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The sum of the infinite series 1 + (2 / 3) + (7 / 3²) + (12 / 3³) + (17 / 3⁴) + (22 / 3⁵) + …… is equal to : a. 9 / 4 b. 15 / 4 c. 13 / 4 d. 11 / 4

s = 1 + (2 / 3) + (7 / 32) + (12 / 33) + (17 / 34) + (22 / 35) + …...(s / 3) = (1 / 3) + (2 / 32) + (7 / 33) + …….... View Article

Which one of the following is true for given three planes.

Consider the three planesP1 : 3x + 15y + 21z = 9,P2 : x – 3y – z = 5, andP3 : 2x + 10 y + 14z = 5Then, which one of the following is... View Article

In an increasing geometric series, the sum of the second and the sixth term is 25 / 2 and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to

a. 35b. 30c. 26d. 32Answer: (a)Let a be the first term and r be the common ratio.ar + ar5 = 25 / 2 and ar2 x ar4 = 25a2r6 = 25ar3 = 5a = 5 / r3... View Article

If [latex]\vec{a}[/latex] and [latex]\vec{b}[/latex] are perpendicular, then [latex]\vec{a}\times(\vec{a}\times(\vec{a}\times(\vec{a}\times\vec{b})))[/latex] is equal to :

a. (1 / 2) |... View Article

The rate of growth of bacteria in a culture is proportional to the number of

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t =... View Article

The value of ∑_n=1¹⁰⁰ ∫_n-1ⁿ e^x-[x] dx, where [x] is the greatest integer ≤ x, is

a. 100 (e - 1)b. 100ec. 100 (1 - e)d. 100 (1 + e)Answer: (a)∑n=1100 ∫n-1n ex-[x] dx= ∫01 e{x} dx + ∫12 e{x} dx + ∫23 e{x} dx... View Article

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

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

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The sum of the infinite series 1 + (2 / 3) + (7 / 3²) + (12 / 3³) + (17 / 3⁴) + (22 / 3⁵) + …… is equal to : a. 9 / 4 b. 15 / 4 c. 13 / 4 d. 11 / 4

Which one of the following is true for given three planes.

In an increasing geometric series, the sum of the second and the sixth term is 25 / 2 and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to

If [latex]\vec{a}[/latex] and [latex]\vec{b}[/latex] are perpendicular, then [latex]\vec{a}\times(\vec{a}\times(\vec{a}\times(\vec{a}\times\vec{b})))[/latex] is equal to :

The rate of growth of bacteria in a culture is proportional to the number of

The value of ∑_n=1¹⁰⁰ ∫_n-1ⁿ e^x-[x] dx, where [x] is the greatest integer ≤ x, is

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

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:

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

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

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

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

A function f is defined on [–3,3] as

A line L passing through origin is perpendicular to the lines

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

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

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

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

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

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

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