CBSE Section A Practice
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SAMADHAN ACADEMY
Building Foundations for Success
CBSE CLASS X: MATHEMATICS SECTION A (20 MCQs)
LCM(7, 21, 28) = 84.
Ratio = 7:84 = 1:12."], ["id" => 2, "topic" => "Real Numbers", "q" => "2.353535... is an:", "sol" => "The decimal is non-terminating but repeating. Therefore, it is a Rational Number."], ["id" => 3, "topic" => "Polynomials", "q" => "If one zero of the quadratic polynomial 4x² + 4x – m is the other zero (implied reciprocal), find m.", "sol" => "Product of zeroes (α * 1/α) = c/a.
1 = -m/4 → m = -4."], ["id" => 4, "topic" => "Polynomials", "q" => "The zeroes of the quadratic polynomial x² + 99x + 127 are:", "sol" => "Since all coefficients are positive, the sum of zeroes is negative and product is positive. Both zeroes must be negative."], ["id" => 5, "topic" => "Polynomials", "q" => "A quadratic polynomial whose one zero is 3 and the product of zeroes is 0, is:", "sol" => "α = 3, αβ = 0 → β = 0.
Sum = 3+0=3. Poly: x² - 3x."], ["id" => 6, "topic" => "Linear Equations", "q" => "8x – 4y + 12 = 0 and 2x – y + 5 = 0 represents two lines which are:", "sol" => "a1/a2 = 4, b1/b2 = 4, c1/c2 = 2.4. Since a1/a2 = b1/b2 ≠ c1/c2, lines are parallel."], ["id" => 7, "topic" => "Linear Equations", "q" => "The line represented by 2y – x = 4 intersects the y-axis at:", "sol" => "On y-axis, x = 0. 2y - 0 = 4 → y = 2. Point is (0, 2)."], ["id" => 8, "topic" => "Quadratic Equations", "q" => "Value(s) of k for which 2x² – kx + k = 0 has equal roots:", "sol" => "D = b² - 4ac = 0.
(-k)² - 4(2)(k) = 0 → k² - 8k = 0 → k = 0 or 8."], ["id" => 9, "topic" => "Quadratic Equations", "q" => "If one root of 3x² – 9x + k – 1 = 0 is reciprocal of the other, then k is:", "sol" => "Product = 1. (k-1)/3 = 1 → k-1 = 3 → k = 4."], ["id" => 10, "topic" => "Arithmetic Progression", "q" => "The 21st term of an AP: – 3, 4, ... is:", "sol" => "a = -3, d = 7.
a21 = a + 20d = -3 + 20(7) = 137."], ["id" => 11, "topic" => "Arithmetic Progression", "q" => "The 5th term from the end of an AP: – 11, – 8, – 5, …, 55 is:", "sol" => "l = 55, d = 3.
Term = l - (n-1)d = 55 - (4)(3) = 43."], ["id" => 12, "topic" => "Coordinate Geometry", "q" => "If points A(5, 4) and B(x, 6) are on a circle with centre (3, 4), find x.", "sol" => "AC = BC (radii). AC = 2.
√(x-3)² + (6-4)² = 2 → (x-3)² + 4 = 4 → x = 3."], ["id" => 13, "topic" => "Triangles", "q" => "Perimeters are 25 cm and 15 cm. If first side is 9 cm, find corresponding side.", "sol" => "Ratio: 25/15 = 9/x → 5/3 = 9/x → x = 27/5 = 5.4 cm."], ["id" => 14, "topic" => "Triangles", "q" => "In trapezium ABCD, AB||DC, AO=(2x+1), OC=(5x-7), DO=(7x-5), OB=(7x+1). Find x.", "sol" => "AO/OC = BO/OD.
(2x+1)/(5x-7) = (7x+1)/(7x-5). Solving gives x = 2."], ["id" => 15, "topic" => "Circles", "q" => "Radii of concentric circles are 4 cm and 5 cm. Find length of chord of outer tangent to inner.", "sol" => "Length = 2 * √(5² - 4²) = 2 * √9 = 6 cm."], ["id" => 16, "topic" => "Trigonometry", "q" => "If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ is:", "sol" => "sin θ = 1 - sin² θ = cos² θ.
So, cos² θ + cos⁴ θ = sin θ + sin² θ = 1."], ["id" => 17, "topic" => "Trigonometry", "q" => "If Δ ABC is right-angled at C, find cos (A + B).", "sol" => "C = 90°, so A + B = 90°.
cos 90° = 0."], ["id" => 18, "topic" => "Probability", "q" => "Two dice thrown. Probability that sum is 8:", "sol" => "Possible: (2,6), (3,5), (4,4), (5,3), (6,2). Total = 5. Total cases = 36. P = 5/36."], ["id" => 19, "topic" => "Mensuration", "q" => "Assertion: CSA of cone (r=3.5, l=4) is 44. Reason: CSA = πrl.", "sol" => "CSA = (22/7) * 3.5 * 4 = 44. Both A and R are true and R is correct explanation."], ["id" => 20, "topic" => "Circles", "q" => "Assertion: Center angle 60°, then tangent angle is 60°. Reason: Tangent length < OP.", "sol" => "Assertion is False (Tangent angle = 180 - 60 = 120°). Reason is True."] ]; foreach ($questions as $q) { echo "
Q{$q['id']} {$q['topic']}
{$q['q']}
"; // Add diagrams for specific geometry questions if ($q['id'] == 14) { echo ''; } elseif ($q['id'] == 15) { echo ''; } elseif ($q['id'] == 19) { echo ''; } echo "
Samadhan Step-by-Step:
{$q['sol']}
{$q['sol']}
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