Title MATHS-A.pdf ✅

HALF YEARLYEXAM (2022 -23) MATHEMATICS (SET-A) TIME: 3 Hours Class: X M.M.: 80 General Instructions: 1. Section I has 16 questions of 1 mark each. 2. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. Attempt any 4 out of 5 sub-parts. 3. Section III – Question No 21 to 26 are Very short answer Type questions of 2 mark each, 4. Section IV – Question No 27 to 33 are Short Answer Type questions of 3 marks each 5. Section V – Question No 34 to 36 are Long Answer Type questions of 5 marks each. 6. Internal choice is provided in4 questions of 1 mark, 2questions of 2 marks,3 question of 3 mark and 1 question of 5 marks. ___________________________________________________________________________________ SECTION-I Q 1. The value of p if the polynomial p x2 -3 (p-1)x-1 is divisible by (x-1) is a) 3 b) 2 c) 1 d) -2 Q 2. The number of 3 digit multiples of 4 are a) 320 b)225 c) 220 d) 250 Q 3. If A,B are zeroes of the polynomial 2x2 - 4x +1 then evaluate A 2+B2 . a) 10 b) 5 c) 3 d) 12 Q4. The value of p for which the equations will represent coincident lines is 3x+2py+7=0 , 6x+(p-1)y+14=0 a) 1/2 b) 1/5 c) -1 d) -1/3 Q 5. The 13th term from the end of the AP 7,9,11,13..........213 is a) 189 b) 191 c) 193 d) 31 Q 6. For what value of k will the consecutive terms 2k+1, 3k+3 and 5k-1 form an AP? a) 2 b) 5 c) 3 d) 6 Q7. If P(a 3 , 2b ) is the mid point of line segment joining the points Q(–6,5) and R (–2,3) then the value of a+b is a) –8 b) –10 c) –5 d) –12 Q8. Find the value of k if the equation x2+2√2kx+18=0 has equal roots Q9. An army contingent of 616 members is to march behind an army band of 32 members in a parade the two groups are to march in exactly same number of columns .What is the maximum number of columns in which they can march? Q 10. If the nth term of an A.P is (2n+1), then find the sum to n terms of the A.P OR If the nth term of A.P is pn + q , find the common difference. Q11. In what ratio does the point (-4,6) divide the line segment joining the points A(–6,10) and B (3, –8). OR Find the ratio in which the x axis divides the line segment joining the points (1, –5) and (–4,5). Q12. Check whether following equations are consistent or not 3X + 2Y = 28 , 6X – Y =1 4 Q13. Find the coordinates of the centroid of a triangle whose vertices are (0,6), (8,12) and (8,0) OR Find the point on x-axis which is equidistant from the points (2, –2) and (–4, 2) Q 14. Find the least number that is divisible by all numbers from 1 to 5(both inclusive). OR Find the HCF of k, 2k, 3k, 4k and 5k where k is any positive integer. Q15. Find a quadratic polynomial whose zeros are 5 – 2√3 and 5 + 2√3. Q16. Solve the quadratic equation 2 x2 + ax – a 2 = 0 for x. SECTION-II


Q26. Solve the quadratic equation 5x2 – 6x – 2 = 0 SECTION IV Q27. If α and β are the zeroes of p(x) a quadratic polynomial such that α + β=24, α – β= 8 then find the quadratic polynomial having α and β as its zeroes. Q28 If AD and PS are medians of the triangles ABC and PQR where ΔABC~ ΔPQR then prove that AB PQ = AD PS Q29 If –5 is a root of the equation 2x2+px-15 =0 and the quadratic equation P(x2+x)+k =0 has equal roots then find the value of k. Q30 Find three numbers in A.P whose sum is 15 and product is 105. OR Reshma wanted to save atleast Rs 6500 to buy a scooty. She saved Rs 450, in first month then raised her savings by Rs20 every month.If she continues this way for next 12 months will she be able to buy her scooty next year? Q31 The sum of a two digit number and the number obtained by interchanging the digits is 132. If 12 is added to the number the new number becomes 5 times the sum of digits, find the number. OR There are 2 examination rooms A and B .If 10 candidates are sent from A to B the number of students in each room is same .However if 5 candidates are sent from B to A number of students in A is double the number of students in B .Find the total no of students who are giving the examination. Q32 Show that (a,a) (–a, –a) and (−√3 a, √3 a) are vertices of an equilateral triangle. Q33 In figure, AB || ED. If AD = 3x + 19, EB =3 x + 4, DC = x + 3 and CE = x find x. SECTION V Q34 State and prove Basic Proportionality Theorem. Q35 Solve for x : x−3 x−4 + x−5 x−6 = 10 3 ,x≠ 4,6 OR Divide 27 into two parts such that sum of their reciprocals is 3 20 . Q36 Draw graph of the following equations of lines : 3x+2y = 8 and 2x-y-3=0.Also from the graph find the area of the triangle formed between the two lines and y axis.