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The hybridization of carbon 1, 2, 3 and 4 respectively are:

a. sp2, sp, sp2, sp3 b. sp2, sp2, sp2, sp3 c. sp2, sp3, sp2, sp3 d. sp3, sp, sp3, sp3 Answer: (a) Hence the answer is a... View Article

Match List-I with List-II-Wurtz reaction, Sandmeyer reaction, Fitting reaction, Gatterman reaction

Match List-I with List-II Choose the correct answer from the option given below: a. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) b. (a)-(iii),... View Article

The nature of charge on resulting colloidal particles when FeCl₃ is added to excess of hot water is:

a. positive b. neutral c. sometimes positive and sometimes negative d. negative Answer: (a) If FeCl3 is added to excess hot water, a... View Article

Identify A in the following chemical reaction.

Identify A in the following chemical reaction. Answer: (c) Hence the answer is c... View Article

2,4-DNP test can be used to identify

a. aldehyde b. halogens c. ether d. amine Answer: (a) The answer is a... View Article

Information Fusion Centre – Indian Ocean Region (IFC-IOR)

It is important to be aware of the various major infrastructure facilities and installations, as well as information systems operated by the... View Article

LiDAR Technology [UPSC Science & Technology Notes]

LiDAR technology is a remote sensing method that makes use of light in the form of a pulsed laser for measuring variable distances to the subject... View Article

01 July 2021: PIB Summary & Analysis

July 01st, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. National Doctors' Day 2. Chartered Accountants' Day 3. Crop Insurance Week 4.... View Article

If e₁ and e₂ are the eccentricities of the ellipse

a) 14 b) 15 c) 17 d) 16 Solution: e1 = √(1-(4/18)) = √7/3 e2 = √(1+(4/9)) = √13/3 Since (e1, e2) lies on the ellipse 15x2 + 3y2 = k... View Article

If for some α and β in R, the intersection of the following three planes x + 4y − 2z = 1, x + 7y − 5z =β and x + 5y + αz = 5 is a line in ³, then α+β is equal to:

a) 0b) 10c) -10d) 2Solution:The given planes intersect in a lineD = Dx = Dy = Dz = 0D = 0 35 - 5β -20 + 4β -2 = 0β= 13α+ β= 10Answer: (b)... View Article

Solve integral problem – Step by Step Solution

a) 2 b) 4 c) 22 d) π2 Solution: Let I = …(i) I = = ..(ii) Adding (i) and (ii) , , …(iii) = ..(iv) Adding (iii) and... View Article

The number of real roots of the equation, e^4x + e^3x – 4e^2x + 1 = 0 is

a) 3b) 4c) 1d) 2Solution:e4x + e3x - 4e2x + ex + 1 = 0e2x + ex - 4 + (1/ex) + (1/e2x) = 0(e2x + (1/e2x)) + (ex + 1/ex) - 4 = 0(ex + 1/ex)2 - 2 +... View Article

The value of cos³ (π/8) cos (3π/8) + sin³ (π/8) sin (3π/8) is:

a) 1/4b) 1/2√2c) 1/2d) 1/√2Solution:cos3 (π/8) cos (3π/8) + sin3 (π/8) sin (3π/8) = cos3 (π/8) [ 4 cos3 (π/8) - 3 cos (π/8)] + sin3 (π/8)[ 3 sin... View Article

Let f be any function continuous on [ , ] and twice differentiable on ( , ). If for all ∈( , ),f’(x)> 0 and f’’(x) < 0, then for any c ∈ (a,b), (f(c) – f(a)])- (f(b) – f(c)]) is greater than

a) (b-c)/(c-a)b) 1c) (c-a)/(b-c)d) (b+a)/(b-a)Solution:c∈(a,b) and f is twice differentiable and continuous function on ( , )LMVT is... View Article

A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at the rate of 50 cm³/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which the thickness of ice decreases, is:

a) 5/6πb) 1/54πc) 1/36πd) 1/18πSolution:Let thickness of ice be x cm.Therefore, net radius of sphere = (10+x) cmVolume of sphere V =... View Article

The product 2^1/4×4^1/16×8^1/48×16^1/128… ..∞ to is equal to

a) 21/4b) 2c) 21/2d) 1Solution:21/4×41/16×81/48×161/128… ∞= 21/4×22/16×23/48×….∞21/4×21/8×21/16×… ∞= 21/4 + 1/8 + 1/16 …∞ = √2Answer: (c)... View Article

If C be the centroid of the triangle having vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0, then the line passing through the points C and P also passes through the point:

a) (-9, -7)b) (-9, -6)c) (7, 6)d) (9, 7)Solution:Coordinates of C are ((3+1+2)/3 , (-1+3+4)/3) = (2,2)Point of intersection of two linesx + 3y -... View Article

Let a be an integer such that all the real roots of the polynomial 2x⁵ + 5x⁴ + 10x³ + 10x² + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to

Solution:Answer: 2Let f (x) = 2x5 + 5x4 + 10x3 + 10x2 + 10x + 10f’ (x) = 10 (x4 + 2x3 + 3x2 + 2x + 1)= 10x2 [x2 + (1 / x2) + 2 [x + (1 /... View Article

If f (x) = ∫ [5x⁸ + 7x⁶] / [x² + 1 + 2x⁷]² dx, (x ≥ 0), f (0) = 0 and f (1) = 1 / k, then the value of K is

Solution:Answer: (28)The normal of plane = PQ = - 2i + 6j - 6ka = –2, b = 6, c = –6 &The equation of plane is – 2x + 6y... View Article

Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, –3, 1) and (2, 3, –5) at the right angles. If a, b, c, d are integers, then the minimum value of (a² + b² + c² +d²) is

Solution:Answer: (6)In equilateral Δ,z12 + z22 + z32 = z1z2 + z2z3 + z1z3z12 + z22 = z1z2 [because z3 = 0](z1 + z2)2 = 3z1z2a2 = 36|a| = 6... View Article