Archives

The maximum value of the term independent of ‘t’ in the expansion of

The maximum value of the term independent of ‘t’ in the expansion of [(tx1/5 + {(1 - x)1/10 / t}]10 where x ∈ (0, 1) is :a. 10!... View Article

The number of seven-digit integers with the sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is:

a. 77b. 42c. 35d. 82Answer: (a)Case - I: 1, 1 , 1, 1, 1, 2, 3Number of ways = 7! / 5! = 42Case - II: 1, 1, 1, 1, 2, 2, 2Number of ways = 7! / [4!... View Article

If the curve y = y(x) represented by the solution of the differential equation (2xy² – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to

Answer:1Given,(2xy2 – y)dx + xdy = 0⇒ dy/dx + 2y2 – y/x = 0⇒ (–1/y2) . dy/dx + (1/y) (1/x) = 2Let, 1/y =... View Article

Find the value of ab if vectors a and b are given

Let = 3 - α2 + 3= 6 – α2= 6 – 4= 2... View Article

The total number of two digit numbers ‘n’, such that 3ⁿ+7ⁿ is a multiple of 10, is

Answer: 45Let n = 2t; t ∈ N3n = 32t = (10 - 1)t=10p + (–1)t= 10p ± 1If n = even then 7n + 3n will not be multiple of 10So, if n... View Article

If the curves x = y⁴ and xy = k cut at right angles, then (4k)⁶ is equal to

Answer: 4If the curves x = y4 and xy = k cut at right angles... View Article

A function f is defined on [–3,3] as

A function f is defined on [–3,3] as where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable... View Article

A line L passing through origin is perpendicular to the lines

A line L passing through origin is perpendicular to the lines If the co-ordinates of the point in the first octant on L2 at the distance of... View Article

If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)²⁰²² is divided by 8 is

Answer: 1Let x = 4k + 3(2020 + x)2022= (2020 + 4k + 3)2022= (2024 + 4k - 1)2022= (4A – 1)2022=2022C0(4A)2022(–1)0 +... View Article

The value of [latex]\int_{-2}^2|3x^2-3x-6|dx[/latex] is

Answer: 19 x2-x-2=(x–2)(x+1)... View Article

If [latex]\lim_{x \rightarrow 0} \frac{ax-(e^{4x}-1)}{ax(e^{4x}-1)}[/latex] exists and is equal to b, then the value of a – 2b is

(-16)/(4a+4a)=(–16)/32=–1/2=ba-2b = 4–2((–1)/2) = 4+1 = 5... View Article

If 0 < x, y < π and cos x + cos y – cos (x + y) = 3/2, then sin x + cos y is equal to:

a. (1+√3)/2b. (1–√3)/2c. √3/2d. 1/2 Answer: (a)... View Article

cosec[2 cot^–1( 5) + cos^–1(4/5) ] is equal to

a. 75/56b. 65/56c. 56/33d. 65/33 Answer: (b)cosec[2 cot–1( 5) + cos–1(4/5) ]... View Article

The shortest distance between the line x – y = 1 and the curve x² = 2y is:

a. 1/2b. 0c. 1/(2√2)d. 1/√2 Answer: (c)Shortest distance must be along common normalm1 (slope of line x–y = 1) = 1 ⇒slope... View Article

Let A be a 3 × 3 matrix with det(A) = 4. Let R_i denote the i^th row of A. If a matrix B is obtained by performing the operation R₂→ 2R₂ + 5R₃ on 2A, then det(B) is equal to:

a. 64b. 16c. 80d. 128 Answer: (a)... View Article

Let α and β be the roots of x² – 6x – 2 = 0. If a_n = αⁿ – βⁿ for n ≥ 1, then the value of (a₁₀–2a₈)/(3a₉ ) is

a. 4b. 1c. 2d. 3Answer: (c)α and β be the roots of... View Article

A function f(x) is given by f(x) = 5^x/(5^x+5), then the sum of the series:f(1/20) + f(2/20) + f(3/20) + …… + f(39/20) is equal to:

a. 19/2b. 49/2c. 39/2d. 29/2Answer: (c)f(x) = 5x/(5 x + 5)....(i)⇒ f(2–x) = 52–x/(52–x +5)⇒f(2–x) =... 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