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MathsMediumMCQ2019 · 12 Jan Shift 1

Q70.Let C1 and C2 be the centres of the circles x2 + y2 −2x −2y −2 = 0 and x2 + y2 −6x −6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1 QC2 is : JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 6 (2) 4 (3) 8 (4) 9

What This Question Tests

The problem involves finding the centers and radii of two circles, then determining the points of intersection. The quadrilateral formed by the centers and intersection points is a kite, which can be divided into two congruent triangles. The area is found by calculating half the product of the diagonals or twice the area of one right-angled triangle formed.

Concepts Tested

Equation of circleCenter and radius of circleCommon chordArea of quadrilateral

Formulas Used

General equation of circle: x^2+y^2+2gx+2fy+c=0

Center (-g, -f)

Radius r = sqrt(g^2+f^2-c)

Distance formula

📚 NCERT Sections This Tests

3.10In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured

Chemistry Class 11 · Chapter 3

70% match

3.10 In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below: A/ mol L–1 0.20 0.20 0.40 B/ mol L–1 0.30 0.10 0.05 r0/mol L–1s–1 5.07 × 10–5 5.07 × 10–5 1.43 × 10–4 What is the order of the reaction with respect to A and B? 3.11 The following results have been obtained during the kinetic studies of the reaction: 2A + B ® C + D Experiment [A]/mol L–1 [B]/mol L–1 Initial rate of formation of D/mol L–1 min–1 I 0.1 0.1 6.0 × 10–3 II 0.3 0.2 7.2 × 10–2 III 0.3 0.4 2.88 × 10–1 IV 0.4 0.1 2.40 × 10–2 Determine the rate law and the rate constant for the reaction. 3.12 The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table: Experiment [A]/ mol L–1 [B]/ mol L–1 Initial rate/ mol L–1 min–1 I 0.1 0.1 2.0 × 10–2 II – 0.2 4.0 × 10–2 III 0.4 0.4 – IV – 0.2 2.0 × 10–2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 s–1 (ii) 2 min–1 (iii) 4 years–1 3.14 The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample. 3.15 The experimental data for decomposition of N2O5 [2N2O5 ® 4NO2 + O2] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 102 × [N2O5]/ 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 mol L–1 (i) Plot [N2O5] against t. (ii) Find the half-life period for the reaction. (iii) Draw a graph between log[N2O5] and t. (iv) What is the rate law ? Chemistry 86 Reprint 2025-26 (v) Calculate the rate constant. (vi) Calculate the half-life period from k and compare it with (ii).

5.11Draw All The Isomers (Geometrical And Optical) Of:

Chemistry Class 11 · Chapter 5

70% match

5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+

5.12Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of

Chemistry Class 11 · Chapter 5

70% match

5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?