Angle between tangents to the curve y = x^2 - 5x + 6 at the points (2, 0) and (3, 0) is : Option 1: 0° Option 2: 45° Option 3: 60° Option 4: 90°

Answer: 90°. Solution: dy/dx = 2x - 5. At (2,0): slope m_1 = -1. At (3,0): slope m_2 = 1. m_1 * m_2 = -1, so tangents are perpendicular. Angle = 90°.

Calculus

Application of Derivatives

Easy

core

Angle between tangents to the curve $y = x^2 - 5x + 6$ at the points (2, 0) and (3, 0) is :

$0°$

$45°$

$60°$

$90°$

✅ Correct Option: 4

$\frac{dy}{dx} = 2x - 5$ .

At $(2,0)$ : slope $m_1 = -1$ .

At $(3,0)$ : slope $m_2 = 1$ .

$m_1 \cdot m_2 = -1$ , so tangents are perpendicular. Angle $= 90°$ .

2025: 3 June Shift 1

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(A) The critical points of f(x) are -2 and 3.

(B) The function f(x) increases in the interval $(3, \infty)$

(D) The function f(x) increases in the interval (-2,3)

Choose the correct answer from the options given below:

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For the function $f(x) = (x-1)^3(x-2)^2$

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	$f(x) \geq 0$	I. $x \in (-\infty,1) \cup \left(1,\frac{8}{5}\right) \cup (2,\infty)$
B.	$f(x) < 0$	II. $x \geq 1$
C.	$f(x)$ is increasing if	III. $x < 1$
D.	$f(x)$ is decreasing if	IV. $x \in \left(\frac{8}{5},2\right)$

Choose the correct answer from the options given below: