Correct Answer: $2 \sqrt{153}$

Solution :
Given:
The radius of the bigger circle $r_1= 16$
The radius of the smaller circle $r_2= 8$
Distance between the centres, $d = 26$
So, the length of the direct common tangent, $l = \sqrt{d^2-(r_1-r_2)^2}$
$= \sqrt{26^2-(16-8)^2}$
$=\sqrt{676-64}$
$= \sqrt{612}$
$=2\sqrt{153}$
So, the length

Correct Answer: UX

Solution : Given:
DF, GJ, KM, NQ, RT, ?

First term→ DF → D + 2 = F

Second term → GJ → F + 1 = G; G + 3 = J

Third term → KM → J + 1 = K; K + 2

Correct Answer: EXUHV

Solution : Given:
CAKES is written as FXNBV and ABUSE is written as DYXPH.

Add and subtract 3 alternately from the place value of each letter of CAKES to obtain the required code –
C + 3 = F; A – 3 = X; K + 3

Correct Answer: 26

Solution : Given:
4 × 3 = 14; 5 × 4 = 18; 6 × 5 = 22

Multiply 2 by the sum of the numbers on the L.H.S.
Like, 4 × 3 = 14→(4 + 3) × 2 = 7 × 2 = 14
5 ×

Correct Answer:

Solution : Since the rotation of the figure is not allowed, we will check where the question figure can exactly fit itself in the given option figures.

From the above, it is clear that the given question figure is embedded in the second option figure. Hence, the second

Correct Answer: 2.5 cm

Solution : Given:
A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls.
Radius = $\frac{3}{2}$ cm
So, the volume of the sphere = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{3}{2})^3$ cm³
The diameters of two of the new balls are $\frac{3}{2}$

Correct Answer: 30 litres

Solution : Given: A mixture of acid and water contains 20% acid.
The mixture's ratio = $\frac{(\text{20% acid})}{(\text{80% water})}$ = $\frac{20}{80}$ = 1 : 4.
Let there be $x$ litres of acid in the mixture. Additionally, $4x$ litres of water should be added to the mixture.

Correct Answer: 1

Solution : The first option is the correct answer.

"To fly into a rage" means to suddenly become very angry or lose one's temper explosively or uncontrollably. It describes a rapid and intense escalation of anger or fury. In the third part of the sentence, "flowed" must

Correct Answer: $\frac{a^2}{b \sqrt{b^2-a^2}}$

Solution :
Given: $\sin 23^{\circ}=\frac{a}{b}$
To find: $\sec 23^{\circ}-\sin 67^{\circ}$
By using the figure in the form of a perpendicular, base, and hypotenuse.
$\sin 23^{\circ}=\frac{p}{h} =\frac{a}{b}$
So, base$=\sqrt{b^2-a^2}$
$\sec 23^{\circ} =\frac{b}{\sqrt{b^2-a^2}}$
$\sin 67^{\circ}=\frac{\sqrt{b^2-a^2}}{b}$
Putting the values, we get:
$\sec 23^{\circ}-\sin 67^{\circ}$ =$\frac{b}{\sqrt{b^2-a^2}}-\frac{\sqrt{b^2-a^2}}{b}$
= $\frac{a^2}{b \sqrt{b^2-a^2}}$
Hence,

Correct Answer: Bohag Bihu

Solution : The correct answer is Bohag Bihu.

The boisterous celebration, known as the Bohag Bihu or Rongali Bihu, heralds the arrival of spring and the Assamese New Year. Important holidays in Assam include Baikho, Rongker, Baishagu, Bihu, Ali-Ai-Ligang, and Rajini Gabra.