Explanation

Explanation

This is an arithmetic sequence with:

• First term $a=1$

• Common difference $d=4-1=3$

General formula for the
$n$th term of an arithmetic sequence:

$$T_n = a + (n - 1)d$$

We need the 101st term:

$$$$
T_{101} = 1 + (101 - 1) times 3 = 1 + 100 times 3 = 1 + 300 = boxed{301}

Explanation

(Using formula: range = (v²/g) = (12×12)/10 = 14.4; then divide by 2 for max range: 7.2 m)

Explanation

Blade → The flat, leaf-like part

Stipe → The stem-like structure

Holdfast → Anchors the organism to a surface (like a root)

These are characteristic parts of macroscopic algae (especially brown algae like Laminaria or Sargassum).

Explanation

CaCO₃ (Calcium carbonate)

No, it is not hygroscopic.

It does not absorb moisture significantly → NOT a desiccating agent

Explanation

• Total amount = 129,000

• People involved:

  • 5 sons → each gets 5x

  • 4 daughters → each gets 4x

  • 3 nephews → each gets x

Let the amount each nephew gets be x

Now express the total amount in terms of x:

• Nephews: $3x$
  

• Daughters: $4\times 4x=16x$

• Sons: $\mathrm{<br>}$

• Total = $3x+16x+25x=44x$

Set up the equation:

$$44x = 129000 Rightarrow x = frac{129000}{44} = ₹2931.82overline{72}$$44​=2931.8272

Explanation

• Black part = 1​/8 of the total length

• White part = 1​ /4of the total length

• Grey part = 5.25 cm

• Total length =?

Let total length be $x$ cm.

Then:

$$text{Black} = frac{1}{8}x, quad text{White} = frac{1}{4}x, quad text{Grey} = 5.25 , text{cm}$$

Add them all:

1/8​x+1​/4x+5.25=x

Convert $frac{1}{4}x$ to same denominator:

$$frac{1}{8}x + frac{2}{8}x + 5.25 = x Rightarrow frac{3}{8}x + 5.25 = x$$

Now solve:

x−3/8​x=5.25⇒5/8​x=5.25

Multiply both sides by 8:

5x=42⇒x=42​/5=8.4cm

Explanation

Given:

• Radius of the circle$r=4$ meters

• Arc length (distance along the circumference), $s=14$ meters

We are to find the displacement, which is the straight-line distance between the starting and ending points of the arc.

Step 1: Find the angle subtended by the arc at the center (θ in radians):

$$theta = frac{s}{r} = frac{14}{4} = 3.5 , text{radians}$$

Step 2: Use the chord length formula to find displacement:

Displacement=2rsin(θ/2​)
=2×4×sin(3.5/2​)=8×sin(1.75)
sin(1.75radians)≈0.983
$$\text{Displacement}\approx 8\times 0.983\approx 7.864\text{meters}$$

Explanation

Although the Balmer series mainly falls in the visible region, its limiting line (as $n\to \infty$) shifts into the UV region.

Explanation

 In $text{K}_2text{Cr}_2text{O}_7$, total oxidation state must be 0. K = +1, O = –2, so Cr must be +6 to balance the equation:

$$2(+1)+2(x)+7(–2)=0\Rightarrow x=+6$$