Mathematics_Today_-_October_2016

SECTION-I Single Correct Answer Type If AxBx r rr r r = ⎛− ⎝⎜ ⎞ ⎠⎟ ⎧ ⎨ ⎪ ⎩⎪ ⎫ ⎬ ⎪ ⎭⎪ = = ∞ = ∞ ∑ ∑ 1 2 22 0 0 sin , sin , then ...

SECTION-II Multiple Correct Answer Type If G GG abc,, be unit vectors such that G G abc⊥ , is inclined at the same angle to bo ...

⇒ (x – 2014) (x – 2015) + (x – 2015) (x – 2013) + (x – 2013)(x – 2014) = 0 ⇒ g(x) = 0 [say] ∴ g(2013) = (–1)(–2) = 2 > 0, g(2 ...

Similarly, cosθ=. GG bc^ ...(ii) ∵ G G GG ab ab⊥∴. = 0 Also, GG G G G cpaqbrab=++×() ∴ GG GG G=++ × G GGG ac paa qab ra a b.. .. ...

Suppose a quadratic function f(x) = ax^2 + bx + c (a, b, c ∈ R and a ≠ 0) satisfies the following conditions : (1) When x ∈ R, ...

Moreover, when t = –4, for any x ∈ [1, 9], we have always (x – 1) (x – 9) ≤ 0 ⇔−^1 + ≤ 4 (),xx 412 that is f(x – 4) ≤ x. Therefo ...

But fx( ) fx( ) xt x xt (^21) x 2 2 2 1 1 2 2 1 2 1 − = − − − = − + − + ++ ()[() ] ()() , xxtxx xx xx 21 12 12 2 2 1 2 22 11 a ...

number z corresponding to a point on the segment DE satisfies z=+λλλ⎜⎛⎝^1 ab+ i⎞⎠⎟+ − ⎝⎜⎛ +bc+ i⎠⎟⎞ ≤≤ 42 1 3 42 () , 01 Substit ...

CATEGORY-I For each correct answer one mark will be awarded, whereas, for each wrong answer, 25% of full mark (1/4) will be dedu ...

Five speakers A, B, C, D and E have been asked to deliver a lecture in a meeting. In how many ways can their lectures be arrang ...

If the circles x^2 + y^2 – 4rx – 2ry + 4r^2 = 0 and x^2 + y^2 = 25 touch each other, then r satisfies (a) 4r^2 + 10r ± 25 = 0 ( ...

In a triangle ABC, 2 2 22 cosAC ac. acac − = + + − Then (a) B = π/3 (b) B = C (c) A, B, C are in A.P. (d) B + C = A A line pa ...

(b) : We h a v e 22 2 21 2 −cosx= tanxx⇒−⎝⎜⎛ tan ⎟⎞⎠=cosx ⇒−⎛⎝⎜ ⎞⎠⎟= − + 21 2 1 2 1 2 2 2 tan tan tan x x x ⇒−⎛⎝⎜ ⎞⎠⎟ − + + ⎛ ...

Area of the triangle =^1 2 absinC =+{}⋅ = + ⎛ ⎝⎜ ⎞ ⎠⎟ 1 2 312 3 33 2 ()sinπ cm^22 cm (b) : Let AB = 3, BC = 5, CD = 2, DA = x a ...

(a) : Let P(h, k) divides the chord AB in the ratio 2 : 1. OD⊥AB, where O is the centre of the circle and D is the foot of the ...

(a, b, c) : Here tanA, tanB are the roots of the equation abx^2 – c^2 x + ab = 0 Therefore, tanABtan c tan tan ab += AB= 2 and ...

The value of tan22 2 2tan tan tan 16 2 16 3 16 5 16 π πππ+++ ++tan^226 tan 16 7 16 ππ is equal to (a) 24 (b) 34 (c) 44 (d) non ...

SOLUTIONS (b) : Let θ=π ⇒ θ=π 16 8 2 Ist and last gives tan^2 θ + cot^2 θ =^8 14 2 − − cos θ Similarly other terms. (c) : fx ...

SOLUTION SET-165 (c) : Focus is 0 1 4 ⎛⎝⎜, ⎞⎠⎟ P A(1, 2) M S y=−^14 1 Directrix is y=−^14 4 PS + PA = PM + PA, takes minimum v ...

If A, B, C be the centres of three co-axial circles and t 1 , t 2 , t 3 be the lengths of the tangents to them from any point, ...