CBSE Maths Test Paper 2020-Class X
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 20 comprises of 20 questions of one mark each.
(iii) Section B: Q. No. 21 to 26 comprises of 6 questions of two mark each.
(iv) Section C: Q. No. 27 to 34 comprises of 8 questions of three mark each.
(v) Section D: Q. No. 35 to 40 comprises of 6 questions of four mark each.
(vi) Use of Calculators are not permitted.
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Question 1 of 40
1. Question
1 point(s)If one of the zeroes of the polynomial \(x^2+3x+k \) is \( 2\), the value of \(k \) is
CorrectIncorrectHint
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Question 2 of 40
2. Question
1 point(s)The total number of factors of a prime number is
CorrectIncorrectHint
one and the number itself
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Question 3 of 40
3. Question
1 point(s)The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6 is
CorrectIncorrectHint
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Question 4 of 40
4. Question
1 point(s)The value of k for which the system of equation \(x+y-4=0 \) and \(2x+ky=3 \) has no solution is
CorrectIncorrectHint
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Question 5 of 40
5. Question
1 point(s)The HCF and LCM of 12, 21, 15 are
CorrectIncorrectHint
HCF of 12, 21 and 15 = 3
LCM -
Question 6 of 40
6. Question
1 point(s)The value of \(x \) for which \(2x,x+10 \) and \(3x+2 \) are \(3 \) consecutive terms of an AP is
CorrectIncorrectHint
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Question 7 of 40
7. Question
1 point(s)The first term of an AP is p and common difference is q then its \(10^{\text{th}} \) term is
CorrectIncorrectHint
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Question 8 of 40
8. Question
1 point(s)The distance between the points \((a\cos\theta+b\sin\theta,0) \) and \(0,a\sin\theta-b\cos\theta \) is
CorrectIncorrectHint
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Question 9 of 40
9. Question
1 point(s)If the point \(p(k,0) \) divides the line segment joining the point \(A(2-2) \) and \(B(-7,4) \) in the ratio \(1:2 \) the value of \(k \) is
CorrectIncorrectHint
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Question 10 of 40
10. Question
1 point(s)The value of P for which the points \(A(3,1),B(5,P) \) and \(C(7,-5) \) are collinear is
CorrectIncorrectHint
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Question 11 of 40
11. Question
1 point(s)In figure, \(\triangle \)ABC is circumscribing a circle the length of BC is
CorrectIncorrectHint
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Question 12 of 40
12. Question
1 point(s)Given \(\triangle ABC\sim\triangle PQR \), is \(\dfrac{AB}{PQ}=\dfrac{1}{3} \) then \(\dfrac{ar(\triangle ABC)}{ar(\triangle PQR)}= \)
CorrectIncorrectHint
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Question 13 of 40
13. Question
1 point(s)ABC is an equilateral \(\triangle \) of side \(2a \) the length of one of its altitude is
CorrectIncorrectHint
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Question 14 of 40
14. Question
1 point(s)\(\dfrac{\cos80^o}{\sin10^o}+\cos5a^o\ \text{cosec}\ 31^o= \)
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Question 15 of 40
15. Question
1 point(s)The value of \(\sin^2\theta+\dfrac{1}{1+\tan^2\theta}= \)
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Question 16 of 40
16. Question
1 point(s)The ratio of the length of a vertical rod and the length of its shadow is \(1:\sqrt3 \). Find the angle of elevation of the sun at that moment
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Question 17 of 40
17. Question
1 point(s)Two cones have their heights in the ratio \(1:3 \) and radii in the ratio \(3:1 \). What is the ratio of their volumes?
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Ratio -
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Question 18 of 40
18. Question
1 point(s)A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant?
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P(consonant)
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Question 19 of 40
19. Question
1 point(s)A die is thrown once. What is the probability of getting a number less than 3?
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P(number less than 3)
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Question 20 of 40
20. Question
1 point(s)If the mean of first n natural numbers is 15. Find n
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Question 21 of 40
21. Question
2 point(s)Show that \((a-b)^2,(a^2+b^2) \) and \((a+b)^2 \) are in AP
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As the common difference is same, so they are in AP -
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Question 22 of 40
22. Question
2 point(s)If \(DE||AC \) and \(DC||AP \), prove that \(\dfrac{BE}{EC}=\dfrac{BC}{CP} \)
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In
So, (Basic proportionality theorem)…(1)
In
So, ….(2)
From equation (1) and (2) we get
(Proved) -
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Question 23 of 40
23. Question
2 point(s)The rod AC of a TV disc antenna is fixed at right angle to the wall AB and a rod CD is supporting the disc. If AC = 1.5 m long and CD = 3 m
Find (i) \(\tan\theta \)
(ii) \(\sec\theta+\text{cosec}\theta \)
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(i)
(ii)
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Question 24 of 40
24. Question
2 point(s)A piece of wire 22 cm long is but into the form of an arc of circle subtending an angle of \(60^o \) at its centre. Find the radius of the circle. \(\left(\text{use}\ \pi=\dfrac{22}{7}\right) \))
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Question 25 of 40
25. Question
2 point(s)If a number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that \(x^2\leqslant4 \)?
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Total number of outcomes
Favourable outcomes -
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Question 26 of 40
26. Question
2 point(s)Find the mean of the following distribution
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Question 27 of 40
27. Question
3 point(s)Find the quadratic polynomial whose zeroes are reciprocal of the zeroes of the polynomial \(f(x)=ax^2+bx+c\ a\ne0,c\ne0 \)
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Required quadratic polynomial -
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Question 28 of 40
28. Question
3 point(s)If 4 is the zero of the cubic polynomial \(x^3-3x^2-10x+24 \), find its other two zeroes
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other two zeroes are -3 and 2 -
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Question 29 of 40
29. Question
3 point(s)In a fight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced to 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight
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Let the speed of aircraft be
km/hr
Speed of aircraft km/hr
Duration of flight hour -
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Question 30 of 40
30. Question
3 point(s)Find the area of triangle \(PQR \) formed by the points \(P(-5,7),Q(-4,-5) \) and \(R(4,5) \)
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Question 31 of 40
31. Question
3 point(s)In the figure \(\angle D=\angle E \) and \(\dfrac{AD}{DB}=\dfrac{AE}{EC} \), prove that \(BAC \) is an isosceles triangle
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So, is an isosceles triangle -
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Question 32 of 40
32. Question
3 point(s)If the point \(C(-1, 2) \) divides internally the line segment joining \(A(2,5) \) and \(B(x,y) \) in the ratio \(3:4 \). Find the coordinates of \(B \)
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The coordinates of are -
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Question 33 of 40
33. Question
3 point(s)If \(\sin\theta+\cos\theta=\sqrt3 \) then prove that \(\tan\theta+\cot\theta=1 \)
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Question 34 of 40
34. Question
3 point(s)A cone of base radius 4 cm is divided into 2 parts by drawing a plane through the mid-point of its height and parallel to its base compare the volume of two parts
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Ratio of volume
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Question 35 of 40
35. Question
4 point(s)Show that the square of any positive integer cannot be of form \((5q+2) \) or \((5q+3) \) for any integer \( q\)
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Let
be any positive integer
Case -1
Case -2
Case – 3
Case – 4
Case – 5
So, square of any positive integer cannot be of the form or for any integer -
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Question 36 of 40
36. Question
4 point(s)The sum of four consecutive numbers in AP is 32 and ratio of the product of first and last terms to the product of two middle terms is \(7:15 \). Find the numbers
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Let four consecutive numbers be
Four numbers are -
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Question 37 of 40
37. Question
4 point(s)Solve \(1+4+7+10+….+x=287 \)
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-
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Question 38 of 40
38. Question
4 point(s)A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are \(30^o \) and \(45^o \) respectively. Find the height of the tower. \((\sqrt3=1.73) \)
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Question 39 of 40
39. Question
4 point(s)A bucket in the form of a frustum of a cone of height 30 cm with radii of its lower end and upper ends are 10 cm and 20 cm respectively. Find the capacity of the bucket
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Capacity
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Question 40 of 40
40. Question
4 point(s)The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village change the distribution to ‘more than’ type distribution and draw its ogive
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![\sqrt{\left[0^2-(a\cos\theta+b\sin\theta)^2+(a\sin\theta-b\cos\theta)-0\right]}\\ \\ =\sqrt{a^2\cos^2\theta+b^2\sin^2\theta+2a\cos\theta \ b\sin\theta+a^2\sin^2\theta+b^2\cos^2\theta-2a\sin\theta\ b\cos \theta}\\ \\ =\sqrt{a^2(\cos^2\theta+\sin^2\theta)+b^2(\sin^2\theta+\cos^2\theta)}\\ \\ =\sqrt{a^2+b^2}](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-70e3a7be30012b52651b621ec64fe82c_l3.png "Rendered by QuickLaTeX.com")
![\dfrac{1}{2}[22-30-42]=0\\ \\ -8=4P\Rightarrow P=-2](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-a8b392524cf75ac4b31c315e144c7339_l3.png "Rendered by QuickLaTeX.com")
(Basic proportionality theorem)…(1)
….(2)
(Proved)
km/hr
km/hr
hour![\mathrm{ar(\triangle PQR)=\dfrac{1}{2}[-5(-5-5)-4(5-7)+4(7+5)]\\ \\ =\dfrac{1}{2}[50+8+48]\\ \\ =53\ sq\ units}](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-1f8061c21611a8befdb799de633969f1_l3.png "Rendered by QuickLaTeX.com")
is an isosceles triangle
are 
be any positive integer
or 
for any integer 
![x=a_n=1+3n-3=3n-2\\ \\ S_n=287\\ \\ \Rightarrow \dfrac{n}{2}[1+3n-2]=287\\ \\ \Rightarrow 3n^2-n-574=0\\ \\ \Rightarrow (n-14)\ (3n+41)=0\\ \\ \Rightarrow n=14\\ \\ x=3n-2=3\times14-2=40](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-9cb03ae2a60300f7f4c91cd73d645b5a_l3.png "Rendered by QuickLaTeX.com")
