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Consider the following reactions:

Consider the following reactions: ‘x’, ‘y’ and ‘z’ in these reactions are respectively. a) 4, 5 & 5 b) 5,... View Article

The statement that is not true about ozone is:

a) in the stratosphere, it forms a protective shield against UV radiation. b) in the atmosphere, it is depleted by... View Article

The increasing order of the following compounds towards HCN addition is:

The increasing order of the following compounds towards HCN addition is: a) (iii) < (i) < (iv) < (ii) b)... View Article

The value of the integral ∫₀^π |sin 2x| dx is

I = ∫0π |sin 2x| dx = 2 ∫0π/2 |sin 2x| dx = 2 ∫0π/2 sin 2x dx = 2... View Article

The sum of 162^th power of the roots of the equation x³ – 2x² + 2x – 1 = 0 is

Let roots of x3 – 2x2 + 2x – 1 = 0 be ɑ, β, γ. (x3 – 1) –... View Article

The difference between degree and order of a differential equation that represents the family of curves given by y² = a (x + (√a / 2)), a > 0 i

y2 = a (x + (√a / 2)) Differentiating w.r.t. 2yy’ = a y2 = 2yy’ [x + (√2yy’ /... View Article

Let (λ, 2, 1) be a point on the plane which passes through the point (4, – 2, 2). If the plane is perpendicular to the line joining the points (– 2, – 21, 29) and (– 1, – 16, 23), then (λ / 11)² – (4λ / 11) – 4 is equal to

Let (λ, 2, 1) be a point on the plane which passes through the point (4, – 2, 2). If... View Article

If √3 (cos² x) = (√3 – 1) cos x + 1 the number of solutions of the given equation when x ∈ [0, π / 2] is

√3 t2 – (√3 – 1) t – 1 = 0, where t = cos x Now, t = {(√3... View Article

The number of solutions of the equation log₄ (x – 1) = log₂ (x – 3) is

(1 / 2) log2 (x − 1) = log2 (x − 3) ⇒ x − 1 = (x − 3)2... View Article

Let m, n ∈ N and gcd (2, n) = 1. If 30 ³⁰C₀ + 29 ³⁰C₁ + ….. + 2 ³⁰C₂₈ + 1 ³⁰C₂₉ = n . 2^m, then n + m is equal to

Let S = ∑r=030 (30 – r) 30Cr = 30 ∑r=03030Cr – ∑r=030 r 30Cr = 30 * 230 –... View Article

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 ⇒... View Article

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

Required area area of △PQR Area = (1 / 2) * 4 * 2 = 4 This is a bonus... 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,... 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... 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 / 5 a. 39 / 5 a. − 39 / 5 a. 44 / 5 Answer: (d)... 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 / 212 b. 15 / 213 c. 15 / 214 d. 15 / 28 Answer: (b) P (x... View Article

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