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Let f be differentiable for all x. If f(1) = -2 and f’(x) ≥ 2 for all x ∈ [1, 6] then

(a) f(6) < 8 (b) f(6) ≥ 8 (c) f(6) ≥ 5 (d) f(6) ≤ 5 Solution: Given that f is differentiable for all x. f’(x) ≥ 2 f(1) = -2... View Article

If 12500 = 5^a×2^b, Find a and b.

Solution: Given 12500 = 5a×2b 12500 = 5×5×5×5×5×2×2 = 55×22 So a = 5 and b = 2.... View Article

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

(a) 9 (b) 10 (c) 12 (d) 20 Solution: Given excluding stoppages, the speed of a bus is 54 kmph. Distance travelled by bus in 1 hour, excluding... View Article

In the figure given below AD is a median and BL, CM are pendicular drawn from B and C respectively on AD and AD produced to M. Then show that BL = CM

Solution: BL ⊥ AD DM ⊥ CM In ∆BLD and ∆CMD, ∠BLD = ∠CMD = 900 ∠BDL = ∠CDM (vertically opposite angles) BD = DC (AD is median to BC) ∆BLD ≅... View Article

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls (ii) letters, and (iii) announcements.

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls (ii) letters, and (iii) announcements.... View Article

Let S = {x | x is a positive multiple of 3 less than 100}, P = {x | x is a prime number less than 20}. Then n(S) + n(P) is

(a) 34 (b) 41 (c) 33 (d) 30 Solution: Given S = {x | x is a positive multiple of 3 less than 100} So S = {3, 6, 9, 12, …99} n(S) =... View Article

If a, b, c are positive real numbers such that a+b+c = 18, find the maximum value of a²b³c⁴

Solution: We use A.M ≥ G.M Given a+b+c = 18 ..(i) We have to find the maximum value of a2b3c4. On dividing the number a into equal parts as of... View Article

Write the sets in set builder form. A = {1, 4, 9, 16, 25} , B = {1, 8, 27, 64, 125}

Solution: Given A = {1, 4, 9, 16, 25} Here 1, 4, 9, 16, 25 are squares of natural numbers upto 5. A = {1, 4, 9, 16, 25} = {x : x = n2,... View Article

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90⁰. BD is the perpendicular from B on AC. The circle through B, C and D is drawn. Construct the tangents from A to this circle.

Solution: Construction steps: 1. Draw the line segment BC = 8 cm 2. Measure angle 900 at point B so that angle B = 900. 3. Take B as centre.... View Article

Three tangents are drawn at random to a given circle: Show that the odds are 3 to 1 against the circle being inscribed in the triangle formed by them.

Solution: The incircle is the largest circle inscribed that fits in a triangle. The sides of the triangles are the tangents to this circle. Let... View Article

The calculated spin only magnetic moment of cr2+ is

Solution: Electronic configuration of the Cr2+ ion is [Ar]4s03d4 Number of unpaired electrons (n) = 4 Spin only magnetic moment ... View Article

Reaction A+B→C+D follows following rate law: rate =k[A]1/2[B]1/2. Starting with initial conc. of 1 M of A and B each, what is the time taken for concentration of A to become 0.25 M?

Solution: In the given equation A+B→C+D Given rate constant = 2.303 × 10−3 sec Rate=K [A]1/2[B]1/2 The order of reaction is = 1 For the... View Article

How much water must be added to 300 ml of 0.2m solution of CH3COOH (Ka=1.8×10 −5) for the degree of dissociation of the acid to double?

Solution: CH3COOH ⇋ CH3COO- + H+ α = degree of dissociation α = √ (Ka/C) Where Ka is dissociation constant and C = concentration Let C1=... View Article

The molecule which is not hydrolysed by water at 25 degree celsius is ? (a) AlCl3, (b) SiCl4 (c) BF3 (d) SF6

Solution: (a) AlCl3 + 3H2O → Al(OH)3 + 3 HCl (b) SiCl4 + 4H2O → Si(OH)4 + 4 HCl (c) BF3 + 3H2O → B(OH)3 + 3 HCl (d) SF6 is not hydrolysed... View Article

The value of which of the following unit of concentration will not change with the change in temperature?(a)molarity (b) molality (c) normality (d) formality

Solution (B) Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. Molality = moles... View Article

which of the following compound has highest rate of decarboxylation (a) CH3COOH (b) C6H5COOH (c) C6H5CH2COOH (d) CH3COCH2COOH

Solution: (D) CH3COCH2COOH is a β-keto acid. β-keto acid is a molecule in containing a ketone on the β-carbonof a carboxylic acid.... View Article

When copper sulphate dissolves in the ammonium hydroxide one deep blue complex is formed. what is the co-ordination no of copper in this complex?

The complex's coordination number [Cu(NH3)4] SO4 is a four-letter word. The complex's geometry was formed. The metal ions will be perturbed to... View Article

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