### Set 1

**Find Solutions at the end of every section**

**Five different film actors namely Amit, Shahrukh, Anil, Sunil and Akshay are engaged in the shooting of five different movies with five different actresses Madhuri, Kareena, Aishwarya, Shilpa, and Juhi not necessarily in the same order, in different studios. The director of each film decided to set a record by making the films as early as possible. (i) Aishwarya’s studio is between Amit’s and Akshay’s studios. (ii) Shahrukh’s director who doesn’t have Aishwarya as an actress in the shooting took three fourths as many as the number of days taken by Sunil’s Director. (iii) Akshay’s studio number is 417. (iv) Anil’s film took more days than Amit’s, while Amit’s film took more days than Aishwarya’s to get finalised. (v) The director from studio number 418 took 16 days lesser then the director from studio number 415, to complete his film.**

(vi) Shilpa’s film took 8 days more than Amit’s and two days more than Juhi’s.

(vii) Madhuri’s studio number is 416.

(viii) Madhuri’s film took 8 day less then Aishwarya’s film and Anil’s films took maximum number of days for completion.

1.Who is opposite of Kareena in her film ?

(a) Amit

(b) Shahrukh

(c) Akshay

(d) Sunil

2.The director of which studio made the film in the least number of days ?

(a) 415

(b) 416

(c) 417

(d) 418

3.Name of the actress of studio No. 417 ?

(a) Kareena

(b) Aishwarya

(c) Juhi

(d) None

4.Sunil’s film was completed in ?

(a) 44 days

(b) 40 days

(c) 32 days

(d) None

5.Anil’s opposite was ?

(a) Juhi

(b) Shilpa

(c) Aishwarya

(d) Madhuri

```
1. (A) 2.(B) 3.(C) 4.(C) 5.(B)
```

Shahrukh’s film must be 24 days

Anil’s film must be 48 days.

Sunil’s film must be 32 days.(x=32)

### Set 2

**Find Solutions at the end of every section**

**A wooden cuboid of dimensions 9 x 7 x 5 unit is painted in a fixed pattern.**

(i) The two opposite faces in the front and back are painted in red with 9 x 7 cuts.

(ii) The other two opposite faces on the sides are painted in green with 7 x 5 cuts.

(iii) The remaining top and bottom faces are painted in blue.

The cuboid is cut into 315 small cubes.

1.How many cubes have all the three faces coloured ?

(a) 8

(b) 32

(c) 24

(d) None of these

2.How many cubes have two faces coloured ?

(a) 60

(b) 142

(c) 105

(d) None of these

3.How many cubes have one face coloured ?

(a) 142

(b) 105

(c) 71

(d) None of these

4.How many cubes have no face coloured ?

(a) 142

(b) 60

(c) 105

(d) None of these

5.How many cubes have two faces coloured, that too Red and Green ?

(a) 14

(b) 20

(c) 32

(d) None of these

```
1.(A) 2.(A) 3.(A) 4.(C) 5.(B)
```

1. In all these kinds of questions, the number of cubes which would be painted on three sides would always be the corner cubes. There would be 8 corner cubes.

2. The two faces colored cubes would be the cubes along each edge (except for the corner cubes). It can be visualized that the top edges of the cube would have 7+7+3+3=20 cubes and the bottom edges would also have the same number ( i.e. 20 cubes). The vertical edges would have a further 7+7+7+7=28 cubes.

Out of the total of 68 cubes which are on the edges, 8 cubes would be corner cubes. Hence, the number of cubes painted on two sides would be 68-8=60

Out of the total of 68 cubes which are on the edges, 8 cubes would be corner cubes. Hence, the number of cubes painted on two sides would be 68-8=60

3. The number of one face colored cubes would be : On the front and back surfaces: 7 x 5 + 7 x 5= 70 cubes( You can remember this as (m-2)x(n-2) where m and n are the number of rows and columns on the surface in question). On the top and bottom surfaces : 5 x 3 + 5 x 3=30 cubes.

On the lateral surfaces : 7 x 3 + 7 x 3=42 cubes. Thus a total of 142 cubes would have one side painted.

On the lateral surfaces : 7 x 3 + 7 x 3=42 cubes. Thus a total of 142 cubes would have one side painted.

4. The number of cubes with no face colored would be given by 7 x 5 x 3=105 [which can again be remembered as (m-2)(n-2)(p-2) where m, n and p are the number of parts in which the cube surfaces have been cut- in this case m=9, n=7 and p=5]

5. The cubes along the vertical edges would be painted both red and green. There are 5 such cubes ( with 2 faces coloured) on each of the 4 edges of the cuboid. Thus, the total number of cubes which would be painted on two sides( in red and green) would be 5 x 4=20.

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