CURRENT ELECTRICITY
1) A conductor of resistance 4 Ω can pass a current up 2.5 A through it. Calculate the potential difference required across the conductor.
2) Calculate the amount of work done in moving a charge of 5 C through a potential difference of 25V. What will be the potential difference if this amount of work is done in moving a charge of 10C ?
3) A metallic wire of length 1m is stretched to double its length in such a way that there is no change in density of the wire . Calculate the ratio of the final resistance.
4) A wire of length 15m and uniform cross section of 6x 10⁻⁷m² has a resistance of 5Ω. Calculate the resistivity of the material of the wire.
5) When a potential difference of 4V is applied across the ends of a wire of 10m length, a current of 2A flows through it. Calculate
a) the resistance per unit length of the wire.
b) the resistance of 4m length of this wire.
6) A battery supplies a current of 0.8 A through a 2Ω resistor and a current of 0.4A through a 5Ω resistor. Calculate the internal resistance of the battery.
7) What will be the equivalent resistance of three resistors of 4Ω, 8Ω and 16 Ω if these are connected in
a) series.
b) parallel.
8) A lamp of resistance 800 Ω, a fire alarm of resistance 30 Ω and a vacuum cleaner of resistance 200Ω are connected in parallel to the mains supply of 240 V. Calculate the current through each appliance and the total current supplied by the mains.
9) The effective resistance of two resistors is 25Ω. If the resistance of one of the resistors is 10 Ω, what is the resistance of the other resistors ?
10) The effecttive resistance of three resistors connected to a battery is 5 Ω. If R₁ = 10Ω, R₂ = 15Ω, what will be the value of R₃ ? Draw a circuit diagram with the flow of current across each resistor.
11) A parallel pair of resistors of values 4Ω and 12 Ω are together connected in series with another resistors of value 3 Ω and battery of emf 24 V. Draw a circuit diagram and calculate the current across each resistor .
12) The figure below shows
V-I graphs of two metallic conductors for series and parallel combination. Which graph represents parallel combination ?
13) The lengths of three conducting wires of same materials are in the ratio 1:2:3. The area of cross section of each wire is same, if these wires are joined in parallel across a battery, what will be the ratio of the currents in them ?
14) In the given circuit diagram,
the emf of the cell is 5 V and its an internal resistance is 2.5 Ω. Calculate the current flowing in the circuit.
15) Find the current flowing through the given circuit connected to a cell of supply 5V. 
16) From the circuit flow diagram given below,
Calculate the current flowing through the circuit.
17) Three resistors of 8Ω, 4 Ω and 2 Ω are connected together in such a way that the total resistance is greater than 8Ω but less than 10 Ω. Suggest a suitable arrangement of how these resistors can be possibly combined and calculate the total resistance.
18) In the given diagram,
A₁, A₂ and A₃ are three ammeters of negligible resistance. The reading of ammeter A₃ is 1A. Calculate
a) the readings of ammeter A₁ and A₂.
b) the total resistance of the circuit.
19) The diagram below
shows three resistors of 5Ω, 8Ω and 10Ω connected to a battery of emf 10V. Calculate
a) the potential difference across the parallel resistors 8Ω and 10Ω.
b) the current through 8Ω resistors.
20) A cell of emf 2.5 V and internal resistance 1.5 Ω is connected to resistors of 5 Ω and 15Ω in series. Draw a circuit diagram and calculate
a) the current in the circuit.
b) the potential difference across each resistor.
c) the total potential difference across the cell.
21) An electric motor draws a current of 5 A from a 220V line. Determine the power of the motor and the energy consumed in 2 hour.
22) A heater has a power of 1.1 kW at 220V.
a) Find the resistance of the heater. 44Ω
b) Calculate the energy in kWh consumed in a week if the heater is used daily for 4h.
23) An electric heater draws 5A of current for 10 minute when connected to 230V power supply. Find the heat energy developed.
24) Find the current flowing through an electric bulb rated as 100W, 220V when connected to a 110 V supply. What will be the power consumed now?
25) Three bulbs, A, B and C, are connected in parallel across 110V source . The rating of bulb is 5oW, 110V, bulb B is 20W,110 V and bulb C is 100 W, 110V
a) Calculate the current flowing in each bulb. 0.45A, 0.18A, 0.9A
b) Which bulb will glow the brightest ?
26) Two resistors with resistance R₁ = 5Ω and R₂=7Ω are connected in series across a battery of emf of 16V. Draw a circuit diagram and find
a) the electrical energy consumed by each resistor in 30 second.265.33J,
b) total power developed in the circuit.
27) In the previous example, if the resistors are connected in parallel instead of series, what would be the electrical energy consumed by each resistor. Draw a circuit diagram for the same.
28) two bulbs are rated as 40W, 220 V and 40W, 110 V, respectively. Compare the resistance of two bulbs.
29) A geyser is rated 1.5kW, 250V. It is connected to 250V mains. Calculate
a) the current drawn by the geyser. 6A
b) electrical energy consumed in 10h in joules.
c) cost of energy consumed at Rs3.50 per kWh.
30) Four tube lights of 40 W each, two fans of 100W each and three bulbs of 60W each operate on an average of 8h per day. If the cost of energy is Rs2.50 per kWh, calculate the monthly bill.
Test paper
1) If the Root the equation x²- 6x + k=0 are real and distinct, then the value of k is
a) >-9 b) >-6 c) < 6 d) <9
2) The tables of the values of x and y, where x is proportional to y.
x: 6 12 N
y: M 18 6
What are the value of M and N?
a) 4,9 b) 9,3 c) 9,4 d) 12,9
3) Shows below is a horizontal water tank composed of a cylinder and two hemispheres.
The tank is filled up to height of 7m. Find the surface area of the tank in contact with water. Use π= 22/7
4) In the adjoining diagram,
5) Study the graph and answer each of the following:
a) Name the curve plotted
b) total number of students
c) the medium marks
d) number of students scoring between 50 and 80 marks.
6) in the given diagram,
∆ ABC is a right angled at B, BDFE is a rectangle. AD= 6cm, CE= 4cm and BC= 12cm
a) prove that ∆ ADF ~ ∆ FEC
b) prove that ∆ ADF ~ ∆ ABC
c) find the length of FE
d) find area of ∆ ADF : area ∆ ABC
7) Show below the table illustrating the monthly income distribution of a company with 100 employees
Income no of employees
0-4 55
4-8 15
8-12 06
12-16 08
16-20 12
20-24 4
Using step deviation method. Find the mean monthly income of an employee.
8) a tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 7m each and the total height of the tent is 14m. Find the
a) quantity of air contained inside the tent.
b) radius of the sphere whose volume is equals to the quantity of air inside the tent.
9) The angle of depression of two ships A and B on opposite sides of a lighthouse of height 100m are respectively. 60° and 30°. The line joining the two ships passes through the foot of the lighthouse.
a) find the distance between the two ships A and B.
b) give your final answer correct to the nearest whole number.
10) 1) Roots of the equation 3x² - 2√6x +2=0 are
a) ±√(2/3) b) √(2/3), √(2/3) c) - √(2/3), √(2/3) d) √(2/3), √(3/2)
11) The sum of the first 16 terms of the AP 10, 6, 2 is :
a) -320 b) 320 c) -350 d) -300
12) The roots of the quadratic equation x²- 5x +5=0 are
a) real and equal
b) real and unequal
c) rational d) imaginary
13) 30th of AP 10, 7, 4,... is :
a) 97 b) 77 c) -77 d) -87
14) the sum of 1+ 3+ 7+ ....199 is
a) 10000 b) 9000 c) 8000 d) 8500
15) The discriminant of the quadratic equation x²- 2x +1=0:
a) =0 b) > 0 c) < 0 d) none
16) Which term of the AP 72, 68, 64,......is 0.
a) 15 b) 18 c) 19 d) 20
TEST PAPER -3
1) In the adjoining figure,
a) angle PSR= angle OQS.
b) the triangle PSR and SQT are similar.
c) PR. QT = RS. ST
d) If PS= 9cm and PQ= 15cm, Write down the value of (PR. RS)/(QT. ST).
2) A copper wire when bent in the form of square encloses an area of 121cm². If the same wire is bent into form of a a circle, find the area of the circle.
3) From the adjoining ∆ ABC,
Hence prove that AB²= BC. BD.
If AB= 6cm, BD= 4cm and AC= 8cm, calculatethe AD.
4) The diagram represents the wiper of a car with the dimensions given in the diagram. Calculate
a) the shaded area swept by the wiper.
b) the perimeter of the shaded area.
5) The annual salaries of a group of employees are given in the following table :
Salaries number of persons
45 3
50 5
55 8
60 7
65 9
70 4
75 7
Calculate the mean salary. Also calculate the median salary.
6) In cyclic quadrilateral ABCD,
a) EF= CF.
b) ∆ BCF ≡ ∆ DEF.
7) From a solid cylinder of height 12cm and base radius 5cm, a conical cavity of the same height and base is hollowed out. Find
a) the volume, of the remaining solid.
b) the surface, of the remaining solid.
8) A well is to be dug with 6m inside diameter and 20m in depth . Find the volume of the earth to be excavated. The earth taken out is spread all around to a width of 3 m to form an embankment . Find the height of the embankment .
9) Find the value of :
(Sun⁴30+ 2 sin²30 cos²30+ cos⁴30)(Sin²90+ cos²90+ tan²45)².
10) For the following distribution, calculate the mean:
Class frequency
10-16 2
16-22 20
22-28 10
28-34 6
34-40 12
Draw a histogram for the above data and estimate the mode.
TEST PAPER - 2
1) The shadow of a flag post 25m high is 25√2m. Find the angle of elevation of the Sun.
2) A conical tent has a circular base area 0.375 hectares. if its height is 20m, finds its capacity.
3) The sum of two radii of two circles is 18.5cm and the difference of their circumference is 22cm. Find the radius of the bigger circle.
4)
5) in the given figure
AB || CD and O is the centre of the circle. If angle BED= 35°, find angle ACD.
6) a) The line x - y = 3 divides the join of (3,4) and (8,3) in the ratio m: n. Find the ratio.
7)
8)
9)
10)
11)
Section II
12)
13)
14)
15) From the following table, find the frequency distribution and calculate the mean marks:
Marks no of students
less than 8 4
Less than 16 10
less than 24 22
Less than 32 41
less than 40 50
16)
17) Prove: sin⁶x + cos⁶x = 1 - 3 sin²x + 3 sin⁴x.
18) Two spheres of the same metal weight 1kgf and 7kgf. The radius of the smaller sphere is 2.5cm. The spheres are melted to form a single big sphere . Find the diameter of bigg sphere.
19) MT and NT are tangents to two circles . Prove that M,B,N and T are concyclic points.
(Use alternate segment property and prove that angle MBN + Angle T = 180°)
20) ∆ ABC and ∆ PQR are similar and their areas are 1089cm² and 2304 cm² respectively. If AB= 22cm, find PQ.
21)
22) The difference between the reciprocals of two consecutive multiples of 3 is 1/468. Find the numbers.
23)
Read the following instructions carefully and follow them:
i) This question paper contains 38 questions . All questions are compulsory.
ii) Question paper is divided into FIVE section- Section A, B, C, D, E.
iii) In section A, question number 1 to 8 are multiple choice questions (MCQs) and question number 19 and 20 are Assertion - Reason reasons based questions 1 mark each
iv) In section B, question number 21 to 25 are very short answersVSA) type questions of 2 marks each.
v) In section C, question number 26 to 31 are short answers (SA) type questions carrying 3 marks each.
vi) In section D, question number 32 to 35 are long answer (LA) type questions carrying 5 marks each.
vii) In section E, question number 36 to 38 are case based integrated units of assessment questions carrying 4 marks each. Internal choice is provided in 2 marks question in each case study.
viii) There is no overall choice. However , an internal choice has been provided in 2 questions in section B, 2 questions in Section C, 2 question in section D and 3 questions in Section E.
ix) Draw neat figures wherever required . Take π=22/7 wherever required if not stated.
x) Use of calculator is not allowed.
SECTION - A
Section A Consists of Multiple choice Type Questions of 1 mark each.
1) Let p be a prime number and k be a positive integer
If p divides k², then which of the these is DEFINITELY divisible by p?
k/2 k 7k k³
a) only k b) only k and 7k c) only k, 7k and 7k³ d) all k/2, k, 7k and 7k³
2) In figure, the graph of a polynomial p(x) is shown . The number of zeros of p(x) is
3) Which of these is a QUADRATIC equation having one of its roots as zero ?
i) x³+ x²= 0 ii) x²- 2x= 0 iii) x²- 9= 0
a) only (i) b) only (ii) c) only (i) and (ii) d) only (ii) and (iii)
4) Two linear equations in variable x and y are given below:
a₁x + b₁y + c= 0 ; a₂x+ b₂y + c=0
Which of the following pieces of information is independently sufficient to determine a solution exists or not for this pair of linear equation ?
5) 4 groups in a class were asked to come up with an arithmetic progression (AP), Shown below are their responses:
Group Arithmetic progression
M 4, 2, 0, -2...
N 41, 38.5, 36, 33.5....
O -19, -21, - 23, - 25,.....
P - 3,-3,-3 ,-3.....
Which of these groups correctly came up with an AP?
a) only groups M and O
b) only groups N and O
c) only groups M, N and O
d) all groups - M, N, O and P
6) ∆ABC is a triangles such that AB: BC= 1:2. Point A lies on the y-axis and the coordinates of B and C are known.
Which of the following formula can DEFINITELY be used to find the coordinate of A?
i) Section formula ii) distance formula
a) only (i) b) only (ii) c) both (i) and (ii) d) neither (i) nor (ii)
7) If three (0,0),(3,√3) and (3,£) form an equilateral triangle , then £ equals to
a) 2 b) -3 c) -4 d) none
8) Leela has a triangular cabinet that fits under his staircase. There are four parallel shelves as shown
(Note: The figure is not to scale)
a) 183cm b) 36cm c) 54 cm d) 86.4cm
9) Ankit joins the centre of the two pulleys and observes line the segments P₁S₁ and P₂S₂ when extended meet at a point X.
a) OQ b) QX c) XS₂ d) P₂S₂
10) The area of the circle that can be inscribed in a square of 6cm is
a) 36π cm² b) 18π cm² c) 12π cm² d) 9π cm²
11) if x tan60° cos 60°= sin 60° cot 60°, then x =
a) cos 30° b) tan 30° c) sin 30° d) cot 30°
12) If cotx = 1/√3, the value of sec²x + cosec²x is
a) 1 b) 40/9 c) 38/9 d) 16/3
13) In the figure below , what is the length of AB ?
14) If I+2, 4k -6 and 3k-2 are three consecutive terms of AP, then the value of k is
a) 3 b) - 3 c) 4 d) - 4
15) If the sum of the first n terms of an AP be 3n² + n and its common difference is 6, then its first term is
a) 2 b) 3 c) 1 d) 4
16) For an event E, P(E)+ P(E') = x, then the value of x³- 3 is
a) -2 b) 2 c) 1 d) - 1
17) Look at the numbers of shown below:
i) - 0.5 ii) 0.00001 iii) 1/2 iv) 1 v) 1.00001 vi) 99%
Which of the above numbers represents probabilities of events?
a) only (i) and (iii) b) only (i),(ii) (iii) and (iv)
c) only (ii) (iii), (iv) and (v)
d) only (ii) 0, (iii) , (iv) and (v)
18) In a cards game, there are 10 cards, 1 to 10. Two players , seated facing each other, randomly choose 5 cards each. They arrange their cards in ascending order of the number on the cards as shown.
In a random game, what is the probability that the sum of the difference is 24 ?
a) 0 b) 1/5 c) 1/2
d) cannot be calculated without knowing the cards chosen by each player
Directions: Two statements are given below - one labelled Assertion (A) and the other labelled Reason(R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).
a) both (A) and (R) are true and (R) is the correct explanation of the (A)
b) Both (A) and (R) are true but (R) is not correct explanation of the (A).
c) (A) is true but (R) is false .
d) (A) is false but (R) is true.
19) Assertion (A): If the zeros of quadratic polynomials ax²+ bx + c are both positive, than a, b and c all have the same sign.
Reason (R): if two of the zeros of a cubic polynomials are zero, then it does not have linear and constant terms.
20) Assertion (A): if in two right triangles, one of the acute angles of one triangle is equals to an acute angle of the other triangle, then triangles will be similar.
Reason (R): in ∆OQR and ∆MST, angle P= 65°, angle Q= 25°, angle M= 90° and angle S= 25°, then ∆QPR similar to ∆TSM.
SECTION - B
Section B consists of 5 questions of 2 marks each.
21) Show that 7 - √5 is irrational, given that root √5 is irrational.
22) In the given figure
23) In the figure,
24) A) Evaluate : tan²30 sin 30+ cos 60 sin²90 tan²60 - 2 tan 45 cos² 0 sin 90.
OR
B) if a cosx+ b sin x = m and a sinx - b cosx = n, prove that m²+ n²= a²+ b².
25)A) a piece of wire 22 cm long is bent into the form of an Arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle. (Use π=22/7)
OR
B) The diameter of the wheel is 1.26m. What is the distance covered in 500 revolutions?
SECTION - C
Section C consists of 6 questions of 3 marks each.
26) A dining hall has a length of 8.25m, breadth of 6.75m, and height of 4.50m. What is the length of the longest unmarked ruler that can be measure the three dimensions of the hall ? Show that your steps and give valid reasons.
27) Write the discriminant of the quadratic equation (x + 4)²= 3(7 x - 4).
28)A) Places A and B are 80km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of the car ps.
OR
B) A train covered a certain distance at the uniform speed. If the train would have been 6 kmph faster, it would have taken 4 hours less than the scheduled time. and, if the train were slower by 6kmph; it would have taken 6 hours more than the scheduled time. Find the length of the journey.
29)A) In the given figure
OR
B) Two concentric circles are of radii 5cm and 3cm. Find the length of the chord of the longer circle which touches the smaller circle.
30) Show that: (1+ secx)/secx = sin²x/(1 - cosx).
31) Find the mean of the following data using assumed mean method:
Class: 0-5 5-10 10-15 15-20 20-25
Frequency: 8 7 10 13 12
SECTION - D
Section D consists of 4 questions of 5 marks each.
32) A) The two palm trees are of equal heights are standing opposite to each other on either side of the river , which is 80m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees in the distances of the point from the trees. (use √3=1.73)
OR
B) The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of a tower from the root of the building is 60°. If the tower is 50m high, then find the height of the building.
33)! Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea-sets, crockery and ceramic tile works . a huge portion of the ceramic used in the country is supplied by the Khurja and is also referred as "The ceramic Town".
Following are the few pottery objects of Khurja.
Students found the shapes of the object very interesting and they could easily relate them with mathematical shapes, viz sphere , hemisphere, cylinder etc. Maths teacher who was accompanying the students asked following questions:
i) The internal radius of hemispherical bowl (filled completely with water) is 9cm and radius and height of cylinderical jar is 1.5cm and 4cm respectively. If the hemispherical bowl is to be emptied in cylinderical jars, then how many cylindrical jars are required? (5/2)
ii) If in the cylindrical jar full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar? (5/2)
34) A) Priti and Arun are both driving to their respective offices from the same home. Priti drives towards the East at an average speed of 30 kmph for 12 minutes and then towards the South at an average of speed of 60 km per hour for 3 minutes. Arun drives towards the West at an average speed of 30 kmph for 4 minutes and the towards the North at an average speed of 45 kmph for 4 minutes.
What is the straight-line distance between Priti 's office and Arun's office? Show your steps and represent the given scenario on the coordinate plane.
OR
B) 3 player are standing on the circle at points A(-5,0), B(1,0) and C(3,4). A ball if placed at a point that is equidistance from all 3 players.
i) What are the coordinates of the ball ? (3)
ii) The fourth player is standing at the point D(-5,4). Is he/she standing on the circle. (2)
Show your steps and give valid reason.
35) The king, queen and jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card:
a) of spade
b) of black king
c) of club
d) of jack
SECTION - E
Case study based questions are compulsory.
36)
The school auditorium must be constructed to accommodate atleast 1500 people. The chairs are to placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
i) If the first circular row has 30 seats, how many seats will be there in there in the 10th row ? (1)
ii) For 1500 seats in the auditorium, how many rows in need to be there ? (2)
OR
If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10th row ?
iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row ? (1)
37)
In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1m from each other along AD, as shown in given figure. Niharika run 1/4th distance AD on the 2nd line and posts a green (G) flag. Preet runs 1/5th distance AD on the eighth line and posts a red(R) flag.
i) Find the position of green flag ? (1)
ii) Find the position of red flag? (1)
iii) What is the distance between both the flags. (2)
OR
If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag ?
38) At a toll plaza, an electronic toll collection system has been installed. FASTag can be used to pay the fare. The tag can we posted on the windscreen of a car.
At the toll plaza a tag scanner is placed at a height of 6m from the ground. The scanner reas the information on the tag of the vehicle and debit the desired toll amount from the linked bank account.
For the tag scanner to function properly the speed of the car needs to be less than 30 kmph . A car with a tag installed at a height of 1.5m from the ground enters the scanner zone .
i) The scanner gets activated when the car's tag is at a distance of 5m from it.
Give one trigonometric ratio for the angle between the horizontal and the line between the car tag and the scanner the scanner ? (1)
ii) The scanner reads the complete information in the car's tag while the angle between the tag and scanner changes from 30° to 60° due to car movement. What is the distance moved by the car ? (2)
OR
A vehicle with a tag pasted at a height of 2m from the ground stops in the scanner zone. The scanner reads the data at a angle of 45°. What is the distance between the tag and the scanner ?
iii) Which trigonometric ratio in a right triangle vary from 0 to 1 ? (1)
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