Maths

The negation of the Boolean expression p∨(¬p∧q) is equivalent to:

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Contributor-Level 10

p∨ (¬p∧q) = (p∨¬p)∧ (p∨q)=T∧ (p∨q)=p∨q. Negation is ¬p∧¬q.

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2 months ago

The shortest distance between the lines (x-1)/0 = (y+1)/-1 = z/1 and x+y+z+1=0, 2x-y+z+3=0 is:

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Contributor-Level 10

Family of planes: x+y+z+1+? (2x-y+z+3)=0. Parallel to line means dot product of normals is zero.

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If {p} denotes the fractional part of the number p, then {3²⁰⁰/8}, is equal to

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(80+1)? /8 = (¹C?80? +.+¹C? )/8. Remainder is 1/8.

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2 months ago

If Σᵢ₌₁ⁿ(xᵢ-a)=n and Σᵢ₌₁ⁿ(xᵢ-a)²=na, (n,a>1) then the standard deviation of n observations x₁,x₂,.,xₙ is:

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Contributor-Level 10

S.D.=√ (Σ (x-a)²/n - (Σ (x-a)/n)²) = √ (a-1).

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lim(x→1) ∫₁ˣ (t-1)² cos(t²)dt / ((x-1)sin(x-1))

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Maths Ncert Solutions Maths class 12th

Contributor-Level 10

Kindly go through the solution

BONUS

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2 months ago

If the value of (1 + 2/3 + 6/3² + 10/3³ + .upto ∞) / (log?.?(1/3 + 1/3² + 1/3³ + .upto ∞)) is l, then l² is equal to……….

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Raj Pandey

Contributor-Level 9

The expression inside log is a GP sum: (1/3)/ (1-1/3) = 1/2.
log? (1/2) = 1/2.
The series S = 1+2/3+6/3²+.
S - S/3 = 1 + 4/3² + 4/3³ + . = 1 + (4/9)/ (1-1/3) = 1+2/3=5/3.
(2/3)S = 5/3 ⇒ S=5/2.
l = (5/2)/ (1/2)=5. l²=25.

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2 months ago

The position of a moving car at time t is given by f(t)=at²+bt+c, t>0, where a,b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t?,t?] is attained at the point:

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Contributor-Level 10

Average speed = (f (t? )-f (t? )/ (t? -t? ) = a (t? +t? )+b.
Instantaneous speed = f' (t)=2at+b.
2at+b=a (t? +t? ) ⇒ t= (t? +t? )/2.

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2 months ago

If α, β are roots of the equation x² + 5√2x + 10 = 0, α > β and P? = α? - β? for each positive integer n, then the value of (P?P? + 5√2P?P?)/(P?P? + 5√2P?²) is equal to……….

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Raj Pandey

Contributor-Level 9

α, β are roots of x²+5√2x+10=0. α+β=-5√2, αβ=10.
P? + 5√2P? + 10P? = 0.
So P? +5√2P? =-10P? P? +5√2P? =-10P?
Expression = P? (-10P? )/P? (-10P? ) = 1.

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2 months ago

Consider the following frequency distribution:
| Class: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|
| Frequency: | α | 110 | 54 | 30 | β |
If the sum of all frequencies is 584 and median is 45, then |α - β| is equal to…….

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Raj Pandey

Contributor-Level 9

α+110+54+30+β=584 ⇒ α+β=390.
Median=45. L=40, N=584, C=α+110+54=α+164, f=30, h=10.
45 = 40 + [ (292- (α+164)/30]*10 = 40 + (128-α)/3.
5 = (128-α)/3 ⇒ 15=128-α ⇒ α=113.
β = 390-113=277.
|α-β|=164.

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2 months ago

The region represented by {z = x+iy∈C: |z|-Re(z)≤1} is also given by the inequality:

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