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The number of integral values of ‘k’ for which the equation 3 sin x + 4 cos x = k + 1 has a solution, k ∈ R is

3 sin x + 4 cos x = k + 1⇒ −5 ≤ k + 1 ≤ 5⇒ −6 ≤ k ≤ 4−6, −5, −4, −3, −2,... View Article

The area bounded by the lines y = |x – 1| – 2 is

Required area area of △PQRArea = (1 / 2) * 4 * 2 = 4This is a bonus question as the second curve is also not given.If the second curve is x -... View Article

In the circle given below, let OA = 1 unit, OB = 13 unit and PQ perpendicular to OB. Then, the area of the triangle PQB (in square units) is :

In the circle given below, let OA = 1 unit, OB = 13 unit and PQ perpendicular to OB. Then, the area of the triangle PQB (in square units) is :a.... View Article

Let R = {P,Q)|P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1,–1) is the set :

a. S = {(x, y)|x2 + y2 = 1}b. S = {(x, y)|x2 + y2 = 4}c. S = {(x, y)|x2 + y2 = √2}d. S = {(x, y)|x2 + y2 = 2}Answer: (d)P(a, b) , Q(c, d),... View Article

If (1, 5, 35), (7, 5, 5), (1, λ, 7) and (2 λ, 1, 2) are coplanar, then the sum of all possible values of λ is:

a. − 44 / 5a. 39 / 5a. − 39 / 5a. 44 / 5Answer: (d)Let P (1, 5, 35), Q (7, 5, 5), R (1, λ, 7) and S (2 λ, 1, 2)⇒... View Article

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to the probability of getting 9 heads, then the probability of getting 2 heads is:

a. 15 / 212b. 15 / 213c. 15 / 214d. 15 / 28Answer: (b)P (x = 9) = P (x = 7)⇒ nC9 (1 / 2)n-9 (1 / 2)9 = nC7 (1 / 2)n-7 (1 / 2)7⇒ nC9 (1... View Article

Find the limit of given trignometry function

The value of is : a. 3/4 b. 2/√3 c. 4/3d. 2/3 Answer: (c)... View Article

The value of ∫_-π/2^π/2 cos² x / [1 + 3^x] dx is:

a. 2πb. 4πc. π / 2d. π / 4Answer: (d)Let I = ∫-π/2π/2 cos2 x / [1 + 3x] dxI = ∫-π/2π/2 [cos2 x] / [1 + 3-x] dx=... View Article

Let f be any function defined on R and let it satisfy the condition:

Let f be any function defined on R and let it satisfy the condition:|f (x) - f (y)|≤ |(x - y)2|, ∀ x, y ∈ R. If f (0) = 1, then... View Article

The maximum slope of the curve y = (1 / 2) x⁴ – 5x³ + 18x² – 19x occurs at the point:

a. (2, 9)b. (2, 2)c. (3, 21 / 2)d. (0, 0)Answer: (b)dy / dx = 2x3 - 15x2 + 36x - 19Let f (x) = 2x3 - 15x2 + 36x - 19f’ (x) = 6x2 - 30x + 36... View Article

The intersection of three lines x – y = 0 and x + 2y = 3 and 2x + y = 6 is a:

a. Equilateral triangleb. Right angled trianglec. Isosceles triangled. None of the aboveAnswer: (c)AB = AC = √5, BC = √2Hence, the... View Article

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is : a.6 b. 1 c. 4 d. 12

Answer: (c)Let A = a2 + 2b2 + c2 = 1a = 1, b = 0, c = 0a = 0, b = 0, c = 1a = –1, b = 0, c = 0c = –1, b = 0, a = 0... View Article

If (sin^-1x) / a = (cos^-1 x) / b) = (tan^-1 y) / c; 0 < x < 1, then the value of cos (πc / [a + b]) is:

a. [1 - y2] / 2yb. [1 - y2] / [1 + y2]c. 1 - y2d. [1 - y2] / y √yAnswer: (b)(sin-1 x) / a = (cos-1 x) / b) = (tan-1 y) / c(sin-1 x) / a =... View Article

The value of [latex]\begin{bmatrix} (a+1)(a+2) & a+2 & 1\\ (a+2)(a+3) & a+3 & 1\\ (a+3)(a+4) & a+4 & 1 \end{bmatrix}[/latex] is

a. –2 b. (a + 1) (a + 2) (a + 3) c. 0 d. (a + 2) (a + 3) (a + 4) Answer: (a)... View Article

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