Correct Answer: 3

Solution : According to the dice rule, if two positions of the same dice are given with two common faces but in different orientations then out of those two common faces the faces that are not common are opposite to each other.

Therefore, the opposite face of the 1 is 3. Hence, the third option is correct.

Correct Answer:

Solution : In the 3D view of dice,
1. Each face out of the three faces in the 3D view should be from all the pairs.
2. Two opposite faces cannot appear adjacently in the 3D view of a folded cube figure. So, the opposite pairs of faces are as follows –

So, in the 3D view of dice, the face opposite the face showing  is . Hence, the first option is correct.

Correct Answer: $\sqrt{63}$

Solution :
Draw PT perpendicular to QR.
PT = $\frac{\sqrt3}{2}\times 9=\frac{9\sqrt3}{2}$ cm
QT = $\frac{9}{2}$ cm
Given, QR = 3QS ⇒ QS = $\frac{9}{3}$ = 3 cm
ST = QT – QS =$\frac{9}{2} -3$ = $\frac{3}{2}$
Using Pythagoras' theorem: Hypotenuse² = Base² + Perpendicular²
PS² = PT²  + ST²
(PS)² = $(\frac{9\sqrt3}{2})^2 + (\frac{3}{2})^2$
⇒ $(PS)^2=\frac{243}{4} + \frac{9}{4}$
⇒ $(PS)^2=\frac{252}{4}$
⇒ $(PS)^2=63$
⇒ $PS=\sqrt{63}$
Hence, the correct answer is $\sqrt{63}$ cm.

Correct Answer: 3

Solution : The correct choice is the third option.

The correct term is "keep quiet", which means to remain silent or not speak. "Keep quite" is incorrect. Quite means completely or entirely, whereas quiet means making little or no noise.

Therefore, the correct sentence is: I did not like his comments on my paper, but I had no alternative as I had agreed to keep quiet.

Correct Answer: S T U L K T U

Solution : Given:
_ L _ _ K S _ T U _ S L _ _ K

To fill the series we have to divide the series –    _ L _ _ K / S _ T U _ / S L _ _ K
Let's check each option –
First option: L U S K T U K;  L L U S K / S K T U T / S L U K K (No repeated pattern has been found)
Second option: U T S K T L U; U L T S K / S K T U T / S L L U K (No repeated pattern has been found)
Third option: S T U L K T U;  S L T U K / S L T U K / S L T U K (SLTUK is repeated in the series)
Fourth option: K T U L U T S; K L T U K / S L T U U / S L T S K (No repeated pattern has been found)

So, the series becomes→S L T U K S L T U K S L T U K. Hence, the third option is correct.

Correct Answer:

Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure. So, the left side of the reflected image will appear as the right side, and the right side will appear as the left side. However, the top and bottom of the reflected image will remain the same.
Thus, the correct mirror image of the given figure will be –

Hence, the third option is correct.

Correct Answer: 20

Solution : Let the speed of the forward journey be $x$ km/hr.
Speed of return journey will = $(x + 10)$ km/hr
Time taken in return journey = $\frac{300}{(x + 10)}$ hours
Time taken in forward journey = $\frac{300}{x}$ hours
According to the question,
⇒ $\frac{300}{x} -\frac{300}{x+10} = 5$
⇒ $\frac{300(x + 10) - 300x}{x(x + 10)} = 5$
⇒ $300x + 3000 - 300x = 5x^2+50x$
⇒ $3000 = 5x^2 + 50x$
⇒ $5x^2 + 50x - 3000 = 0$
⇒ $x^2 + 10x - 600 = 0$
⇒ $x^2 + 30x - 20x - 600 = 0$
⇒ $x(x + 30) - 20(x + 30) = 0$
⇒ $(x - 20)(x + 30) = 0$
As speed cannot be negative, so $x=20$ km/hr
Hence, the correct answer is 20.

Correct Answer: Four

Solution : The correct answer is Four.

India had four sites selected for the 2019 UNESCO Asia-Pacific Awards for Cultural Heritage Conservation. Among them, three are located in Mumbai—Flora Mountain, Keneseth Synagogue, and Gloria Church. The fourth site is the Vikram Sarabhai Library in Ahmedabad. The announcement of these awards took place in Malaysia in 2019.

Correct Answer: 64°

Solution :

$\angle APB =128^{\circ}$
Let $\angle OAB = x$
$\angle PAB = 90^{\circ} - x$
Since PA and PB are tangents from the same external point P,
⇒ PA = PB
$\therefore \triangle APB$ is an isosceles triangle.
⇒ $\angle PAB = \angle PBA = 90^{\circ} - x$
In $ \triangle APB$,
$\angle APB + \angle PAB + \angle PBA = 180^{\circ}$
⇒ $128^{\circ} + (90^{\circ} - x) + (90^{\circ} - x) = 180^{\circ}$
⇒ $128^{\circ}  = 2x$
⇒ $x = 64^{\circ}$
Hence, the correct answer is $64^{\circ}$.

Correct Answer: 2005

Solution : The percentage increase in the export of apples in 2003 = $\frac{6.5-5.2}{5.2}$ × 100 = 25%
The percentage increase in the export of apples in 2005 = $\frac{9.9-7.8}{7.8}$ × 100 = 26.92%
The percentage increase in the export of apples in 2006 = $\frac{10.8-9.9}{9.9}$ × 100 = 9.09%
The percentage increase in the export of apples in 2008 = $\frac{11.4-9.5}{9.5}$ × 100 = 20%
The maximum percentage increase in the export of apples to that of the previous years is in 2005.
Hence, the correct answer is 2005.