Shown below is a circle and 2 congruent squares (PQRS & QTUR). ST, SU and UT are

Shown below is a circle and 2 congruent squares (PQRS & QTUR). ST, SU and UT are

A bowl contains 3 red and 2 blue marbles. Roohi wants to pick a red marble.
Which of the following changes could she make so that the probability of picking a red marble.

The graph of a line represented by the equation ax + y + 8 = 0 is shown in the figure below.
(i) Find the value of a.
(ii) Find the point of intersection of this line with the line represented by the equation

Sejal started a business where she sells earrings online. She made Rs 12000 in sales in her first
month. In the second month, when she decreased the price of her product by Rs 20, she sold 40
more items and increased her total sales by Rs 2000.
At what price did she sell the earrings in the second month? Show your work.
OR
A wall (shown below) measures 5 m in length and 4 m in height. The outer portion of the wall
of uniform width ‘x’ m will be painted and the central portion will be tiled. The total budget,
including the tiles at Rs 500 per m2
and paint at Rs 200 per m2
, is Rs 5800.

3) A restaurant stores ice-cream in a box with a dispenser attached for filling ice-cream cones. The
dimensions of the box and the ice-cream cones used by the restaurant are shown in Figure 1
below. To make each serving of dessert, the cone is first filled with ice-cream and then topped
with a hemispherical scoop of ice-cream taken from the same box, as shown in Figure 2.
(Note: The figures are not to scale.)
Approximately how many desserts can be served out of a completely filled box of ice-cream?
Show your steps.
(Note: Take π as 22
7
.)
OR
A right-circular cylindrical water tanker supplies water to colonies on the outskirts of a city and
to nearby villages. Each colony has a cuboidal water tank. In villages, people come with matkas

How many colonies in total would one full tanker be able to supply?
ii) If a tanker supplies water to 3 colonies and then goes to a village where 400 people fill
their matkas, roughly how much water is supplied by the tanker in all? Give your
answer in m3
.
Show your work.
(Note: Assume all the tanks/matkas are completely filled without any loss of water;
Take π as 22
7
; Use 1000000 cm3 = 1 m3
.)
34) In the figure below, ST || PQ. All measurements are in units.
Prove that the area of the trapezium PQTS is [
1
2
(𝑎 + 𝑏)ℎ] sq units.

6) Answer the questions based on the given information.
In space exploration missions, ion propulsion engine is an efficient way of travelling. The
first such engine was used in Deep Space 1 spacecraft. It produced a constant acceleration.
Given below are approximate velocities of the engine.
The initial average velocity of the engine in its first month was 27360 km/hour. When the
spacecrafts passed the asteroid, Braille, it reached an average velocity of 55800 km/hour.
Based on the first 6 months of Deep Space 1's monthly average velocity, the following table
Does the average monthly velocity (in km/hour) form an arithmetic progression? Justify your
answer.
ii) The distance travelled by the spacecraft in the first 10 months (or 7300 hours) can be
expressed as 7300p km where p is the sum of average monthly velocity for the first 10 months.
Find p. Show your work.
iii) The spacecraft passed the comet, Borelly, 15 months after it passed Braille.
Find the average monthly velocity of the spacecraft when it passed Borelly. Show your work.
Raycasting is a technique used in the creation of computer games. The basic idea of raycasting
is as follows: the map is a 2D square grid. Using rays generated from an object, this 2D map
can be transformed into a 3D perspective. One of the methods involves sending out a ray from
the player's location. To determine
how far he/she is from a wall or an obstacle, the distance
between the player's coordinates and the coordinate of the wall is calculated. If the player is
The snooker table has six pockets (P1, P2, P3, P4, P5 and P6) and he has shown three balls -
white (W), red (R) and green (G) on the table. The objective of the game is to use the white
ball to hit the coloured balls into the pockets using a cue stick.
i) How much distance will a ray travel if sent from the green ball to the nearest pocket?
Show your work.
ii) Riju wants to place a yellow ball at the midpoint of the line connecting the white and green
balls.
Find the coordinates of the point at which he should place the yellow ball. Show your steps.
The Surya Kiran is an aerobatics demonstration team of the Indian Air Force, and was formed
in 1996. In Surya Kiran demonstrations, fighter pilots perform aerobatic maneuvers in groups
of 3, to entertain an audience.
Anuja and Sarthak are watchinges A, B and C at a Surya Kiran
Anuja is watching the demonstration from the Hawa Mahal, wh