JEE PYQ Pattern (Mixed Difficulty)

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Try the first 5 questions

1.
The equation x^7 + x^5 + x^3 + 1 = 0 has:
2.
If f(x) = x^n, n >= 2, and [f(a+h) - f(a)]/h = f'(a + theta*h) for some theta in (0,1), then as h -> 0, theta approaches:
3.
If f is continuous on [-2, 2], differentiable on (-2, 2), f(-2) = 5, f(2) = 5, and f(0) = 1, which statement is definitely true?
4.
If f is continuous on [-2, 2], differentiable on (-2, 2), f(-2) = f(2) = 5, f(0) = 1, then:
5.
Let f be a differentiable function on [1, 6] with f(1) = -2 and f(6) = 8. Then there exists c in (1, 6) such that f'(c) is equal to:

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