The correct answer is option 3 i.e. 381.

The used pattern is: A² + A + 1

The prime numbers above 10 are 11, 13, 17, 19, and so on.

For 11 : 11² + 11 + 1 = 133

For 13 : 13² + 13 + 1 = 183

For 17 : 17² + 17 + 1 = 307

Similarly For 19,

19² + 19 + 1 = 381

Hence, the correct answer is 381.

The correct answer is option 4 i.e.

Pattern is as follows:

Arrow is rotated in clockwise direction in every step and position of arrow is changed by one step in anticlockwise direction and arrow is colored in alternate step.

The triangle is moved ahead by one step in clockwise direction and filled with colors in alternate step.

Hence, the correct answer is option 4.

The correct answer is option 4 i.e. 1.

4 3 6 8 means 'the tall Xmas tree'

8 1 3 5 means 'bark of the tree'

9 1 2 8 means 'the dog bark loud'

'the' → 8

bark' → 1

Hence, the correct answer is 1.

The correct answer is option 2 i.e. 56.

The logic used here is: (Addition of the positional value of the vowels) × (the number of consonants in a word)

PLACE = (1 + 5) × 3 = 18

Similarly, 

FINGER = (9 + 5) × 4 = 56

So, FINGER = 56

Hence, 56 is the correct answer.

The correct answer is option 1 i.e. W is X's brother's wife.

X # Y * Z & W

X is the brother of Y, Y is the father of Z, Z is the son of W.

Hence, the correct answer is W is X's brother's wife.

The correct answer is option 4 i.e. Only Conclusion II follows.

The least possible Venn diagram is shown below:

Conclusions:

I. All trees are roses: Does not follow (all roses are fruits and all fruits are trees so, some trees are roses but nothing about the rest of the part of trees is known).

II. Some fruits are roses: Follow (all roses are fruits so, some fruits are roses).

Hence, the correct answer is Only Conclusion II follows.

The correct answer is option 1 i.e.

When the mirror is placed in MN, the mirror image will be:

Note: Since the mirror is placed vertically beside the question figure, the image will be formed by inverting the question figure horizontally about the mirror.

That means the left side of the figure will become the right side and vice versa.

Hence, the correct answer is option 1.

The correct answer is option 1 i.e.

The mirror image of the given figure along the mirror is shown below:

Note: Since the mirror is placed vertically beside the question figure, the image will be formed by inverting the question figure horizontally about the mirror.

That means the left side of the figure will become the right side and vice versa.

Hence, the correct answer is option 1.

The correct answer is option 1 i.e. 24.

Given figure:

Triangles: DAE, DEF, DFG, DGC, DAF, DAG, DAC, DEG, DEC, DFC, BAE, BEF, BFG, BGC, BAF, BAG, BAC, BEG, BEC, BFC, DEB, DGB, DAB, DCB

Hence, the correct answer is 24.

The correct answer is option 1 i.e.

The embedded figure is in Option Figure 1, as shown below:

Hence, the correct answer is Option 1.