The correct answer is (b)
Among the four graphs, there is only one graph for which average velocity over the time interval (0,T) can vanish for a suitably chosen T. Which one is it?
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Class 11
Draw a regular hexagon of side 4 cm and construct its incircle.
Solution: Steps to construct: Step 1: Draw a regular hexagon of sides 4cm. Step 2: Draw the angle bisector of A and B. which intersects each other at point O. Step 3: Draw OL perpendicular to AB....
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Solution: Steps to construct: Step 1: Consider a point O on a line, with center O, and radius 3cm, draw a circle. Step 2: Extend its diameters on both sides and cut off OP = OQ = 7cm. Step 3: Mark...
Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent
Solution: Steps to construct: Step 1: Draw a line segment AB = 6cm. Step 2: Draw its perpendicular bisector bisecting it at point O. Step 3: With center O and radius OB, draw a circle. Step 4:...
Use a ruler and compass only in this question. (i) Draw a circle, centre O and radius 4 cm. (ii) Mark a point P such that OP = 7 cm. Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.
Solution: Steps to construct: Step 1: Draw a circle with center O and radius 4cm and mark that point as A. Step 2: Take a point P such that OP = 7cm. Step 3: Bisect OB at M. Step 4: With center M...
(a) In the figure given below, AB is a diameter of the circle. If AE = BE and ∠ADC = 118°, find (i) ∠BDC (ii) ∠CAE
(B) inthe figure given below, AB is the diameter of the semi-circle ABCDE with centre O. If AE = ED and ∠BCD = 140°, find ∠AED and ∠EBD. Also Prove that OE is parallel to BD. Solution: (a) Join DB,...
(a) In figure (i) given below, triangle ABC is circumscribed, find x. (b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.
(a) In figure (i) given below, triangle ABC is circumscribed, find x. (b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x. Solution: (a) From A, AP and AQ are the tangents...
Two concentric circles are of the radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.
Solution: Two concentric circles with center O OP and OB are the radii of the circles respectively, then OP = 5 cm, OB = 13 cm. Ab is the chord of outer circle which touches the inner circle at P....
The tangent to a circle of radius 6 cm from an external point P, is of length 8 cm. Calculate the distance of P from the nearest point of the circle.
Solution: Radius of the circle = 6 cm and length of tangent = 8 cm Let OP be the distance i.e. OA = 6 cm, AP = 8 cm . OA is the radius OA ⊥ AP Now In right ∆OAP, OP2 = OA2 + AP2 (By Pythagoras...
Find the length of the tangent drawn to a circle of radius 3cm, from a point distnt 5cm from the center.
Solution: In a circle with center O and radius 3cm and p is at a distance of 5cm. That is OT = 3 cm, OP = 5 cm OT is the radius of the circle OT ⊥ PT Now in right ∆ OTP, by Pythagoras axiom, OP2 =...
What products are expected from disproportionation reaction of orthophosphorus acid?
$ 1.\,\,{{H}_{3}}P{{O}_{3}}+P{{H}_{3}} $ $ 2.\,\,{{H}_{3}}P{{O}_{4}}+P{{H}_{3}} $ $ 3.\,\,P{{H}_{3}}+{{P}_{2}}{{O}_{5}} $ $ 4.\,\,{{H}_{3}}P{{O}_{3}}+{{P}_{2}}{{O}_{5}} $ Solution: $...
How many tertiary carbon atoms and primary carbon atoms respectively are present in 2-iodo-3, 3-dimethyl pentane?
2,4 0,4 2,3 1,3 Solution: 0,4 We can represent 2-iodo-3, 3-dimethyl pentane as follows: ${{H}_{3}}C-CH(I)-C{{(C{{H}_{3}})}_{2}}-C{{H}_{2}}-C{{H}_{3}}$ As we can see that there are zero carbon atoms...
Which of the following reagents is used to avoid further oxidation of aldehydes?
$ 1.\,\,{{C}_{5}}{{H}_{5}}N{{H}^{+}}Cr{{O}_{3}}Cl $ $ 2.\,\,{{K}_{2}}C{{r}_{2}}{{O}_{7}}/dil.\,{{H}_{2}}S{{O}_{4}} $ $ 3.\,\,dil.\,HN{{O}_{3}} $ $ 4.\,\,Cr{{O}_{3}} $ Solution: $...
Which of the following compounds is used to avoid oxidation in food?
O-hydroxy benzoic acid Acetyl Salicylic acid Ethyl Salicylate Butylated hydroxy Anisole Solution; Butylated hydroxy Anisole Butylated hydroxyanisole (BHA) is an antioxidant made up of...
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer.
Solution:- From the dimensions given in the question, Consider the ∆PQR So, PQ/PA = 12.5/5 = 2.5/1 PR/PB = (PB + BR)/PB = (4 + 6)/4 = 10/4 = 2.5 By comparing both the results, 2.5 = 2.5 Therefore,...
In the given figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM x NP = CN x MP.
Solution:- From the question it is given that, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. We have to prove that, BM x NP = CN x MP Consider the...
Find the equation of a st. line perpendicular to the line 3x – 4y + 12 = 0 and having same y-intercept as 2x – y + 5 = 0.
Solution: Given line: 3x – 4y + 12 = 0 The slope of the line is given by 3x – 4y + 12 = 0 ⇒ 4y = 3x + 12 y = (3/4) x + 3 Thus, slope (m1) = ¾ Now, let the slope of the line perpendicular to the...
Sketch the graphs of the following functions: (i) f (x) = 2 sin x, 0 ≤ x ≤ π (ii) g (x) = 3 sin (x – π/4), 0 ≤ x ≤ 5π/4
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }(sin\text{ }x),\text{ }0\text{ }\le \text{ }(x)\text{ }\le \text{ }\pi \] Since, \[g\text{ }\left( x \right)\text{...
Prove: 1/1.2 + 1/2.3 + 1/3.4 + … + 1/n(n+1) = n/(n+1)
Let, \[P\text{ }\left( n \right)\text{ }=\text{ }1/1.2\text{ }+\text{ }1/2.3\text{ }+\text{ }1/3.4\text{ }+\text{ }\ldots \text{ }+\text{ }1/n\left( n+1 \right)\text{ }=\text{ }n/\left( n+1...
For each of the following compound statements first identify the connecting words and then break it into component statements. (i) All rational numbers are real and all real numbers are not complex. (ii) Square of an integer is positive or negative.
(I) In this sentence 'and' is the associating word The part proclamations are as per the following (a) All normal numbers are genuine (b) All genuine numbers are not perplexing (ii) In this...
Pick the right reply. A thermodynamic state work is an amount (I) used to decide heat changes (ii) whose worth is free of way (iii) used to decide pressure volume work (iv) whose worth relies upon temperature as it were
(ii) An amount which is autonomous of way. solution: Capacities like strain, volume and temperature relies upon the condition of the framework just and not on the way.
Work out the volume involved by 8.8 g of CO2 at 31.1°C and 1 bar pressure. \[R\text{ }=\text{ }0.083\text{ }bar\text{ }dm3\text{ }K1\text{ }mol1.\]
solution: \[\begin{array}{*{35}{l}} ~ \\ pVM\text{ }=\text{ }mRT \\ ~ \\ V=\text{ }mRT/Mp \\ \end{array}\] Here, \[\begin{array}{*{35}{l}} m\text{ }=\text{ }8.8\text{ }g \\ ~ \\ R\text{...
Solve equations using factorization method: x + 1/x = 2.5
Given condition, \[x\text{ }+\text{ }1/x\text{ }=\text{ }2.5\] \[x\text{ }+\text{ }1/x\text{ }=\text{ }5/2\] Taking LCM on L.H.S, we have \[\left( x2\text{ }+\text{ }1 \right)/x\text{ }=\text{...
Work out the all out strain in a combination of 8 g of dioxygen and 4 g of dihydrogen restricted in a vessel of 1 dm3 at 27°C. \[R\text{ }=\text{ }0.083\text{ }bar\text{ }dm3\text{ }K1\text{ }mol1\]
solution : Given: \[Mass\text{ }of\text{ }O2\text{ }=\text{ }8\text{ }g\]
An understudy neglected to add the response blend to the round lined cup at 27 °C however rather he/she set the flagon on the fire. After a pass of time, he understood his error, and utilizing a pyrometer he discovered the temperature of the carafe was 477 °C. What part of air would have been removed out?
solution: Leave the volume of the round lined cup alone V. Then, at that point, the volume of air inside the cup at 27° C is V. Presently, \[\begin{array}{*{35}{l}} ~ \\ V1\text{...
cot x = 3/4, x lies in third quadrant
It is given that We can compose it as We realize that We can compose it as Subbing the qualities Here x lies in the third quadrant so the worth of sec x will be negative We can compose it...
List the names of three electrical gadgets used in your house. Write their power, voltage rating and approximate time for which each one is used in a day. Hence find the electrical energy consumed by each in a month of 30 days.
Which of the following combinations have the same equivalent resistance between X and Y?
In figure (a), the resistors are connected in parallel between X and Y. Let R' be the resistance they have in common. 1 / R' now equals 1 / 2 + 1 / 2 = 2 / 2 ohm ohm ohm ohm ohm o [1] R' = 1 ohm In...
Fig. below shows the I-V characteristic curves for two resistors. Identify the ohmic and non-ohmic resistors. Give a reason for your answer.
The resistors in graphs (a) and (b) are non-ohmic and ohmic, respectively. The I-V graph for (a) is a curve, but the I-V graph for (b) is a straight line or linear.
Give two differences between an ohmic and non-ohmic resistor
Ohmic resistor It follows Ohm's law, which states that V / I is constant for all V or I values. At a given temperature, the slope of the V-I graph is the same for all values of V or I. Non-ohmic...
What are non-ohmic resistors? Give one example and draw a graph to show its current-voltage relationship.
Non-ohmic resistors (also known as non-linear resistances) are conductors that do not obey Ohm's law. LEDs, solar cells, junction diodes, and other similar devices are examples.
Draw a I-V graph for a linear resistor. What does its slope represent?
A linear resistor's I-V graph Slope of the I-V graph: I / V is the slope of the I-V graph. ΔI / ΔV is the reciprocal resistance of the conductor i.e. Slope = ΔI / ΔV = 1 / resistance of the...
Define the term resistance. State its S.I. unit.
The obstruction offered to the flow of current by the conductor is known as its resistance. The S.I. unit of resistance is Ohm.
(a) State whether the current is a scalar or vector? What does the direction of current convey?
(b) State whether the potential is a scalar or vector? What does the positive and negative sign of potential convey?
(a) Current is a scalar quantity. The direction of current conveys that the electrons flow opposite to the direction of flow of current. (b) Potential is a scalar quantity. The positive sign of...
1. Which of the following cells does not exhibit phagocytosis activity?
a. Monocyte b. Neutrophil c. Basophil d. Macrophage correct option – ( c ) explanation – phagocytosis is the activity in which a living cell eats up other cells . Basophil does not show the activity...
Frogs are beneficial for mankind, justify the statement.
It is an important part of the food chain. it help farmers by eating insects and pest and protect him from insect infection. It is also used as a food source for humans in some regions around the...