NDA NDA 2 2026 Mathematics Solved PYQ Paper

Solution

Option (a) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

Let the building height be H, tower height be h, and horizontal separation be D. From the angles of depression, tan α = (H - h)/D and tan β = H/D. Therefore D(tan β - tan α) = h. Using tan β - tan α = sin(β - α)/(cos α cos β), we get D = h cos α cos β / sin(β - α). Also H² + D² = D²(tan²β + 1) = D²sec²β. Substitution gives H² + D² = h²cos²α / sin²(β - α).

The simplified result agrees with option (a). Therefore, option (a) is the required answer.

Solution

Option (d) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

The simplified result agrees with option (d). Therefore, option (d) is the required answer.

Solution

Option (c) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

sine rule the sides are proportional to sinA,sinB,sinC, so the ratio of greatest side

The simplified result agrees with option (c). Therefore, option (c) is the required answer.

Solution

Option (a) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

From A : B : C = 1 : 2 : 7 and A + B + C = 180°, we obtain A = 18° and B = 36°. Use sin 18° = (√5 - 1)/4 and cos 36° = (√5 + 1)/4. Hence sin A cos B = [(√5 - 1)(√5 + 1)]/16 = (5 - 1)/16 = 1/4.

The simplified result agrees with option (a). Therefore, option (a) is the required answer.

Solution

Option (b) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

.

The simplified result agrees with option (b). Therefore, option (b) is the required answer.

Solution

Option (a) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

2bc 5

2ac 35 2ab 7

The simplified result agrees with option (a). Therefore, option (a) is the required answer.

Solution

Option (b) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

Let u = (A + B)/2 and v = (A - B)/2. Then A = u + v, tan u = p, and tan v = q. By the tangent addition formula, tan A = tan(u + v) = (tan u + tan v)/(1 - tan u tan v) = (p + q)/(1 - pq).

The simplified result agrees with option (b). Therefore, option (b) is the required answer.

Solution

Option (a) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

Let u = (A + B)/2 and v = (A - B)/2. Then B = u - v, tan u = p, and tan v = q. By the tangent subtraction formula, tan B = tan(u - v) = (tan u - tan v)/(1 + tan u tan v) = (p - q)/(1 + pq).

The simplified result agrees with option (a). Therefore, option (a) is the required answer.

Solution

Option (b) is correct.

Keep the trigonometric identity in exact form and simplify only after substituting the given values.

The simplified result agrees with option (b). Therefore, option (b) is the required answer.

Solution

Option (d) is correct.

Use the given condition directly, simplify systematically, and compare the final result with the options.

gives the value 2.

The simplified result agrees with option (d). Therefore, option (d) is the required answer.