cbse class 9 mathematics mcqs - studiestoday...other at c, while ar and qb intersect each other at...
TRANSCRIPT
Certain number of persons comprising adults and children went to an exhibition. Entry ticket for the children
is Rs 1.50 and Rs 4.50 for the adults. Total cost of the tickets come out to be Rs 600.
Which of the following pairs of numbers can be the number of adults and childrens?
Mean of five observations is 7, on excluding two observations, the mean reduces to 6. On adding, the
difference of the two excluded observations, the mean of the four observations becomes .
What are the two excluded observations?
Which of the following graph correctly represents the line 4x − 3y = 24?
A. 90, 70
B. 100, 60
C. 110, 50
D. 120, 40
A. 2, 9
B. 6, 13
C. 5, 12
D. 8, 15
A.
B.
C.
D.
The sum of squares of 100 observations was calculated as 7 961. Later, it was found that two values, 53 and
42, were wrongly read as 35 and 24, at the time of calculation. The corrected sum of squares is
If a cone and a cylinder of same radii have the same volume, then what is the ratio of the heights of the cone
and the cylinder?
Use the following information to answer the next question.
The given figure shows a circle with centre O.
What is the measure of ∠OCA?
Use the following information to answer the next question.
A survey is conducted to know the number of mobile phones used in each family of a certain locality of
1000 families. The given data shows the results of the survey.
Number of mobile phones 5 4 3 2 1
Number of families 500 250 150 70 30
What is the probability that a randomly chosen family has 4 mobile phones?
A. 10 730
B. 10 733
C. 11 730
D. 11 733
A. 1:1
B. 1:2
C. 2:1
D. 3:1
A. 10°
B. 15°
C. 20°
D. 25°
What is the length of the line segment joining the mid points of the diagonals of a trapezium that is parallel
to each of the parallel sides having lengths 12 cm and 4 cm.
Use the following information to answer the next question.
The given figure shows a triangle ABC in which medians AD, BE,
and CF intersect at point G.
If the area of ∆ABC is 30 cm2, then what is the area of the shaded region?
Which of the following graphs correctly represents the line 3x + 4y = 12?
A.
B.
C.
D.
A. 2 cm
B. 3 cm
C. 4 cm
D. 6 cm
A. 7.5 cm2
B. 10 cm2
C. 12.5 cm2
D. 15 cm2
The arithmetic mean of a series of 20 items was calculated as 20. While calculating it, an item 13 was
measured as 30. The correct arithmetic mean is
A.
B.
C.
D.
A. 20.25
B. 20.15
Use the following information to answer the next question.
A hemispherical bowl of thickness 0.7 cm is made up of a metal such that the inner radius of the bowl is 2.1
cm. The cost of the metal used is Rs 1.5 per cm3.
What is the approximate cost of the metal used to make such a bowl?
Use the following information to answer the next question.
The given figure shows a circle with centre O.
What is the measure of ∠BOC?
Use the following information to answer the next question.
A die is thrown 400 times and the outcome of each throw is noted down. The given table shows the
frequencies of the outcomes.
Number on the top face of the die 1 2 3 4 5 6
Frequency 100 101 67 34 46 52
What is the probability of getting the number 5 in the next throw?
C. 19.25
D. 19.15
A. Rs 30
B. Rs 35
C. Rs 40
D. Rs 45
A. 45°
B. 55°
C. 70°
D. 80°
A. 0.315
Use the following information to answer the next question.
The given figure shows a quadrilateral ABCD in which the diagonals
AC and BD intersect each other at O. AB = BC, ∠CAD = 25° and
Area (∆AOB) = Area (∆COD).
What is the measure of ∠ABC?
If a variable takes discrete values like x + 4, , then the
median is
f a cone of height 24 cm is surmounted on a cylinder of radius 7 cm and height 30 cm, then what is the ratio
of the curved surface area of the cone to that of the cylinder?
The mean income of a group of workers is and that of another group of workers is . If the number of
workers in the second group is 10 times the number of workers in the first group, then the mean income of
the combined group of workers is
B. 0.21
C. 0.115
D. 0.06
A. 130°
B. 140°
C. 145°
D. 155°
A.
B.
C.
D.
A. 5:12
B. 5:21
C. 12:13
D. 25:26
A cone and a cylinder have the same base area. The height and radius of these two solids are the same. If a
sphere has the same radius as that of the cone, then what is the ratio of the volumes of the cone, the sphere
and the cylinder?
The straight line 2x − 5y = 5 meets the negative y-axis at a point whose coordinates are
The mean of a set of numbers is . If each number is divided by 3, then the new mean is
The total surface areas of the two hemispheres are in the ratio 25: 16. If the sum of their radii is 9 cm, then
what are the respective radii of the two hemispheres?
The arithmetic mean of n numbers is . If the sum of the first (n − 1) numbers is k, then the nth
number is
A.
B.
C.
D.
A. 1: 4: 1
B. 1: 2: 1
C. 1: 4: 3
D. 1: 2: 3
A. (0, − 3)
B. (1, − 2)
C. (1, − 2)
D. (0, − 1)
A.
B.
C.
D.
A. 8 cm and 1 cm
B. 7 cm and 2 cm
C. 6 cm and 3 cm
D. 5 cm and 4 cm
A.
If a cone and a cylinder have the same base area and the same volume, then what is the ratio of their
respective heights?
Use the following information to answer the next question.
The mean weight of a group of 6 students and a teacher is 41 kg. If the teacher is excluded from the group,
then the mean weight gets reduced by 2.5 kg.
What is the weight of the teacher?
If the radius of a sphere is increased by 10%, then what is the percentage increase in the surface area of the
sphere?
Use the following information to answer the next question.
The given figure shows a circle with centre O.
B.
C.
D.
A. 1: 1
B. 3: 1
C. 4: 9
D. 9: 1
A. 42 kg
B. 45 kg
C. 56 kg
D. 57 kg
A. 10%
B. 21%
C. 100%
D. 121%
What is the measure of ∠APD?
Use the following information to answer the next question.
The given figure shows a circle with centre O, where XY is the tangent to the
circle at point A. AB is the angle bisector of XAC.
What is the measure of CAY?
Use the following information to answer the next question.
The given figure shows a parallelogram ABCD in which X and Y are
the mid-points of sides AB and AD respectively.
If the area of ∆CXY = 24 cm2, then what is the area of parallelogram ABCD?
Use the following information to answer the next question.
A. 20°
B. 25°
C. 30°
D. 35°
A. 65°
B. 50°
C. 45°
D. 30°
A. 32 cm2
B. 48 cm2
C. 64 cm2
D. 96 cm2
In the given figure, XY is the tangent at point C of the semi-circle with centre
O.
What is the measure of ∠BCY?
Use the following information to answer the next question.
In the given figure, XY is the tangent at point C of the semi-circle with centre
O.
What is the measure of ∠BCY?
Use the following information to answer the next question.
The given figure shows a quadrilateral ABCD. A line drawn from A
parallel to BD intersects CD produced at Q. BP is a line parallel to
CQ such that QP⊥BP.
If CQ = 22 cm and PQ = 5 cm, then what is the area of quadrilateral ABCD?
A. 20°
B. 30°
C. 40°
D. 50°
A. 20°
B. 30°
C. 40°
D. 50°
A. 55 cm2
B. 65 cm2
Use the following information to answer the next question.
The given figure shows a circle with centre O.
What is the measure of ∠DAC?
Use the following information to answer the next question.
In the given figure, ABCD is a rhombus and PQCB is a
rectangle.
If AC = 12 cm and BD = 16 cm, then what is the measure of PB?
Use the following information to answer the next question.
Ashu hired a cab in the night to go to a party. The cab provider told him that he will charge Rs 1000 for the
cab and an extra charge of Rs 100 will be applicable for each hour after 12:00 a.m.
C. 165cm2
D. 220 cm2
A. 25°
B. 45°
C. 65°
D. 75°
A. 8 cm
B. 9.6 cm
C. 10 cm
D. 12.8 cm
Ashu used the cab for x hours more after 12:00 a.m. If y is the total amount paid by Ashu, then which
equation represents the given situation?
Use the following information to answer the next question.
What is the measure of ∠ABC in the given figure?
Use the following information to answer the next question.
The given figure shows a parallelogram PQRS in which A and B
are any two points in the interior region. AS and BP intersect each
other at C, while AR and QB intersect each other at D.
If area (ASBR) = 35 cm2 and area (ACBD) = 20 cm
2, then what is the area of the shaded portion?
What is the area of the region enclosed by the lines x = 0, y = 0 and x + y = 2?
A. y + 100x = 1000
B. y + 1000 = 100x
C. y = 1000 + 100x
D. y + 100x + 1000 = 0
A. 21°
B. 31°
C. 41.5°
D. 48.5°
A. 35 cm2
B. 50 cm2
C. 55 cm2
D. 70 cm2
The ratio of radii of a cylinder and cone is 1: 3 and the ratio of their heights is 3: 4. What is the ratio of the
volumes of the cylinder and the cone?
Use the following information to answer the next question.
What are the respective values of x and y in the given figure?
If (1, k) is a solution of the equation 2x + 5y = 12, then what is the value of k?
Use the following information to answer the next question.
A.square units
B. square units
C. 2 square units
D. 4 square units
A. 1: 4
B. 3: 4
C. 1: 9
D. 4: 9
A. 40° and 45°
B. 45° and 40°
C. 135° and 165°
D. 160° and 135°
A. −1
B.
C. 2
D.
What is the measure of ∠EFC in the given figure?
If the line ax + by + c = 0 is parallel to x-axis, then which of the following relations is correct?
Use the following information to answer the next question.
A hemispherical tub is full of water. The water is to be emptied in cylindrical bottles. The radius of the
cylindrical bottles is the same as that of the hemisphere. The height of the bottles is one-sixth of their radius.
How many cylindrical bottles can be filled from the water in the hemispherical tub?
Use the following information to answer the next question.
In the given figure, ∆ABC is an isosceles triangle with AB = BC.
A. 59°
B. 76°
C. 104°
D. 121°
A. a = 0
B. b = 0
C. c = 0
D. a = b
A. 2
B. 4
C. 6
D. 8
What are the respective measures of ∠EDC and ∠DEC?
Use the following information to answer the next question.
A metallic cylinder of radius 8 cm and height 20 cm is melted and recasted into 15 equal small spheres.
What is the diameter of each sphere?
Use the following information to answer the next question.
A circle with centre O is shown in the given figure.
What is the measure of ∠BDC?
The slant height and the curved surface area of a cone are 13 cm and 65π cm2 respectively. What is the
volume of the cone?
Use the following information to answer the next question.
A. 64° and 18°
B. 108° and 18°
C. 116° and 64°
D. 134° and 108°
A. 2 cm
B. 4 cm
C. 8 cm
D. 16 cm
A. 60°
B. 80°
C. 100°
D. 120°
A. 49π cm3
B. 95π cm3
C. 100π cm3
D. 169π cm3
In the given figure, a circle with centre O is shown.
What is the measure of ∠BAC?
se the following information to answer the next question.
A function table is given as:
x 5 7 12 19
y 2 4 9 16
The rule followed by the function table is
Use the following information to answer the next question.
The mean weight of ten students is 35 kg. When two more students were included in the group, the mean
increased by 1 kg.
If the weight of both the new students is the same, then what is the weight of each of the new students?
Use the following information to answer the next question.
A. 60°
B. 80°
C. 120°
D. 160°
A. y = x − 1
B. y = x − 2
C. y = x − 3
D. y = x − 4
A. 43 kg
B. 41 kg
C. 39 kg
D. 37 kg
In the given figure, XY = 6 cm and YZ = 8 cm. P and Q are the mid-points of XY
and XZ respectively.
What is the area of ∆XPQ?
Use the following information to answer the next question.
In parallelogram ABCD, AB = 20 cm and BC = 10 cm. P is the mid-point
of side AB. A line through B parallel to PD meets CD at Q and AD
produced at R.
What is the measure of AR?
Use the following information to answer the next question.
The ages of Bob and his father are related by the expression y = 4x − 5 where x is Bob’s age and y is his
father’s age.
Which of the following conclusions is true about the given expression?
A. 6 cm2
B. 8 cm2
C. 12 cm2
D. 14 cm2
A. 15 cm
B. 17 cm
C. 20 cm
D. 30 cm
A. Bob’s father’s age is five less than four times Bob’s age
B. Bob’s father’s age is four less than five times Bob’s age
C. Bob’s father’s age is four times Bob’s age
D. Bob’s father’s age as five times Bob’s age
The mean of eight numbers is 21. If the mean of the first six numbers is 20 and the mean of the last six
numbers is 21.5, then what is the mean of the middle four numbers?
Use the following information to answer the next question.
In the given figure, AB is the diameter of the circle with centre O and D is a point on
the circle. C is a point on AD such that OC⊥AD.
What is the perimeter of ∆ABD if the perimeter of ∆AOC is 20 cm?
Use the following information to answer the next question.
xi fi
20 10
30 7
15 2
25 16
18 4
22 11
What is the mean of the given frequency distribution?
A. 18.5
B. 19
C. 20.25
D. 23
A. 30 cm
B. 40 cm
C. 50 cm
D. 60 cm
A. 21.04
B. 23.08
C. 25.40
D. 27.60
In a class of 80 students, 25 students like to play hockey and 55 students like to play football. What is the
probability that a randomly chosen student likes to play hockey?
Use the following information to answer the next question.
The given frequency distribution table shows the marks obtained by a group of students of a particular class.
Marks obtained 40 52 66 74 90
Number of students 2 3 5 b 4
If the mean of the marks obtained by the students is 68.5, then what is the value of b?
Use the following information to answer the next question.
The given figure shows a circle with ∠XWY = 70° and ∠WZX = 30°.
What is the measure of ∠WXY?
A.
B.
C.
D.
A. 7
B. 6
C. 4
D. 3
A. 70°
B. 80°
C. 100°
D. 110°
Use the following information to answer the next question.
The given figure represents a parallelogram PQRS in which PM and RN
are perpendiculars drawn to the diagonal QS.
If the area of the shaded region is 40 cm2, then what is the area of the parallelogram PQRS?
Use the following information to answer the next question.
Jack’s height is x inches and his brother’s height is y inches. Jack’s brother is one foot shorter than Jack.
Which of the following equations correctly represents the given situation?
Use the following information to answer the next question.
The given figure shows a circle with ∠CAD = 30°, ∠ADE = 15°, and ∠ACD
= 75°.
What are the respective measures of ∠CBE and ∠DEB?
A. 60 cm2
B. 80 cm2
C. 100 cm2
D. 120 cm2
A. x = y + 1
B. y = x + 1
C. x = y + 12
D. y = x + 12
A. 90° and 75°
Use the following information to answer the next question.
In the given figure, O is the centre of the circle. A, B and C are three points on the
circle.
If OC = 8.5 cm and AC = 8 cm, then what is the perimeter of ∆ABC?
Use the following information to answer the next question.
The given figure shows a trapezium PQRS in which PQ||SR. A and B are the
mid-points of diagonals QS and PR respectively.
What is the length of AB?
Use the following information to answer the next question.
B. 90° and 105°
C. 105° and 120°
D. 115° and 135°
A. 31.5 cm
B. 38.5 cm
C. 40 cm
D. 47 cm
A. 5 cm
B. 6 cm
C. 7.5 cm
D. 8.1 cm
What is the value of (∠AOB − ∠ACB)?
Use the following information to answer the next question.
The given table shows the frequency distribution of a particular data.
x f
1 7
3 12
5 m
7 10
9 5
If the mean of the given distribution is 4.7, then what is the value of m?
A. 5
B. 6
C. 11
D. 14
Use the following information to answer the next question.
Two coins are simultaneously tossed 200 times and the following table is obtained.
Two head One head No head
60 88 52
What is the probability of getting two tails.
A. 15°
B. 20°
C. 25°
D. 30°
The mean of thirty numbers is 25. If 15 is subtracted from each of the first 12 numbers and 15 is added to
each of the last 18 numbers, then what will be the mean of the new set of numbers?
Use the following information to answer the next question.
The mean weight of all girls of a class is 36 kg and that of the boys of the class is 42 kg. The mean weight of
all the students of the class is 40 kg.
What is the ratio of the number of girls and boys in the class?
What is the mean of the first five multiples of both the numbers 10 and 3?
Use the following information to answer the next question.
A die is thrown 3000 times and its outcome is noted each time. The given table lists the number of times
each number appeared on the die.
Outcome 1 2 3 4 5 6
Frequency 350 710 420 500 600 420
If the same coin is tossed again, then what is the probability of getting an even number on the die?
A. 0.13
B. 0.26
C. 0.39
D. 0.52
A. 32
B. 31
C. 28
D. 23
A. 1:2
B. 1:4
C. 2:3
D. 3:4
A. 90
B. 95
C. 105
D. 120