class 12

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Match List-I (Electromagnetic wave type) with List-II (Its association/application) and select the correct option from the choice given below the lists :

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Locus of the image of the point (2, 3) in the line $(2x−3y+4)+k(x−2y+3)=0,kϵR$, is a :

If $∫f(x)dx=ψ(x)$, then $∫x_{5}f(x_{3})dx$is equal to

The integral $∫(x_{4}−1)_{41}dx $ equal:

Let PS be the median of the triangle with vertices $P(2,2),Q(6,−1)andR(7,3)$. The equation of the linepassing through $(1,−1)$ and parallel to PS is

A pendulum made of a uniform wire of cross sectional are A has time period T. When an additional mass M is added to its bob, the time period changes to $T_{M}$. If the Young's modulus of the material of the wire is Y then $Y1 $ is equal to : (g = gravitational acceleration)

The sum of first 9 terms of the series $11_{3} +1+31_{3}+2_{3} +1+2+31_{3}+2_{3}+3_{3} +.....$is

If z is a complex number such that $∣z∣≥2$, then the minimum value of $∣∣ z+21 ∣∣ $

Let the population of rabbits surviving at a time t be governed by the differential equation $(dpdtt =21 p(t)−200.$If $p(0)=100$, then p(t) equals