Mathematics Exam Prep: Equations, Geometry, and General Knowledge

THE THEOREM OBJECTIVE 1. Which of the following equations is consistent and unique? (A) 2.x – 3y = 5, – 4x + 6y = 3 (B) 2.x – 3y = 1, 31 – 4y = 1 (C) 2x – 3y = 1, 4x – 6y = 2 (D) x + 2 == 1, 2x + 4y =– 2 2. At what point will the graph of the equation ' + - 2 = () intersect the Y-axis? (A) (2a,0) (C) (0, a+b) (c)(0,- 3. If 2 (B) (a + b, 0) (D) (0, 26) 2x – 3y + p = 0 2x + 3y – q = 0) of the equation (1, 2) then which of the following is true? (A) q – 2p = 0 (C) g + 2p = 0 and solution (B) p – 2q = 0 (D) p + 2q = 0 4. If the sum of a two-digit number and the number obtained by interchanging its digits is 121, what is the sum of the digits? (A) 9 (B)10 (C)11 (D)12 tambukumbhu Matrix Guide MATHEMATICS (A) 2√√a²+b² (C) 24/a? – b (B) / a + b (D)√a²-b² 22. What is the locus of the point that intersects the line segment connecting the poles (0,2) and (2,0) in the ratio 3:2? (A)()(B)(4) ( ) ( 6 (D) (-) 23. If A (5, – 1), B (– 1, 3), C (– 4, – 2), what is the locus of the centroid of AABC? (A) (1,0,0) (c)(0,33) (B)(0,0) 313 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 + 61 + k = 0, then the root of the equation 25. In which of the following cases is a greater than or equal to and a+B+aB, then k is (A)-4 (B)4 6. If x + 4x + k, then which is true? (A) k > 4 2 times? (C)–2 (D)3 = 0, then the root of (B) k < 4, then what is the penalty? (A) Driving under the influence of alcohol (B) Not giving way to an ambulance (C) Not wearing a seat belt (D) Without a helmet Driving 26. In the figure below, if AD=9 cm. and AB=12 cm., then CD= how many cm. ? 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 circumference? (A) 36° (B)72° (C)45° (D)35° 36. If m / A = 70° and m / B = 100° of a regular 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) 1:4/3 (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. m. 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 perfect square and solve: (6x + 5) (1 – 2) = 0 Solution: (61 + 5) (x - 2) = 0 => 6x (x-2)+5(x-2)=0 => 6x2-12x+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 (Both sides multiplied by 4a = 4 x 6 = 24) → 144r – 1681 = 240 144x2 168x+49= 240 +49 (Both sides added by b = (− 7) = 49) .. n = 10 and m = 13 (Answer) 4. ABCD is a parallelogram. ĀÑ ray BD line segment, CD BĞ intersecting at points E, F and G respectively, prove that AE:EG=AF:AG B D E F Given: ABCD is a parallelogram. The ray ĀÑ intersects the line segment BD, CD and BĞ at points E, F and G respectively. Proof: AE:EG=AF:AG Proof: In AABG CF BA = || BC AF = BG AG AF AD => (·. AD = BC) BC AG BG BG = Again in NAED and in AGEB | DAE = / EGB (due to congruence) AED = / GEB (opposite angles) → AADD ~ AGEB (similar angles) AD AE DE BG EG AD => BG EG BE AE = = AF AD AF AG BG AG (proven) == (C) k > 4 (D) k < 4 7. What equation is obtained by expressing 1–24T – 6 = 0 in a biquadratic equation? (A) x + 16r + 36 = 0 (B) x + 8x + 36 = 0 (C) 1 – 16x + 36 = 0 (D) x – 12x + 36 = 0 5. Which of the following equations is not a binomial equation? 3 (A) x- I = 0 I = x² (B) x (C) (1 – 2) (x + 3) = 0 (D) m* – 2x + (2m – 1) = 0 (m # 0) 9. If the sum of the first . number of terms of a parallel progression is 2n' + 3n, then what is its second term? (A) 9 (B)14 (C)5 (D)12 10. If ( -th term of an A. P. is . and 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. In two parallel sequences ) - the ratio of the two nth terms is (n – 1): (n + 1) then what is the ratio of their fifth terms? (A) 1:2 (B)2:3 (C)3:4 (D) 4:5 1 1 12. What is the sum of + + + X 2 2x3 3x4 1 + ? n (n + 1) 1 (A) n + 1 (B) n+1 n (C) n n + 1 A B D (A)7 (B)16 (C)13 (D)6 27. The ratio of the sides of two similar triangles APQR and ADEF is 5:61. If the area of ADEF is 108 sq. cm. then what is the area of APQR in sq. cm.? (A) 108 (B) 120 (C)75 28. Below Which of the following is true? (B) Two similar triangles are always congruent (D) 150 (A) 10 (B)12 (C)13 (D)8 39. How many tangents can be drawn to a circle from a point outside the circle? (A) 1 (B)2 (C)3 (D)4 40. In