Archives

Let S₁ = x² + y² = 9 and S₂ = (x – 2)² + y² = 1

Let S1 = x2 + y2 = 9 and S2 = (x - 2)2 + y2 = 1. Then the locus of the centre of a variable circle S which touches S1 internally and S2... View Article

Let S₁ be the sum of the first 2n terms of an arithmetic progression

Let S1 be the sum of the first 2n terms of an arithmetic progression. Let S2 be the sum of the first 4n terms of the same arithmetic progression.... View Article

Let f : R – {3} → R – {1] be defined by f (x) = (x – 2) / (x – 3). Let g : R – R be given as g (x) = 2x – 3. Then, the sum of all the values of x for which f^-1 (x) + g^-1 (x) = 13 / 2 is equal to

a. 7 b. 5 c. 2 d. 3 Solution: Answer: (b) f-1 (x) + g-1 (x) = 13/2 ⇒ [3x - 2]/[x - 1] + [x + 3]/2 = 13/2 ⇒ 2 (3x - 2) + (x - 1) (x + 3) =... View Article

If 15 sin⁴ θ + 10 cos⁴ θ = 6, for some θ ∈ R, then the value of 27 sec⁶ θ + 8 cosec⁶ θ is equal to:

a. 250b. 500c. 400d. 350Solution:Answer: (a)15 sin4 θ + 10 cos4 θ = 6⇒ 15 sin4 θ + 10 (1 - sin2 θ)2 = 6⇒ 25... View Article

Let g (x) =∫ ₀^t f (t) dt where f is a continuous function

Let g (x) =∫ 0t f (t) dt where f is a continuous function in [0, 3] such that (1/3) ≤ f (t) ≤ 1 for all t ∈ [0, 1] and 0... View Article

Let in a series of 2n observations, half of them are equal to a and the remaining half are equal to -a.

Let in a series of 2n observations, half of them are equal to a and the remaining half are equal to -a. Also by adding a constant b in each of... View Article

A pole stands vertically inside a triangular park ABC. Let the angle of elevation

A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be... View Article

Let the system of linear equations has a non-trivial solution. Then which of the following is true

Let the system of linear equations 4x + λy + 2z = 0 2x - y + z = 0 μx + 2y + 3z = 0, λ, μ ∈ R Has a non-trivial solution. Then which... View Article

The sum of fraction is equal to

Solution: , , , = 504 Answer: (504)... View Article

The number of 4 letter words (with or without meaning) that can be made from the eleven letters of the word “EXAMINATION” is

Solution: Word “EXAMINATION” consists of 2 , 2 , 2 , , , , , Case I: All different letters are selected Number of words formed = 8 4 × 4! =... View Article

tan( + 2 ) is equal to

, α, β ∈ (0, π/2 ), then tan(α + 2β) is equal to _________ . Solution: => tan α = 1/7 => (√2 sinβ) /√2 = 1 √10 => sinβ = 1... View Article

Let f( ) be a polynomial of degree 3 such that (−1) = 10, (1) = −6, ( ) has a critical point at = −1 and ′( ) has a critical point at = 1. Then the local minima at =

Solution: Let the polynomial be f( ) = 3 + 2 + + ⇒ ′ ( ) = 3 2 + 2 + ⇒ ′′( ) = 6 + 2 ′′(1) = 0 ⇒ 6 + 2 = 0 ⇒ = −3... View Article

Let a line = ( > 0) intersect the parabola, ² = at a point , other than the origin. Let the tangent to it at meet the −axis at the point . If area (Δ ) = 4 sq. units, then is equal to

Solution: Let the co-ordinates of 𝑃 be (t 2, t) Equation of tangent at (t 2, t) is y − t = (1/2t) (x − t 2 ) Therefore, co-ordinates of 𝑄 will... View Article

If the 10 ℎ term of an A.P. is 1/20 and its 20^ℎ term is 1/10 , then the sum of its first 200 terms is:

a. b. 100 c. 50 d. Solution: T10 = 1/20 T20 = 1/10 T20 − T10 = 10d => (1/20) = 10d d = 1/200 Therefore, a = 1/200 s200 =... View Article

Solve the system of given linear equations

The system of linear equations λx + 2y + 2z = 5 2λx + 3y + 5z = 8 4x + λy + 6z = 10 has: a. no solution when λ = 2 b. infinitely many... View Article

The differential equation of the family of curves, ² = 4b( + ), ∈ , is:

a. ′′ = ′ b. x( ′) 2 = + 2 ′ c. x( ′ ) 2 = − 2 ′ d. x( ′ ) 2 = 2 ′ − Solution: 2 = 4( + ) … (1) Differentiating both the sides... View Article

Let S be the set of all functions :[0,1] → , which are continuous on [0, 1] and differentiable on (0, 1). Then for every in , there exists a ∈ (0,1), depending on , such that:

a. (f(1)− ( ))/ (1− ) = ′( ) b. |f( ) − (1)| < | ′( )| c. |f( ) + (1)| < (1 + c)| ′ ( )| d. |f( ) − (1)| < (1 − )| ′( )|... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31