General Instructions:
(i) This question paper comprises four sections – A, B, C and D. This question paper carries 40 questions. All questions are compulsory.
(ii) Section A: Q. No.1 to 11 comprises of 11 questions of one mark each.
(iii) Section B: Q. No. 12 to 20 comprises of 9 questions of two mark each.
(iv) Section C: Q. No. 21 to 30 comprises of 10 questions of three mark each.
(v) Section D: Q. No. 31 to 35 comprises of 5 questions of four mark each.
(vi) Use of Calculators are not permitted.
0 of 35 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 35 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

If \(x=\dfrac{1}{2 } \) is a solution of the quadratic equation \( 3x^2+ 2kx 3 = 0, \) find the value of \(k \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The given quadratic equation can be written as,
The tops of two towers of height \(x \) and \(y \), standing on level ground, subtend angles of 30Â° and 60Â° respectively at the centre of the line joining their feet, then find \(x:y \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
When base is same for both towers and their heights are given, i.e., and respectively
Let the base of towers be .
From equations (i) and (ii),
A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Total English alphabets
Number of consonants
P(letter is a consonant)
In Fig., PA and PB are tangents to the circle with centre O such that \(\angle \)APB = 50Â°. Write the measure of \(\angle \)OAB.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
â€¦ [Tangents drawn from external point are equal]
[Angles opposite equal sides]
[Quadratic rule]
… [Triangle rule]
…. [From (i)]
In Fig,, AB is the diameter of a circle with centre O and AT tangent. If \(\angle \)AOQ = 58Â°, find \(\angle \)ATQ.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
â€¦ [Tangent is latex]\bot [/latex] to the radius through the point of contact]
Solve the following quadratic equation for \(x:4x^24a^2x+(a^4b^4)=0 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The given quadratic equation can be written as,
The time (in seconds) taken by 150 atheletes to own a 110 m hurdle race are tabulated below.
Class – 13.8 – 14, 14 – 14.2, 14.2 – 14.4, 14.4 – 14.6, 14.6 – 14.8, 14.8 – 15
Frequency – 2, 4, 5, 71, 48, 20
Find the number of atheletes who have completed the race in less than 14.6 seconds is :
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In the given figure, \(AD \) is the bisector of \(\angle A \). If \(BD=4\ cm,DC=3\ cm \) and \(AB=6\ cm \) then find \(AC \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(P \) is prime number then what is the LCM of \(P,P^2,P^3 \)?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
LCM of
The rational number between \( \sqrt3\) and \(\sqrt5 \) is
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
â€¦. [Tangents drawn from an external point are equal]
â€¦.[Common]
â€¦..(TP and TQ are equally inclined to OT)
…..[CPTC]
….[SAS]
….[Linea pair]
is the right bisector of .
Find the middle term of the A.P. 6,13, 20, â€¦, 216.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The given A.P. is 6, 13, 20, â€¦., 216
Let be the number of terms,
Middle term term
term of the A.P.
If A(5, 2), B(2, 2) and C(2, t) are the vertices of a right angled triangle with \(\angle \)B = 90Â°, then find the value of t.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
is a right angled triangle,
â€¦(i)
Using distance formula,
Putting values of and in equation (i)
Find the ratio in which the point \(P\left(\dfrac{1}{2},\dfrac{3}{2}\right) \) and \(B(2,5) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let divide in the ratio of
Applying division formula,
Required ratio
Find the area of the triangle ABC with A(1, 4) and midpoints of sides through A being (2, 1) and (0, 1).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
P is the midpoint of AB
Q is the mid point of AC
Area of ,
Find that nonzero value of \(k \), for which the quadratic equation \( kx^2 + 1 – 2(k – l)x +x^2 = 0\) has equal roots. Hence find the roots of the equation.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The given quadratic equation can be written as
For equal roots,
Putting put in equation (i)
Roots are .
The angle of elevation of the top of a building from the foot of the tower is 30Â° and the angle of elevation of the top of the tower from the foot of the building is 45Â°. If the tower is 30 m high, find the height of the building.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let height of building be and the distance between tower and building be .
In ,
Now, In
…. [From (i)]
Height of the building is m.
Two different dice are rolled together. Find the probability of getting:
(i) the sum of numbers on two dice to be 5.
(ii) even numbers on both dice.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Total possible outcomes
(i) The possible outcomes are when the sum of numbers on two dice is 5, i.e, 4
Required Probability,
(ii) The possible outcomes are for even numbers on both dice; 9
Required Probability,
If \( S_n\), denotes the sum of first \(n \) terms of an A.P., prove that \(S_{12}=3(S_8S_4) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let be the first term and be the common difference of A.P.
…. [From (i), (ii) & (iii)]
In Fig., APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. [Use \(\pi=\dfrac{22}{7} \)]
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
â€¦ [Given]
Let
is the diameter of small semicircle
Radius of small semicircle,
is the radius of big semicircle,
is the radius of big semicircle,
Total perimeter = Perimeter of small semicircle + Perimeter of big semicircle + OB
Area of shaded region = (Area of small semicircle) + (Area of big semicircle)
In Fig., from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use \(\pi=\dfrac{22}{7} \) and \(\sqrt5=2.236 \))
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let ,
Height of frustum ,
Lower radius of frustum
We know,
Upper radius of frustum
Slant height of frustum
Total surface area of frustum (PQCB)
A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is \(3.5\ cm \) and the total wood used in the making of toy is \(166\left(\dfrac{5}{6}\right)\ cm^3 \). Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of \(\mathrm{Rs.\ 10\ per\ cm^2} \). [Use \(\pi=\dfrac{22}{7} \)]
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the height of cone = h
Radius of cone = Radius of hemisphere = r = 3.5 cm
Volume of solid wooden toy = Volume of hemisphere + Volume of cone
Height of toy
Area of hemispherical part of toy
Cost of painting
In Fig., from a cuboidal solid metallic block, of dimensions \(15\ cm\times10\ cm\times5\ cm \), a cylindrical hole of diameter \(7\ cm \) is drilled out. Find the surface area of the remaining block. [Use \(\pi=\dfrac{22}{7} \)]
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the length, breadth, height of cuboidal block be and respectively.
Total surface area of solid cuboidal block
Radius of cylindrical hole
Area of two circular bases
Curved surface area of cylinder
Required area = (Area of cuboidal block – Area of two circular bases + Area of cylinder)
In Fig., find the area of the shaded region. [Use \(\pi=3.14 \)]
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the side of big square
Let the radius of circle,
Let the side of small square
Area of square ABCD
Area of small square PQRS
Area of 4 semicircles
Required area
= (Area of big square – Area of small square – Area of 4 semicircles)
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is \(\dfrac{29}{20} \) . Find the original fraction.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the denominator and numerator of the fraction be and respectively.
Let the fraction be
By the given condition,
New fraction,
Now denominator then, numerator
The fraction is .
Ramkali required Rs 2500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks. What value is generated in the above situation?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Money required for Ramkali for admission of her daughter = â‚¹2500
A.P. formed by saving 100, 120, 140,â€¦. Upto 12 terms â€¦(i)
Let, and be the first term, common difference and number of terms respectively.
She can send her daughter to school.
Value: Small savings can fulfill our big desires.
Solve for \(x:\dfrac{2}{x+1}+\dfrac{3}{2(x2)}=\dfrac{23}{5x},x\ne0,1,2 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In Fig., tangents PQ and PR are drawn from an external point P to a circle with centre O, such that \(\angle \)RPQ = 30Â°. A chord RS is drawn parallel to the tangent PQ. Find \(\angle \)RQS.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(Tangents drawn from external point are equal)
â€¦. [Angles opposite equal sides are equal]
In ,
… Rule]
and is a transversal
… [Alternate interior angle]
… [Tangent is latex]\bot [/latex] to the radius through the point of contact]
Similarly,
In ,
…. Rule]
From a point P on the ground the angle of elevation of the top of a tower is 30Â° and that of the top of a flag staff fixed on the top of the tower, is 60Â°. If the length of the flag staff is 5m, find the height of the tower.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In ,
(i)
In ,
(ii)
… [From (i)]
Height of Tower
A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) divisible by 2 or 3, (ii) a prime number.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) Numbers divisible by 2 or 3 from 1 to 20 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 3, 9, 15, 20 = 13
Total outcomes = 20
Possible outcomes = 13
P(divisible by 2 or 3) =
(ii) Prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19 = 8
Total Outcomes = 20
Possible outcomes = 8
P(a prime number)
If A(4, 8), B(3, 4), C(0, 5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Join AC to form two triangles.
Given: and
Area of ,
Area of ,
Area of Quadrilateral ABCD
= Area of ABC + Area of ACD
A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let be the height of well and be the radius of well.
Volume of earth taken out after digging the well
Let be the width of embankment formed by using (i)
Total width of well including embankment
Height of embankment
Volume of well = Volume of embankment
So, Volume of embankment
Therefore, width of embankment = 10 m
Water is flowing at the rate of 2.52 km/hr. through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let be the internal radius of the pipe.
Radius of base of tank,
Level of water raised in the tank
If the flow rate in an hour
Then the flow rate in half an hour
So, height of water level
Volume of tank = Volume of pipe
Internal diameter of pipe
Internal diameter of pipe
To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the bigger pipe fill the tank in hrs.
the smaller pipe fills the tanks in hrs.
Hence, the pipe with larger diameter fills the tank in 20 hours and the pipe with smaller diameter fills the tank in 30 hours.
Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are \(\dfrac{3}{4} \) times the corresponding sides of the isosceles triangle.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
A’BC’ is the required triangle.