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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
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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
Write down the converse of following statements:
If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right-angled.
Concept: undefined >> undefined
Write down the converse of following statements:
If all three angles of a triangle are equal, then the triangle is equilateral.
Concept: undefined >> undefined
Write down the converse of following statements:
If x : y = 3 : 2, then 2x = 3y.
Concept: undefined >> undefined
Write down the converse of following statements:
If S is a cyclic quadrilateral, then the opposite angles of S are supplementary
Concept: undefined >> undefined
