JEE Advanced Mathematics question
One or more may match with the same. Column I: (i) If is continuous in and , where , then the value of is (ii) In a triangle , the scalar triple product is equal to (iii) The intercept on the -axis cut off by the normal to the parabola passing through is (iv) If is twice differentiable and provides two equal values of for all , and , then is equal to Column II: (a) 3 (b) 4 (c) 1 (d) 2
Answer: (1)
Solution
**(i)** Split and shift ( in the second part):
f(x) dx = f(x) dx + f(x) dx = f(x) dx + f(z + 1) dz = \{f(x) + f(x+1)\} dx = 1 dx = 1.
So (i) ↔ (c).
**(ii)** The scalar triple product is the determinant of the components:
A &
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