Explanation

If the determinant $|A|\ne 0$, then $A$ is non-singular (invertible), so the homogeneous system $AX=0$ has only the trivial solution $X=0$.

Last updated 24-07-2026 by NA

Explanation

• R = abc / 4Δ is the formula for the Circumradius of a triangle.
• R = Circumradius
• a, b, c = Lengths of the three sides
• Δ = Area of the triangle

Last updated 24-07-2026 by NA

Explanation

$0.2 times 0.25 = 0.05$

$Last\; updated\; 24-07-2026\; by\; NA$

Explanation

Selling Price = Rs. 120
Profit = 20%

$$CP=$$SP×100​ /100+20=120120×100​

=Rs.100

Last updated 24-07-2026 by NA

Explanation

Given:

Since:

Multiplying both sides by: (x+1)(x2−x+1):

Expanding:

Comparing coefficients:

From $A+C=1$:

Substitute into the second equation:

Last updated on 23-07-2026 by NA

Explanation

Profit is divided according to Capital × Time.

• A = $20,000 times 24 = 480,000$
• B = $15,000 times 24 = 360,000$
• C = $20,000 times 18 = 360,000$

Ratio:

$$480000:360000:360000=4:3:3$$

Total parts:

$$4+3+3=10$$

B's share:

3/10×25,000=7,500

$$Last\; updated\; on\; 23-07-2026\; by\; NA$$

Explanation

Let the two values be 4x and 5x.

Since 4 and 5 are co-prime:

LCM(4x,5x)=20x
20x=180
$$x=9$$

Smaller value:

4x=4×9=36

Last updated on 23-07-2026 by NA
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Explanation

LCM of 3 and 4 = 12

1/3​=4/12​
1/4​=3/12​

Now add:

= 4/12 +3/12

=7/12

Last updated on 23-07-2026 by NA

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Explanation

The decimal number is 11.

Binary uses only 0 and 1.

11 = 8 + 2 + 1.

Binary place values: 8, 4, 2, 1.

Therefore, 11₁₀ = 1011₂.

Last update 0n 21-07-2026 by NA

Explanation

 15: 7 :: x: 560

15/7  = x / 560 

15/7 x 560 

x= 15 x 80 

x =  1200

Last update 0n 21-07-2026 by NA