Correct Answer:

Solution : When the given folded paper is unfolded, it will look like –

Hence, the second option is correct.

Correct Answer:

Solution : Because there is no restriction on the rotation of the figure, we will check all the possible angles where the question figure can fit itself in the given option figures.
By comparison of all the option figures, the given question figure is embedded only in the

Correct Answer: 5

Solution : Here, the number 150328 is divisible by 23.
When rearranged in descending order we get = 853210
When 5 times 13 i.e., 65 is subtracted from the new number, we get = 853210 – 65 = 853145
$\therefore$ The resultant number is divisible by 5

Correct Answer: 3

Solution : There's no error in this sentence. Therefore, the correct answer is the third option.

The sentence is grammatically correct and conveys the meaning clearly that the girl being referred to is the one whose brother is a doctor.

Correct Answer: B

Solution : Taking dice positions 1 and 2 with B as the common face.

Moving clockwise from the common face with B –

So, the opposite pairs are –

So, the opposite face to the face containing F is B. Hence, the first option is correct.

Correct Answer: 3-Bromopropene

Solution : The correct option is 3-Bromopropene.

The preferred IUPAC name for allyl bromide is 3-Bromopropene. 

• Molecular Formula: C₃H₅Br
• Structural Formula: CH₂=CH-CH₂Br
• It consists of a three-carbon chain with a double bond between the second and third carbon atoms and a bromine atom attached to the third

Correct Answer: $\cos ^2 \phi-\sin ^2 \phi=\tan ^2 \theta$

Solution : Given,
$\cos^2\theta – \sin^2 \theta = \tan^2 \phi$
⇒ $\frac{\cos^2 \theta – \sin^2\theta}{1} = \frac{\sin^2\phi}{\cos^2 \phi}$
⇒ $\frac{\cos^2 \theta – \sin^2 \theta}{\cos^2\theta + \sin^2 \theta} = \frac{\sin^2\phi}{\cos^2 \phi}$
By Componendo and Dividendo,
⇒ $\frac{\cos^2 \theta}{–\sin^2 \theta} = \frac{\sin^2 \phi

Correct Answer: 14 – 48 

Solution : Let's check the options –
First option: 14 – 48; 48 is not divisible by 14. 
Second option: 12 – 72; 72 ÷ 12 = 6
Third option: 11 – 88; 88 ÷ 11 = 8
Fourth option: 8 – 24; 24 ÷

Correct Answer: $-\frac{1}{3}$

Solution : $\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3+(0.41)^3-8(0.39)^3}$
$=\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3+(0.41)^3-(0.78)^3}$
We know the identity,
If $a+b+c=0$ then $a^3+b^3+c^3=3abc$
Here, $(0.37 + 0.41 - 0.78) = 0 ⇒ (0.37)^3+(0.41)^3-(0.78)^3=-3\times 0.37\times 0.41\times 0.78$
So, $\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3+(0.41)^3-(0.78)^3}$
$=\frac{0.74 \times 1.23 \times 0.13}{-3\times 0.37\times 0.41\times 0.78}$

Correct Answer: 12

Solution : The correct option is 12.

The 12 schedules in the Indian Constitution cover a wide range of topics, including delegation of authority, representation, official languages, and more. There were eight schedules in the original Indian Constitution. It was amended and now the number of