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Board Paper of Class 10 2023 Maths (Basic) Delhi(Set 1) - Solutions

General Instructions 
Read the following instructions carefully and follow them: 

1. This question paper contains 38 questions. All questions are compulsory. 
2. Question paper is divided into FIVE sections Section A, B, C, D and E
3. In section A, question number 1 to 18 are multiple choice questions (MCQs) and question number 19 and 20 are Assertion - Reason based questions of 1 mark each. 
4. In section B, question number 21 to 25 are very short answer (VSA) type questions of 2 marks each. 
5 in section C, question number 26 to 31 are short answer (SA) type questions carrying 3 marks each. 
6. In section D, question number 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
7. In section E, question number 36 to 38 are case based integrated units of assessment questions carrying 4 marks each. Internal choice is provided in 2 marks question in each case study.
8. There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. 
9. Draw neat figures wherever required. Take π = 22/7 wherever required if not stated. 
10. Use of calculators is not allowed. 



  • Question 1
    A quadratic polynomial the sum and product of whose zeroes are −3 and 2 respectively, is :
    (a) x2 + 3x + 2
    (b) x2 − 3x + 2
    (c) x2 − 3x − 2
    (d) x2 + 3x − 2 VIEW SOLUTION


  • Question 2
    (HCF × LCM) for the numbers 70 and 40 is :
    (a) 10
    (b) 280
    (c) 2800
    (d) 70 VIEW SOLUTION


  • Question 3
    If the radius of a semi-circular protractor is 7 cm, then its perimeter is :
    (a) 11 cm
    (b) 14 cm
    (c) 22 cm
    (d) 36 cm VIEW SOLUTION


  • Question 4
    The number 5-35+5 is :
    (a) an integer
    (b) a rational number
    (c) an irrational number 
    (d) a whole number VIEW SOLUTION


  • Question 5
    If p(x) = x2 + 5x + 6, then p(−2) is :
    (a) 20
    (b) 0
    (c) −8
    (d) 8 VIEW SOLUTION


  • Question 6
    Which of the following cannot be the probability of an event?

    (a) 0.1
    (b) 53
    (c) 3%
    (d) 13 VIEW SOLUTION


  • Question 7
    The pair of linear equations x + 2y + 5 = 0 and −3x − 6y + 1 = 0 has :
    (a) a unique solution
    (b) exactly two solutions
    (c) infinitely many solutions
    (d) no solution VIEW SOLUTION


  • Question 8
    If ∆ABC ∼ ∆DEF and A=47°, E=83° then C is equal :
    (a) 47
    (b) 50
    (c) 83
    (d) 130 VIEW SOLUTION


  • Question 9
    If the pair of linear equations x-y=1, x+ky=5 has a unique solution x = 2, y = 1, then the value of k is:
    (a) −2
    (b) −3
    (c) 3
    (d) 4 VIEW SOLUTION


  • Question 10
    The value of  5 sin290°-2 cos2 0° is:
    (a) −2
    (b) 5
    (c) 3
    (d) −3 VIEW SOLUTION


  • Question 11
    The length of the arc of a circle of radius 14 cm which subtends an angle of 60 at the centre of the circle is:
    (a) 443 cm
    (b) 883 cm
    (c) 3083 cm
    (d) 6163 cm VIEW SOLUTION


  • Question 12
    The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is:
    (a) 30
    (b) 45
    (c) 60
    (d) 90 VIEW SOLUTION


  • Question 13
    The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is:
    (a) 2
    (b) 3
    (c) 4
    (d) 5 VIEW SOLUTION


  • Question 14
    From a well -shuffled deck of 52 playing cards, a card is drawn at random. What is the probability of getting a red queen?
    (a) 152
    (b) 126
    (c) 113
    (d) 1213 VIEW SOLUTION


  • Question 15
    A quadratic equation whose one root is 2 and the sum of whose roots is zero, is:
    (a) x2+4=0
    (b) x2-2=0
    (c) 4x2-1=0
    (d) x2-4=0 VIEW SOLUTION


  • Question 16
    Which of the following is not a quadratic equation?
    (a) 2x-12=4x2-2x+1
    (b) 2x-x2=x2+5
    (c) 2x+32+x2=3x2-5x
    (d) x2+2x2=x4+3+4x3 VIEW SOLUTION


  • Question 17
    How many tangents can be drawn to a circle from a point on it? 
    (a) One
    (b) Two
    (c) Infinite
    (d) Zero VIEW SOLUTION


  • Question 18
    The length of the tangent from an external point A to a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is:
    (a) 7 cm 
    (b) 5 cm
    (c) 7 cm
    (d) 25 cm VIEW SOLUTION


  • Question 19
    Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.
    Reason (R): The lengths of tangents drawn from an external point to a circle are equal. 
    (a) Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
    (b) Both Assertion (A) and Reason (R) are true but Reason (R) does not give the 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. VIEW SOLUTION


  • Question 20
    Assertion (A): If one root of the quadratic equation 4x2 − 10x + (k − 4) = 0 is reciprocal of the other, then value of k is 8.
    Reason (R): Roots of the quadratic equation x2 − + 1 = 0 are real.
    (a) Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
    (b) Both Assertion (A) and Reason (R) are true but Reason (R) does not give the 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. VIEW SOLUTION


  • Question 21
    If sinα=12, then find the value of 3cosα-4cos3α. VIEW SOLUTION


  • Question 22
    Find the coordinates of the point which divides the join of A(−1, 7) and B(4, −3) in the ratio 2 : 3.

    OR


    If the points A (2, 3), B (−5, 6), C (6, 7) and D (p, 4) are the vertices of a parallelogram ABCD, find the value of p. VIEW SOLUTION


  • Question 23
    Find the discriminant of the quadratic equation 3x 2x13 = 0 and hence find the nature of its roots.

    OR


    Find the roots of the quadratic equation x2 − x − 2 = 0. VIEW SOLUTION


  • Question 24
    In the adjoining figure, PT is a tangent at T to the circle with center O. If TPO = 30º, find the value of x.
    VIEW SOLUTION


  • Question 25
    In the adjoining figure, A, B and C are points on OP, OQ and OR respectively such that AB||PQ and AC||PR. Show that BC||QR.
    VIEW SOLUTION


  • Question 26
    Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients. VIEW SOLUTION


  • Question 27
    Prove that 1+tan2 A1+cot2 A=sec2 A-1 VIEW SOLUTION


  • Question 28
    A lending library has a fixed charge for first three days and an additional charge for each day thereafter. Rittik paid ₹27 for a book kept for 7 days and Manmohan paid ₹21 for a book kept for 5 days. Find the fixed charges and the charge for each extra day.

    OR


    Find the values of 'a' and 'b' for which the system of linear equations 3+ 4y = 12, (a + bx + 2 (a – b) y = 24 has infinite number of solutions. VIEW SOLUTION


  • Question 29
    A die is rolled once. Find the probability of getting:
    (i)  an even prime number.
    (ii) a number greater than 4.
    (iii) an odd number. VIEW SOLUTION


  • Question 30
    Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector. VIEW SOLUTION


  • Question 31
    Prove that the lengths of tangents drawn from an external point to a circle are equal.

    OR


    Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.
    VIEW SOLUTION


  • Question 32
    The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30º than when it was 60º. Find the height of the tower.

    OR


    From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. VIEW SOLUTION


  • Question 33
    Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.

    OR


    In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k. VIEW SOLUTION


  • Question 34
    The following table gives the monthly consumption of electricity of 100 families:
     
    Monthly Consumption (in units) 130-140 140-150 150-160 160-170 170-180 180-190 190-200
    Number of families 5 9 17 28 24 10 7

    Find the median of the above data. VIEW SOLUTION


  • Question 35
    The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends. Length of the cylindrical part is 7m and radius of cylindrical part is 72m.
    Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
    VIEW SOLUTION


  • Question 36
    Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle. One such campaign board made by class X student of the school is shown in the figure.  


    Based on the above information, answer the following questions:

    (i) Find the coordinates of the point of intersection of diagonals AC and BD.

    (ii) Find the length of the diagonal AC.

    (iii) (a) Find the area of the campaign Board ABCD.

    OR

      (b) Find the ratio of the length of side AB to the length of the diagonal AC.
    VIEW SOLUTION


  • Question 37
    Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. 


    Based on the above information, answer the following questions:

    (i) How many guests Khushi can invite at the most?

    (ii) How many apples and bananas will each guest get ?

    (iii) (a) If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most ?

    OR

     (b) If the cost of l dozen of bananas is ₹60, the cost of 1 apple is ₹15 and cost of 1 mango is ₹20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes. 
    VIEW SOLUTION


  • Question 38
    Observe the figures given below carefully and answer the questions:
    Figure A 
     

    Figure B
     

    Figure C
     


    (i) Name the figure(s) wherein two figures are similar.

    (ii) Name the figure(s) wherein the figures are congruent.

    (iii) (a) Prove that congruent triangles are also similar but not the converse.

    OR

    (b) What more is least needed for two similar triangles to be congruent?
    VIEW SOLUTION
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