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MATHEMATICS 2025
(Science Pre-Engineering Group)
TIME: 3 Hours (100 Marks)
SECTION 'A' (Multiple Choice Questions)(40)
NOTES: : i) This section consists of 20 part questions and all are to be answered. Each part question carries one mark.
ii) Do not copy the part questions in your answer script. Write only the answer in full against the proper number of the question and its part.
iii) All notations are used in their usual meanings. The use of Scientific Calculator is allowed.
1. Choose the correct answer for each from the given options:
(i) If Z = -3i + 4, then Z̄ =: *3i + 4 ✓ *3i - 4 *-3i + 4 *-3i - 4
(ii) For n is an even integer, then in is equal to: *i *-i *1 or -1 ✓ *i or -1
(iii) The number of non-zero rows in echelon form of a matrix is called: *Order of a matrix *Rank of matrix ✓ *Leading column *Leading row
(iv) The cofactor A22 of
| 1 | 2 | 4 |
| -1 | 2 | 5 |
| 0 | 1 | -1 |
= : *0 *-1 *1 ✓ *2
(v) If O be the origin and OP = 2î + 3ĵ - 4k̂ and OQ = 5î + 4ĵ - 3k̂ then PQ is equal to: *7î + 7ĵ - 7k̂ *-3î + ĵ - k̂ *3î + ĵ + k̂ ✓ *-7î + 7ĵ + 7k̂
(vi) The volume of tetrahedron determined by the vectors ā, b̄ and c̄ is: *[ā, b̄, c̄] *13 [ā, b̄, c̄] *16 [ā, b̄, c̄] ✓ *ā.(b̄ × c̄)
(vii) If an - an-1 = n + 1 and an = 14 then a5 = : *3 *5 ✓ *14 *20
(viii) If an+1 + bn+1an + bn is an A.M between a and b, then n is equal to: *1 ✓ *2 *0 *3
(ix) Σn+110 n0 is: *10 *9 ✓ *1 *8
(x) If n = 0, then (n+1)!n! = : *0 *1 ✓ *n *∞
(xi) The number of ways that a machine of n beads of different colours be made is: *(n + 1)! *n!2 *(n-1)!2 *(n - 1)! ✓
(xii) The number of terms in the expansion of (1 + x)7 is: *7 *8 ✓ *9 *10
(xiii) For |x| < 1 then 1 - x + x2 - x3 + ⋯ is equal to: *(1 + x) *(1 - x)-1 ✓ *(1 + x)-2 *(1 - x)-2
(xiv) Inverse of a function exists if f is: *Injective *Bijective ✓ *Surjective *Inverse
(xv) Domain of the function f(x) = x2x2 - 4 is the set of all real numbers except: *4 *3 *2 *±2 ✓
(xvi) sin θ2 is equal to: * ± √1 + sin θ2 * ± √1 - cos θ2 ✓ * ± √1 + cos θ2 * ± √1 - sin θ2
(xvii) Hero's formula is: * Δ = s(s - a)(s - b)(s - c) * Δ = √(s - a)(s - b)(s - c) * Δ = √[s(s - a)(s - b)(s - c)] ✓ * Δ = a + b + c2
(xviii) A circle which touches one side of the triangle externally and two extended sides internally is called: *circum-circle *in-circle *tri-circle *escribed-circle ✓
(xix) The graph of linear function is: *straight line ✓ *circle *parabola *triangle
(xx) cos (sin-1 12) = : *2√3 *2√3 *√32 ✓ *12√3
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