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A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.
Concept: undefined >> undefined
The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are
| Column C1 | Column C2 |
| (a) Parallel to y-axis is | (i) λ = `-3/4` |
| (b) Perpendicular to 7x + y – 4 = 0 is | (ii) λ = `-1/3` |
| (c) Passes through (1, 2) is | (iii) λ = `-17/41` |
| (d) Parallel to x axis is | λ = 3 |
Concept: undefined >> undefined
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Evaluate `lim_(h -> 0) ((a + h)^2 sin (a + h) - a^2 sina)/h`
Concept: undefined >> undefined
Evaluate: `lim_(x -> 1) ((1 + x)^6 - 1)/((1 + x)^2 - 1)`
Concept: undefined >> undefined
If `lim_(x -> 1) (x^4 - 1)/(x - 1) = lim_(x -> k) (x^3 - l^3)/(x^2 - k^2)`, then find the value of k.
Concept: undefined >> undefined
`1/(ax^2 + bx + c)`
Concept: undefined >> undefined
Let `f(x) = {{:((k cos x)/(pi - 2x)",", "when" x ≠ pi/2),(3",", x = pi/2 "and if" f(x) = f(pi/2)):}` find the value of k.
Concept: undefined >> undefined
If `f(x) = {{:(x + 2",", x ≤ - 1),(cx^2",", x > -1):}`, find 'c' if `lim_(x -> -1) f(x)` exists
Concept: undefined >> undefined
Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.
Concept: undefined >> undefined
Which of the following is the converse of the statement?
“If Billu secure good marks, then he will get a bicycle.”
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If x = y and y = 3, then x = 3.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If n is a natural number, then n is an integer.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If all three sides of a triangle are equal, then the triangle is equilateral.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If x and y are negative integers, then xy is positive.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If natural number n is divisible by 6, then n is divisible by 2 and 3.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If it snows, then the weather will be cold.
Concept: undefined >> undefined
Write down the contrapositive of the following statements:
If x is a real number such that 0 < x < 1, then x2 < 1.
Concept: undefined >> undefined
Write down the converse of following statements:
If a rectangle ‘R’ is a square, then R is a rhombus.
Concept: undefined >> undefined
Write down the converse of following statements:
If today is Monday, then tomorrow is Tuesday.
Concept: undefined >> undefined
Write down the converse of following statements:
If you go to Agra, then you must visit Taj Mahal.
Concept: undefined >> undefined
