I – Pre Board

X – Maths
GENERAL INSTRUCTIONS:
 All questions are compulsory. This question paper has 5 sections A to E.
 Section A has 20 MCQs carrying 1 mark each.
 Section B has 5 questions carrying 2 marks each.
 Section C has 6 questions carrying 3 marks each.
 Section D has 4 questions carrying 5 marks each.
 Section E has 3 case study based questions carrying 4 marks each with sub-parts of the values of 1, 1 and 2 marks each
respectively.
 Draw neat diagrams wherever required. Draw graphs only on the graph sheet provided.
 Take π = 22/7 wherever required if not stated.
SECTION – A [ 20 × 1 = 20 ]
23
Q. 1. If a = , then a is
25
(a). an integer (b). a whole no. (c). rational (d). irrational
Q. 2. The sum of the zeroes of a polynomial is 0 and its one zero is 3. The polynomial is
(a). x2 + 9 (b). x2 − 9 (c). x2 + 3 (d). x2 − 3
Q. 3. The system of equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution. The value of k is
(a). 0 (b). 2 (c). 6 (d). 8
2
Q. 4. If the equation ax + bx + c = 0 has real and equal roots, then c =
−𝑏 𝑏 −𝑏2 𝑏2
(a). (b). (c). (d).
2𝑎 2𝑎 4𝑎 4𝑎
Q. 5. Which term of the A.P. 21 , 42 , 63 , 84 , …….. is 231 ?
(a). 9th (b). 10th (c). 11th (d). 12th
Q. 6. In the adjoining figure,
if DE ∥ BC , then the
value of x is
(a). 4 (b). 4.5
(c). 6 (d). 6.5

Q. 7. The distance of the point P(x , y) from the origin is

(a). √𝑥 2 + 𝑦 2 units (b). √𝑥 2 − 𝑦 2 units (c). √𝑥 + 𝑦 units (d). √𝑥 − 𝑦 units
𝑛
Q. 8. If ( 𝑎 × 5) ends with the digit zero for any natural number n , then a is
(a). any natural no. (b). an even no. (c). an odd no. (d). none of these
1 1
Q. 9. If α and β are the zeroes of the polynomial p(x) = 4x2 + 3x + 7 , then + is equal to
𝛼 𝛽
7 7 3 3
(a). − (b). (c). − (d).
3 3 7 7
Q. 10. If a pair of linear equations in two variables is consistent , then the graph lines of these equations are
(a). always intersecting (b). always parallel
(c). always coincident (d). either intersecting of coincident
Q. 11. The discriminant of the quadratic equation (x + 2)2 = 0 is
(a). 4 (b). 2 (c). −2 (d). 0
1 1−2𝑘 1−4𝑘
Q. 12. The common difference of the A.P. , , , ……. is
2𝑘 2𝑘 2𝑘
(a). 1 (b). − 1 (c). k (d). 2k
Q. 13. Two poles of heights 6m and 11m stand vertically upright on a plane ground. If the distance between their
feet is 12m , the distance between their tops is
(a). 11m (b). 12m (c). 13m (d). 14m
Q. 14. AD is a median of ∆ABC. If the co-ordinates of A , B and C are (7 , −3) , (5 , 3) and (3 , −1) respectively,
then the co-ordinates of D are
(a). (8 , 2) (b). (6 , 0) (c). (5 , −2) (d). (4 , 1)
Q. 15. The zeroes of the quadratic polynomial p(x) = x2 + 99x + 127 are
(a). both positive (b). both negative (c). both equal (d). one positive one negative
5
Q. 16. If 37x + 43y = 123 and 43x + 37y = 117 , then x + y is equal to
(a). 2 (b). 3 (c). 5 (d). 7
Q. 17. The quadratic equation 9x2 − 6x − 2 = 0 has
(a). no real roots (b). two equal roots (c). two distinct roots (d). more than two roots
Q. 18. If ∆ABC ~ ∆DEF such that AB = 9.1 cm and DE =6.5 cm. If the perimeter of ∆DEF is 25 cm , then the
perimeter of ∆ABC is
(a). 34 cm (b). 35 cm (c). 36 cm (d). 36 cm
ASSERTION – REASON QUESTIONS
In Q.No. 19 & 20 , a statement of Assertion(A) is followed by a statement of Reason(R). Choose the
correct option from the four options provided :
Q. 19. Statement A (Assertion) : a , b , c are in A.P. , if and only if 2b = a + b
Statement R (Reason) : The sum of first n odd natural numbers is n2
(a). Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b). Both assertion (A) and reason (R) are true but reason (R) is not correct explanation of assertion (A).
(c). Assertion (A) is true but Reason (R) is false.
(d). Assertion (A) is false but Reason (R) is true.
Q. 20. Statement A (Assertion) : Point (0 , 2) is the point of intersection of y-axis with the line 3x + 2y = 4
Statement R (Reason) : The distance of the point (0 , 2) from the x-axis is 2 units
(a). Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b). Both assertion (A) and reason (R) are true but reason (R) is not correct explanation of assertion (A).
(c). Assertion (A) is true but Reason (R) is false.
(d). Assertion (A) is false but Reason (R) is true.

SECTION – B [ 5 × 2 = 10 ]
n
Q. 21. Check whether 15 can end with digit zero for any natural number n.
3 −1
Q. 22. If and are the zeroes of a quadratic polynomial , then find the polynomial.
2 3
OR
Find the zeroes of the quadratic polynomial p(x) = x2 − 11.
Q. 23. Find the values of k for which the quadratic equation 9x2 + 3kx + 4 = 0 has two equal real roots.
Q. 24. Which term of the A.P. 3 , 8 , 13 , 18 , …….. is 83 ?
OR
1
How many terms are there in the A.P. 18 , 15 , 13 , ………. , − 47 ?
2
Q. 25. Find the roots of the quadratic equation 3x2 − 2√6x + 2 = 0.

SECTION – C [ 6 × 3 = 18 ]
Q. 26. If α and β are the zeroes of the polynomial p(x) = 4x2 − 5x − 1 , then find the value of α2β + αβ2
Q. 27. The first and last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, then find the
number of terms in the A.P. ?
Q. 28. Find the greatest number of 6 digits which is exactly divisible by 15 , 24 and 36.
OR
It is given that √2 is irrational, then prove that 5 + 3√2 is irrational.
Q. 29. Solve for x and y : 8x + 5y = 9; 3x + 2y = 4
Q. 30. The height of a right angled triangle is 7 cm less than its base. If the hypotenuse is 17cm, then find the base
and height of the triangle.
OR
The sum of squares of two consecutive positive integers is 365. Find the integers.
Q. 31. In the adjoining figure, If LM ∥ CB and LN ∥ CD ,
𝐴𝑀 𝐴𝑁
then prove that =
𝐴𝐵 𝐴𝐷

6
 SECTION – D [ 4 × 5 = 20 ]
Q. 32. Prove that √7 is irrational.
Q. 33. Draw the graphs of the linear equations 2x + y = 6 and 2x – y = −2 on the same graph sheet. Also find the
area of the triangle formed by these two graph lines and the x – axis.
OR
1 1
A fraction becomes when 2 is subtracted from the numerator and it becomes when 1 is subtracted
3 2
from the denominator. Find the fraction.
Q. 34. The co-ordinates of A and B are (−2 , −2) and (2 , −4) respectively. If point P lies on the line segment AP
3
such that AP = AB , then find the co-ordinates of P.
7
Q. 35. State and prove the Thales Theorem.
OR
AD and PM are the medians of triangles ABC and PQR respectively. If ∆ABC ~ ∆PQR , then prove
𝐴𝐵 𝐴𝐷
that =
𝑃𝑄 𝑃𝑀

SECTION – E [ 3 × 4 = 12 ]
( Case Study Based Questions )
Q. 36. Due to strong winds a loose electric
wire got bent in the shape of a certain
mathematical shape as shown in the
adjoining picture.
Observe the picture and diagram, and answer the following questions :
(i). Name the shape (graph) in which the wire is bent. [1]
(ii). Name the polynomial that is represented by this graph. How many zeroes are there ? [1]
(iii). Find the polynomial whose zeroes are represented in the graph. [2]

Q. 37. A whole-sale timber merchant stacked 200 lumber logs in this manner :
20 logs in the first (bottom) row , 19 logs in the next row , 18 in the
next row to it and so on as shown in the given picture.
Based on the above information, answer the following questions :
(i). Do the manner of stacking the logs follow an A.P. ?
If yes, then what is the common difference ? [1]
(ii). How many logs are there in the 7th row ? [1]
(iii). What is the number of rows in which the 200 logs are stacked ? [2]

Q. 38. A school organises the sports events in a rectangular ground ABCD.

The tracks are marked with a gap of 1m each in the form of straight lines.
120 flower pots are placed at a distance of 1m each along the side AD.
Reeta runs 1/3rd of the distance in the 2nd line along AD and posts her red flag.
Babita runs 1/5th of the distance in the 8th line and posts Her blue flag.
Based on the given information, answer the following questions :
(i). What are the co-ordinates of the point of Red flag ? [1]
(ii). What are the co-ordinates of the point of Blue flag ? [1]
(iii). If Geeta posts her green flag exactly at the mid-point of the line joining these two points, what will be
co-ordinates of the point of her green flag ? [2]