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(i)(a): Radius of the archery target = 50cm .
∴ Area of archery target $=\pi \times 50^2 cm^2=2500 \pi cm^2$
∴ Area of gold scoring region $=\pi \times 10^2 cm^2=100 \pi cm^2$
∴,Probability that the arrow hits in gold scoring region $=\frac{100 \pi}{2500 \pi}=\frac{1}{25}$
(ii) (b): Area of red scoring region $=\pi\left(20^2-10^2\right) cm ^2=300 \pi cm^2$
∴ Probability that the arrow hits in red scoring area $=\frac{300 \pi}{2500 \pi}=\frac{3}{25}$
(iii) (d): Area of blue scoring region $=\pi\left(30^2-20^2\right) cm ^2=500 \pi cm^2$
∴ Probability that the arrow hits in blue scoring region $=\frac{500 \pi}{2500 \pi}=\frac{1}{5}$
(iv) (c): Area of black scoring region $=\pi\left(40^2-30^2\right) cm ^2=700 \pi cm^2$
∴ Probability that the arrow hits in black scoring region $=\frac{700 \pi}{2500 \pi}=\frac{7}{25}$
∴ Area of archery target $=\pi \times 50^2 cm^2=2500 \pi cm^2$
∴ Area of gold scoring region $=\pi \times 10^2 cm^2=100 \pi cm^2$
∴,Probability that the arrow hits in gold scoring region $=\frac{100 \pi}{2500 \pi}=\frac{1}{25}$
(ii) (b): Area of red scoring region $=\pi\left(20^2-10^2\right) cm ^2=300 \pi cm^2$
∴ Probability that the arrow hits in red scoring area $=\frac{300 \pi}{2500 \pi}=\frac{3}{25}$
(iii) (d): Area of blue scoring region $=\pi\left(30^2-20^2\right) cm ^2=500 \pi cm^2$
∴ Probability that the arrow hits in blue scoring region $=\frac{500 \pi}{2500 \pi}=\frac{1}{5}$
(iv) (c): Area of black scoring region $=\pi\left(40^2-30^2\right) cm ^2=700 \pi cm^2$
∴ Probability that the arrow hits in black scoring region $=\frac{700 \pi}{2500 \pi}=\frac{7}{25}$
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There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.
Raghav has a field with total area of $1260 m^2$. He uses it to grow wheat and rice. The land used to grow wheat i.e. wheatland is rectangular in shape while the riceland is in the shape of a square as shown in the following figure. The length of wheatland is 3 metre more than twice the length of riceland.
(i) If the length of the riceland is $x$ metre, then total length of the field (in metres) is
(a) $(2 x+2)$ $\qquad$ (b) $3 x+3$ $\qquad$ $\qquad$ (c) $4 x+4$ $\qquad$ (d) $3 x+5$
(ii) The perimeter of the field is
(a) $8 x+6$ $\qquad$ (b) $6 x+8$ $\qquad$ (c) $3 x+4$ $\qquad$ (d) $4 x+3$
(iii) If the total area of the field is $1260 m^2$, then the value of $x$ is
(a) 10 $\qquad$ (b) 15 $\qquad$ (c) 20 $\qquad$ (d) 25
(iv) The area of the wheat land is
(a) $400 m^2$ $\qquad$ (b) $760 m^2$ $\qquad$ (c) $820 m^2$ $\qquad$ (d) $860 m^2$
→(i) If the length of the riceland is $x$ metre, then total length of the field (in metres) is
(a) $(2 x+2)$ $\qquad$ (b) $3 x+3$ $\qquad$ $\qquad$ (c) $4 x+4$ $\qquad$ (d) $3 x+5$
(ii) The perimeter of the field is
(a) $8 x+6$ $\qquad$ (b) $6 x+8$ $\qquad$ (c) $3 x+4$ $\qquad$ (d) $4 x+3$
(iii) If the total area of the field is $1260 m^2$, then the value of $x$ is
(a) 10 $\qquad$ (b) 15 $\qquad$ (c) 20 $\qquad$ (d) 25
(iv) The area of the wheat land is
(a) $400 m^2$ $\qquad$ (b) $760 m^2$ $\qquad$ (c) $820 m^2$ $\qquad$ (d) $860 m^2$
Rinku was very happy to receive a fancy jumbo pencil from his best friend Rohan on his birthday. Pencil is a basic writing tool, when sharpened its shape is a combination of cylinder & cone as given in the picture.
Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are made up of wood & plastic but we should promote pencils made up of eco-friendly material (many options available in the market these days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i) Find the slant height of the sharpened part.
(ii) Find curved surface area of sharpened part (in terms of $\pi$).
(iii)(A) Find the total surface area of the pencil (in terms of $\pi$).
OR
(B)The pencil’s total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of $\pi$)?
→Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are made up of wood & plastic but we should promote pencils made up of eco-friendly material (many options available in the market these days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i) Find the slant height of the sharpened part.
(ii) Find curved surface area of sharpened part (in terms of $\pi$).
(iii)(A) Find the total surface area of the pencil (in terms of $\pi$).
OR
(B)The pencil’s total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of $\pi$)?
A stopwatch was used to find the tie that it took a group of students to run 100 . The following table exhibits the tie intervals and the nuber of students copleting the 100 race in these intervals:
(i) Estiate the ean tie taken by a student to finish the race.
(a) 54$\quad$ (b) 63$\quad$ (c) 43$\quad$ (d) 50
(ii) What will be the upper liit of odal class?
(a) 20$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 80
(iii) The construction of cuulative frequency table is useful in deterining the
(a) Mean$\quad$ (b) Median$\quad$ (c) Mode$\quad$ (d) All of the above
(iv) The su of lower liits of edian class and odal class is
(a) 60$\quad$ (b) 100$\quad$ (c) 80$\quad$ (d) 140
→| Tie (in sec) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| No. of students | 8 | 10 | 13 | 6 | 3 |
(i) Estiate the ean tie taken by a student to finish the race.
(a) 54$\quad$ (b) 63$\quad$ (c) 43$\quad$ (d) 50
(ii) What will be the upper liit of odal class?
(a) 20$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 80
(iii) The construction of cuulative frequency table is useful in deterining the
(a) Mean$\quad$ (b) Median$\quad$ (c) Mode$\quad$ (d) All of the above
(iv) The su of lower liits of edian class and odal class is
(a) 60$\quad$ (b) 100$\quad$ (c) 80$\quad$ (d) 140
→
London eye is an amusement ride consisting of a rotating upright big wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas or pods) attached to the rim in such a way that as the wheel turns, they are kept upright usually by gravity. After taking a ride in London eye, Anu came out from the crowd and was observing her friends who were enjoying the ride. She was curious about the different angles and measures that the wheel will form. She makes a figure as given below.
(i) In Fig. the measure of $\angle R O Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $150^{\circ}$ $\qquad$ (d) $90^{\circ}$
(ii) In Fig. 8.33, The measure of $\angle R Q P$ is
(a) $75^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $30^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iii) In Fig. 8.33, the measure of $\angle R S Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $75^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $30^{\circ}$
(iv) In Fig. 8.33, the measure of $\angle O R P$ is
(a) $90^{\circ}$ $\qquad$ (b) $70^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $60^{\circ}$
→(i) In Fig. the measure of $\angle R O Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $100^{\circ}$ $\qquad$ (c) $150^{\circ}$ $\qquad$ (d) $90^{\circ}$
(ii) In Fig. 8.33, The measure of $\angle R Q P$ is
(a) $75^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $30^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iii) In Fig. 8.33, the measure of $\angle R S Q$ is
(a) $60^{\circ}$ $\qquad$ (b) $75^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $30^{\circ}$
(iv) In Fig. 8.33, the measure of $\angle O R P$ is
(a) $90^{\circ}$ $\qquad$ (b) $70^{\circ}$ $\qquad$ (c) $100^{\circ}$ $\qquad$ (d) $60^{\circ}$
A highway underpass is parabolic in shape as shown in the following picture.
(i) If the highway overpass is represented by $x^2-2 x-8$. Then its zeros are
(a) $2,-4$ $\qquad$ (b) $4,-2$ $\qquad$ (c) $-2,-2$ $\qquad$ (d) $-4,-4$
(ii) Number of zeros of the polynomial representing highway overpass is equal to number of points where the graph of polynomial
(a) intersects $x$-axis
(b) intersects $y$-axis
(c) intersects $y$-axis or $x$-axis
(d) none of these
(iii) Graph of quadratic polynomial is a
(a) straight line $\qquad$ (b) circle $\qquad$ (c) parabola $\qquad$ (d) ellipse
(iv) The representation of Highway Underpass whose one zero is 6 and sum of the zeros is 0 , is
(a) $x^2-6 x+2$ $\qquad$ (b) $x^2-36$ $\qquad$ (c) $x^2-6$ $\qquad$ (d) $x^2-3$
→(i) If the highway overpass is represented by $x^2-2 x-8$. Then its zeros are
(a) $2,-4$ $\qquad$ (b) $4,-2$ $\qquad$ (c) $-2,-2$ $\qquad$ (d) $-4,-4$
(ii) Number of zeros of the polynomial representing highway overpass is equal to number of points where the graph of polynomial
(a) intersects $x$-axis
(b) intersects $y$-axis
(c) intersects $y$-axis or $x$-axis
(d) none of these
(iii) Graph of quadratic polynomial is a
(a) straight line $\qquad$ (b) circle $\qquad$ (c) parabola $\qquad$ (d) ellipse
(iv) The representation of Highway Underpass whose one zero is 6 and sum of the zeros is 0 , is
(a) $x^2-6 x+2$ $\qquad$ (b) $x^2-36$ $\qquad$ (c) $x^2-6$ $\qquad$ (d) $x^2-3$
Four persons John, Saurabh, Salim and Ratan are sitting in a courtyard at points $A, B, C$ and $D$ respectively as shown in Fig. 6.19. The Courtyard has been divided into small squares by drawing equality spaced horizontal and vertical lines. Taking $O X$ and $O Y$ as the coordinate axes, answer the following questions:
(i) The coordinates of points $A$ are
(a) $(4,3)$ $\qquad$ $\qquad$ (b) $(3,4)$ $\qquad$ (c) $(3,3)$ $\qquad$ (d) $(4,4)$
(ii) By joining $A$ to $B, B$ to $C, C$ to $D$ and $D$ to $A$, the figure formed is not a
(a) rhombus $\qquad$ (b) square $\qquad$ (c) parallelogram $\qquad$ (d) trapezium
(iii) The distance between the mid-points of $A C$ and $B D$ is
(a) 2 $\qquad$ (b) 3 $\qquad$ (c) 0 $\qquad$ (d) 1
(iv) Area of $\triangle A B C$ is
(a) 18 sq. units $\qquad$ (b) 9 sq. units $\qquad$ (c) 12 sq. units $\qquad$ (d) 16 sq. units
→(i) The coordinates of points $A$ are
(a) $(4,3)$ $\qquad$ $\qquad$ (b) $(3,4)$ $\qquad$ (c) $(3,3)$ $\qquad$ (d) $(4,4)$
(ii) By joining $A$ to $B, B$ to $C, C$ to $D$ and $D$ to $A$, the figure formed is not a
(a) rhombus $\qquad$ (b) square $\qquad$ (c) parallelogram $\qquad$ (d) trapezium
(iii) The distance between the mid-points of $A C$ and $B D$ is
(a) 2 $\qquad$ (b) 3 $\qquad$ (c) 0 $\qquad$ (d) 1
(iv) Area of $\triangle A B C$ is
(a) 18 sq. units $\qquad$ (b) 9 sq. units $\qquad$ (c) 12 sq. units $\qquad$ (d) 16 sq. units
Johan and Jayant are very close friends. They decided to go to Ranikhet with their families in Separate cars. Johan's car travels at a speed of $x km / hr$ while Jayant's car travels $5 km / hr$ faster than Johan's car. Johan took 4 hours more than Jayant to complete the Journey of 400 km .
(i) The distance covered by Jayant's car in two hours is
(a) $2(x+5) km$ $\qquad$ (b) $(x-5) km$
(c) $2(x+10) km$ $\qquad$ (d) $(2 x+5) km$
(ii) The quadratic equation describing the speed of Johan's car is
(a) $x^2-5 x-500=0$ $\qquad$ (b) $x^2+4 x-400=0$
(c) $x^2+5 x-500=0$ $\qquad$ (d) $x^2-4 x+400=0$
(iii) The speed of Johan's car is (in km/hour)
(a) 20 $\qquad$ (b) 15 $\qquad$ (c) 25 $\qquad$ (d) 10
(iv) The speed of Jayant's car in $km / hr$ is
(a) 25 $\qquad$ (b) 20 $\qquad$ (c) 30 $\qquad$ (d) 15
→(i) The distance covered by Jayant's car in two hours is
(a) $2(x+5) km$ $\qquad$ (b) $(x-5) km$
(c) $2(x+10) km$ $\qquad$ (d) $(2 x+5) km$
(ii) The quadratic equation describing the speed of Johan's car is
(a) $x^2-5 x-500=0$ $\qquad$ (b) $x^2+4 x-400=0$
(c) $x^2+5 x-500=0$ $\qquad$ (d) $x^2-4 x+400=0$
(iii) The speed of Johan's car is (in km/hour)
(a) 20 $\qquad$ (b) 15 $\qquad$ (c) 25 $\qquad$ (d) 10
(iv) The speed of Jayant's car in $km / hr$ is
(a) 25 $\qquad$ (b) 20 $\qquad$ (c) 30 $\qquad$ (d) 15
represents the golden ratio spiral. The sequence $0,1,1,2,3,5,8,13$ is called a Fibonacci sequence in which each term (except the first two terms) is obtained by adding the previous two terms of the sequence.
(i) The next two numbers in the sequence are
(a) 223 and 367 $\qquad$ (b) 233 and 367 $\qquad$ (c) 223 and 377 $\qquad$ (d) 233 and 377
(ii) A rational number has terminating decimal expansion, if the denominator is of the form
(a) $2^m \times 5^n$ $\qquad$ (b) $3^m \times 5^n$ $\qquad$ (c) $2^m \times 3^n$ $\qquad$ (d) $3^m \times 4^n$
where $m, n$ are non-negative integers.
(iii) Which of the following rational numbers (formed by taking the ratio of a term to its previous term) has terminating decimal expansion?
(a) $\frac{5}{3}$ $\qquad$ (b) $\frac{21}{13}$ $\qquad$ (c) $\frac{13}{8}$ $\qquad$ (d) $\frac{34}{21}$
(iv) HCF of two consecutive numbers in the given sequence (except the first 3 terms) is
(a) 1 $\qquad$ (b) 0 $\qquad$ (c) 2 $\qquad$ (d) 3
→(i) The next two numbers in the sequence are
(a) 223 and 367 $\qquad$ (b) 233 and 367 $\qquad$ (c) 223 and 377 $\qquad$ (d) 233 and 377
(ii) A rational number has terminating decimal expansion, if the denominator is of the form
(a) $2^m \times 5^n$ $\qquad$ (b) $3^m \times 5^n$ $\qquad$ (c) $2^m \times 3^n$ $\qquad$ (d) $3^m \times 4^n$
where $m, n$ are non-negative integers.
(iii) Which of the following rational numbers (formed by taking the ratio of a term to its previous term) has terminating decimal expansion?
(a) $\frac{5}{3}$ $\qquad$ (b) $\frac{21}{13}$ $\qquad$ (c) $\frac{13}{8}$ $\qquad$ (d) $\frac{34}{21}$
(iv) HCF of two consecutive numbers in the given sequence (except the first 3 terms) is
(a) 1 $\qquad$ (b) 0 $\qquad$ (c) 2 $\qquad$ (d) 3