RS COACHING CENTRE
REVISION EXAM 12 -BATCH 1
CLASS:X MARKS 80
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DATE: 19.02.23 Time: 2 hours
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SECTION – A
(Attempt ALL questions from this section)
Question 1.
Choose the correct answer
i) A dealer in Agra bought some goods worth ₹𝟏𝟐, 𝟎𝟎𝟎. If the rate of GST is
18%, then the amount paid by the dealer is
a) ₹14,000 b) ₹14,160 c) ₹15,000 d) ₹16,180
ii)Roots of the equation (x-1)2-5(x-1)-6=0 are
a) 7,0 b) 6,0 c) 7,6 d) 6,-7
iii. If (x-2) is a factor of x2+5x+p, then the value of p is
a) 10 b) 12 c) -13 d) -14
iv)Two matrices A and B of order 2× 𝟑 each. The order of the matrix A+B is
a) 2×3 b) 4× 𝟑 c) 2× 𝟔 d) 3× 𝟐
v)8th term of the AP 5,8,11,… 38, from the end is
a) 22 b) 20 c) 17 d) 16
vi. The reflection of the point P(0,-1) in the x-axis is
a) (1,0) b) (-1,0) c) (0,0) d) (0,1)
vii)In the figure, BD and CE intersect each other at P. ∆PBC~∆𝑷𝑫𝑬 by
a) AA similarity b) SAS similarity
c) SSS similarity d) RHS similarity
viii)If Himanshu reshaped a cone of heigh h cm and radius of base r cm into
a cylinder , then which of the following options is always correct ?
a) Volume of cone = Volume of cylinder
b) Surface area of cone = Surface area of cylinder
c) Radius of cone = Radius of cylinder
d) None of the above
ix) If -1≤ 3+4x<23, x∈ 𝑹, then:
a) {-1≤ 𝒙 < 𝟓, 𝒙 ∈ 𝑹} b) {-1< 𝒙 ≤ 𝟓, 𝒙 ∈ 𝑹}
c) {−𝟐 ≤ 𝒙 < 𝟓, 𝒙 ∈ 𝑹} d) {-2< 𝒙 ≤ 𝟓, 𝒙 ∈ 𝑹}
x) The probability of drawing a black face card from a deck of 52 playing
cards is
𝟏 𝟑 𝟏 𝟏
a) b) c) d)
𝟏𝟐 𝟐𝟔 𝟐 𝟏𝟑
𝟐 𝟏
xi) If M=[1,-2], N=[ ], then: The matrix MN is
−𝟏 𝟐
𝟒
a) [4,3] b) [-4,3] c) [4 -3] d) [ ]
−𝟑
xii) The mid-point of the line segment joining the points A(-1,4) and
B(-3,-2) is
a) (-2,-3) b) (1,3) c) -2,1 d)2,1
xiii) In the given figure, O is the centre of the circle. If <ABC=20°, then
<AOC is equal to
a) 20° b) 40° c) 60° d) 10°
xiv) The sum of first n terms of an AP is Sn=3n2-4n. The first term of the AP
is
a) -1 b) 1 c) 3 d) 6
xv) The mode of the given observations 5,3,2,7,5,9,3,8,5 is
a) 3 b) 5 c) 9 d) 2
QUESTION 2
(i) Use factor theorem to factories 6x3+ 17x2+4x−12 completely.
(ii) Solve the following in equation and represent the solution set on the
number line.
𝟑𝒙 𝒙
+𝟐 < 𝒙+𝟒 ≤ + 𝟓 𝒙∈𝑹
𝟓 𝟐
(iii) Draw a Histogram for the given data, using a graph paper
Weekly Wages (in Rs.) No. of People
3000-4000 4
4000-5000 9
5000-6000 18
6000-7000 6
7000-8000 7
8000-9000 2
9000-10000 4
Estimate the mode from the graph.
QUESTION 3
(i)In the figure given below, O is centre of the
circle and AB is a diameter. If AC=BD and
<AOC=720. Find (a) <ABC (b) <BAD (c) <ABD
𝒔𝒊𝒏𝑨 𝒄𝒐𝒔𝑨
(ii)Prove that − = 𝒔𝒊𝒏𝑨 − 𝒄𝒐𝒔𝑨
𝟏+𝒄𝒐𝒕𝑨 𝟏+𝒕𝒂𝒏𝑨
(iii) In what ratio is the line joining P(5,3) and Q (-5, 3) divided by the y axis?
Also find the coordinates of the point of intersection.
Section B (40 Marks)
Attempt any four questions from this Section
QUESTION 4
(i) A solid spherical ball of radius 6 cm is melted and recast into 64 identical
spherical marbles. Find the radius of each marble.
(ii) Each of the letters of the word ‘AUTHORIZES’ is written on identical
circular discs and put in a bag. They are well shuffled. If a disc is drawn at
random from the bag, what is the probability that the letter is:
a) a vowel
b) One of the first 9 letters of the English alphabet which appears in the given
work
c) One of the last 9 letters of the English alphabet which appears in the given
word?
(iii) Mr. Bedi visits the market and buys the following articles:
Medicines costing `950, GST @ 5%
A pair of shoes costing `3000, GST @ 18%
A Laptop bag costing `1000 with a discount of 30%, GST @ 18%
a) Calculate the total amount of GST paid.
b) The total bill amount including GST paid by Mr.Bedi.
QUESTION 5
(i)Solve the following Quadratic Equation x2−7x+3=0 Give your answer
correct to two decimal places.
𝒙 𝟑
(ii) Given A = [ ]
𝒚 𝟑
if A2=3I, where I is the identity matrix of order 2, find x and y.
(iii) The mean of the following data is 16. Calculate the value of f.
Marks 5 10 15 20 25
No.of Students 3 7 f 9 6
QUESTION 6
𝟑 𝟎 −𝟒 𝟐
(i)If A = [ ] and B= [ ] Find 𝑨𝟐 − 𝟐𝑨𝑩 + 𝑩𝟐
𝟓 𝟏 𝟏 𝟎
(ii) In the given figure AB = 9cm, PA = 7.5cm and PC = 5cm.
Chords AD and BC intersect at P.
(a) Prove that ∆PAB ~ ∆PCD
(b) Find the length of CD.
(iii) From the top of a cliff, the angle of depression of the top and bottom of a
tower are observed to be 45o and 60o respectively. If the height of the tower
is 20m. Find: (a)the height of the cliff
(b) the distance between the cliff and the tower.
QUESTION 7
(i)Find the value of ‘p’ if the lines, 5x - 3y + 2 = 0 and
6x – py + 7 = 0 are perpendicular to each other. Hence find the equation
of a line passing through (-2, -1) and parallel to 6x – py + 7 = 0.
(ii) Using properties of proportion find x : y, given:
𝒙𝟐 + 𝟐𝒙 𝒚𝟐 + 𝟑𝒚
=
𝟐𝒙 + 𝟒 𝟑𝒚 + 𝟗
(iii) Calculate the median, lower quartile, upper quartile, interquartile range,
semi interquartile range, range and mode.
Weight (in nearest kg) 50 46 55 48 53 54 52
No. of students 8 7 1 5 10 2 12
QUESTION 8
(i) What must be added to the polynomial 2x3-3x2-8x, so that it leaves a
remainder 10 when divided by 2x+1?
(ii) Mr. Sonu has a recurring deposit account and deposits `750 per month for
2 years. If he gets `19125 at the time of maturity, find the rate of interest.
(iii) Use graph paper for this question. Take 1 cm = 1 unit on both x and y
axes.
a) Plot the following points on your graph sheets: A(-4,0) B(-3,2) C(0,4) D(4,1)
and E(7,3)
b) Reflect the points B, C, D and E on the x-axis and name them as B’, C’, D’
and E’ respectively.
c) Join the points A, B, C, D, E, E’, D’, C’, B’ and A in order.
d) Name the closed figure formed
QUESTION 9
(i) 40 students enter for a game of shot-put competition. The distance thrown
(in metres) is recorded below:
Distance in m 12-13 13-14 14-15 15-16 16-17 17-18 18-19
Number of students 3 9 12 9 4 2 1
Use a graph paper to draw an ogive for the above distribution.
Use a scale of 2 cm =1m on one axis and 2 cm =5 students on the other axis.
Hence using your graph find:
a) the median b) Upper Quartile
c) Number of students who cover a distance which is above 16½ m
√𝟐𝒂+𝟏+ √𝟐𝒂−𝟏
(ii) If 𝒙= prove that 𝒙𝟐 − 𝟒𝒂𝒙 + 𝟏 = 𝟎
√𝟐𝒂+𝟏− √𝟐𝒂−𝟏
QUESTION 10
(i) If the 6th term of an A.P is equal to four times its first term and the sum of
first six terms is 75 find the first term and the common difference.
(ii) The difference of two natural numbers is 7 and their product is 450. Find
the numbers
(iii) Draw a circle of radius 2.5cm. Take a point P outside the circle at a
distance of 5.8 cm from its centre. Draw two tangents to the circle from the
point
