Mathematics Guide: Objective & Subjective Problems with Solutions

THE PRAMEYA OBJECTIVE 1. Which of the following equations is consistent and unique? (A) 2.x – 3y = 5, – 4x + 6y = 3 (B) 2x – 3y = 1, 3x – 4y = 1 (C) 2x – 3y = 1, 4x – 6y = 2 MATRIX GUIDE MATHEMATICS (B) aè + b 2 a- (A) 24/a+b (C) 2/a° – b? (D) / a – b 1, 2x + 4y = 2 =- Y 22.( 0,2) and (2,0) are the intersections of the vertices (D) x + 2y = x 2. a + 2 = 0) The graph of the equation ! - At which point will it intersect the x-axis? (A) (2a,0) (B) (a + b, 0) (c) (0, a+b) (D) (0,2b) 3. If 2 2x – 3y + p = 0 21 + 3y – q = 0 is the equation (1, 2) then which is true? (A) q – 2p = 0 (C) g + 2p = 0 and the solution is (B) p – 2q = 0 (D) p + 2q = 0 4. If the sum of a two-digit number and its digits is 121, what is the sum of the digits? (A) 9 (B)10 (C)11 (D)12 What is the locus of the points that intersect the line segment in the ratio 3:2? (a) (— —+) (b) — +) (D)(-) 6 (c)(3) 23. If A (5, – 1), B (– 1, 3), C (– 4, - 2), what is the position of the centre of gravity of AABC? (A) (1,0,0) (c)(0,5) (B)(0,0) (D) (10.5) 24. For how many months is the pollution certificate valid for a new vehicle? (A) 19 (B)13 (C)5 (D) 1 5. If 3x + 6.1 + k = 0, find the roots of the equation 25. In which of the following cases is the maximum a and o and a+B+aB == how many? Then the value of k is (A) –4 (B)4 (C) – 2 (D)3 6. If the roots of x + 4x + k = 0 are real then (A) k > 4 then which is true? (B) k < 4 (C) k > 4 (D) k < 4 7. 1–24 –6= 0 is a two-digit number (A) x + 16x + 36 = 0 (B) x + 8x + 36 = 0 (C) x – 16x + 36 = 0 (D) x – 12x + 36 = 0 What is the penalty for driving under the influence of alcohol? (A) Driving under the influence of alcohol (B) Not giving way to an ambulance (C) Not wearing a seat belt (D) Driving without a helmet 26. In the figure below, AD=9 cm. m. and AB=12 cm. m. Then CD= how many cm. m. ? B (A) 20° (B)15° (C)30° (D) 35° 35. What is the measure of the angle subtended by each side of an isosceles decagon at the centre of its circumcircle? (A) 36° (B)72° (C)45° (D) 35° 36. If m / A = 70° and m / B = 100° of an inscribed quadrilateral ABCD, what is the difference between the other two angles? (A) 80° (B)70° (C)40° (D)30° 37. If the degree measure of an arc in a circle is 60, what is the ratio of the corresponding radius to the diameter? (A) 1:1 (C)1:2 (B) 1:/3 (D)/3: 1 38. In the figure below, AP=4 cm. m. And BQ=8 cm. m. . If the perimeter of the triangle is 36 cm. then how many cm. is AC? 10th Edition ANSWERS Thursday 1 January 2026. Thursday 1 January 2026 1.(B), 2.(D), 3.(A), 4.(C), 5.(B), 6.(D), 7.(C), 8.(A), 9.(A), 10.(C), 11,(B), 12.(D), 13.(C), 14.(C), 15.(A), 16.(B), 17.( B), 18.(C), 19.(D), 20.(A), 21.(A), 22.(C), 23.(B), 24.(D), 25.(B), 26.(A), 27.(C), 28.(C), 29.(D), 30.(B), 31.(A), 32.(C), 33.(D), 34.(B), 35.(A), 36.( D), 37.( C), 38.( A), 39.( B), 40.( D), 41.( C), 42.( A), 43.( B), 44.( D), 45.( C), 46.( A), 47.( A), 48.( D), 49.( B), 50.( C) SUBJECTIVE 1. Convert to square root and solve: (6x+5) (x-2) = 0 Solution (6x + 5) (x – 2) = 0 => = = 6x (x-2)+5(x-2)=0 6x? – 12x + 5x – 10 = 0 6x? – 7x – 10 = 0 ( Here a = 6, b =- 7, c =– 10) 6x? – 7x = 10 => => (Polar term taken to R.H.S.) 24 (6x* – 71) = 24 × 10 (Multiply both sides by 4a = 4 x 6 = 24) 144r – 168x = 240 => - 144x2 168x+49=240+49 (Add both sides by b = ( – 7) = 49) => (12x-7)=289 12.1–7=+289 .. n = 10 gm = 13 (Answer) 4. ABCD is a parallelogram. If the ray BD intersects the line segment, CD and BĞ at points E, F and G respectively, prove that AE:EG=AF:AG B A E < C G D Given: ABCD is a parallelogram. Ray BD intersects line segment CD and BÜ at points E, F and G respectively. Proof: AE:EG=AF:AG Proof: In AABC CF BA => => BC AF BG AG AF BC AD AG BG BG AD = BC) Again in NAED and AGEB | DAE = / EGB (due to congruent angles) AED = / GEB (opposite angles) → AAED AGEB (similar angles) AD AE DE = = BE => BG EG AD AE BG EG AE AF => = EG AG AC AD = AC) (Proved) Which equation is obtained when expressed in equation? 5. Which of the following equations is not a biconvex equation? 3 (A) x I 2 (B) x- = 0 I (C) (1 – 2) (x + 3) = 0 (D) mx* – 2x + (2m – 1) = 0 (m + 0) 9. If the sum of the first . number of terms of an equation is 2n + 3n, then what is its second term? (A) 9 (B)14 (C)5 (D)12 10. If the a -th term of an A. P. is . and the b -th term is . then what is the 10th term? (A) a + b + 10 (C) a + b – 10 (B) a + 10b (D) 10a +b 11. If the ratio of the 'nt -th terms of two equations is (n – 1): (n + 1 ), then what is the ratio of their fifth terms? (A) 1:2 (B)2:3 (C)3:4 1 1 1 × 2+2 3+3 × 4 2x3 What is the sum of x? + 12. x 1 + n (n + 1) 1 (A) (B) n+1 n + 1 (C) n n (D) n + 1 (D)4:5 A B (A) 7 (B)16 (C)13 (D)6 27. The ratio of the sides of two similar triangles APQR and ADEF is 5:6. If the area of ADEF is 108 sq. cm. then what is the area of APQR? (A) 108 (B) 120 (C)75 28. Which of the following statements is true? (D) 150 (A) Two polygons with the same number of sides are similar. (B) Two similar triangles are always congruent (C) Two similar triangles are