12th Math

Bihar Board 12th Maths Important Questions Long Answer Type Part 1 in Hindi

Bihar Board 12th Maths Important Questions Long Answer Type Part 1 in Hindi

BSEB 12th Maths Important Questions Long Answer Type Part 1 in Hindi

प्रश्न 1.
निम्न को सिद्ध करें –

प्रश्न 2.
निम्नलिखित का मान ज्ञात करें :
(i) tan-1 [2 cos (2sin-1 1/2)]

उत्तर:

प्रश्न 3.

प्रश्न 4.

Continuity and differentiability

प्रश्न 1.
एवं के बीच संबंध ज्ञात करें जबकि फलान f(x) निम्न रूप से परिभाषित है f(x) =

 पर संतत है
उत्तर:

प्रश्न 2.

उत्तर:

प्रश्न 3.
ज्ञात करें [LATEX]\frac{d y}{d x}[/LATEX] –
(i) y = cosx · cos 2x · cos 3x
(i) r = 2at2, y = at4
(iii) x = a cosθ, y = b secθ
(iv) x = 4t, y = 4/t
(v) x = cosθ – cos 2θ, y = sinθ – sin 2θ
(vi) x = a( cost + log tan t/2, y = a sint
उत्तर:
(i) ∵ y = (cos x · cos 2x) cos 3x
Diff. w. r. to x.

प्रश्न 4.

∵ L.H.S. at x = 3
f(x) is differentiable at x = 3 and f’ (3) = 12

प्रश्न 5.
(i) If f(x) = x2 + 2x + 7 find f'(3)
(ii) If f(x) = x2 + 7x + 4
Find f (2) & (5)
उत्तर:
(i) Given f(x)= x2 + 2x + 7
By formula,

(ii) Given f(x) = x2 + 7x + 4 By formula

प्रश्न 6.

उत्तर:
दिया गया है, फलन f(x), x = c पर अवकलित है।
∴ f(x), x = c संतत भी होंगे

f(c) = c2
∵ c2 = ac + b = c2
Now f(x) is differentiable at x = c

Bihar Board 12th Maths Important Questions Long Answer Type Part 2 in Hindi 21
∴ L.H.S =R.H.S
∴ a = 2c
समी० (i) & समी० (ii) से
c2 = 2c2 + b
⇒ b = c2 & a= 2c

प्रश्न 7.
यदि फलन f(x) =  प्रत्येक स्थान पर अवकलित हो तो a और b का मान ज्ञात करें।
उत्तर:
For x ≤ 1, f(x) =x<sup[>2 + 3x + a = polynomial
For x> 1,
f(x) = bx + 2 = polynomial.
∵ Polynomial function में सभी स्थान अवकलित होता है।
∴ Therefore f(x) is differentiable for all x > 1 and also for all x < 1.
∴ f(x) is continuous at x = 1
∴ L.H.S. = R.H.S. = f(1)]
Bihar Board 12th Maths Important Questions Long Answer Type Part 2 in Hindi 22
Again f(x) is differentiable at x = 1
∴ L.H.S. at x = 1 = R.H.S. at x = 1


[समी (1)से]
या, 5 = b ⇒ B = 5
समीकरण (i) से,
a – 5 + 2 = 0
या, a – 3 = 0
∴ a = 3

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