 \theta(1+\cos \theta)(1-\cos \theta)=\lambda$.
View full solution →Prove that the tangents drawn at the ends of a diameter of a circle are parallel
In the given figure, ABCD is a rectangle. P is mid-point of DC. If QB = 7 cm, AD = 9 cm and DC = 24 cm, then prove that $\angle APQ =90^{\circ}$.
View full solution →One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
i. a king of red colour
ii. a face card
iii. a red face card
iv. the jack of hearts
v. a spade
vi. the queen of diamonds
i. a king of red colour
ii. a face card
iii. a red face card
iv. the jack of hearts
v. a spade
vi. the queen of diamonds
Prove that: $\frac{\cos ^3 \theta+\sin ^3 \theta}{\cos \theta+\sin \theta}+\frac{\cos ^3 \theta-\sin ^3 \theta}{\cos \theta-\sin \theta}=2$.
View full solution →In $\triangle P Q R$, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sinP, cosP and tanP.
View full solution →In a given figure, two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If $\angle APB =70^{\circ}$, find $\angle ACB$.
View full solution →Aditya is walking along the line joining points (1,4) and (0,6). Aditi is walking along the line joining points (3,4) and (1,0). Represent the graph and find the point where both cross each other
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:
| Expenditure (in ₹) | Frequency |
| 1000-1500 | 24 |
| 1500-2000 | 40 |
| 2000-2500 | 33 |
| 2500-3000 | 28 |
| 3000-3500 | 30 |
| 3500-4000 | 22 |
| 4000-4500 | 16 |
| 4500-5000 | 7 |
A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the solid. Find how much more space it will cover.
A solid is in the shape of a hemisphere surmounted by a cone. If the radius of hemisphere and base radius of cone is 7 cm and height of cone is 3.5 cm, find the volume of the solid. (Take $\pi=\frac{22}{7}$ )
View full solution →Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that $\triangle A B C \sim \triangle P Q R$.
View full solution →The sum of squares of two consecutive multiples of 7 is 637. Find the multiples.
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