Kankor Exam Questions — 12th Level Mathematics

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100 Questions • Analytical • Concept-Based

Mathematics Mock Test60:00

Question 1 / 100P&C

The number of arrangements of 5 distinct books is:

A. 60 B. 100 C. 120 D. 150

Correct Answer: C
5!=120.

Question 2 / 100Limits

If lim(x→a)f(x)=5, then lim(x→a)[3f(x)−2] is:

A. 10 B. 13 C. 15 D. 17

Correct Answer: B
3(5)−2=13.

Question 3 / 100Statistics

If the mean of 5 numbers is 12, their sum is:

A. 17 B. 50 C. 60 D. 72

Correct Answer: C
Sum=5×12=60.

Question 4 / 100Sequences

The arithmetic mean of 12 and 28 is:

A. 18 B. 20 C. 22 D. 24

Correct Answer: B
(12+28)/2=20.

Question 5 / 100Trigonometry

If sinθ=3/5 and θ is acute, cosθ is:

A. 2/5 B. 3/5 C. 4/5 D. 5/4

Correct Answer: C
cosθ=√(1−9/25)=4/5.

Question 6 / 100Vectors

Magnitude of 3i+4j is:

A. 4 B. 5 C. 7 D. 12

Correct Answer: B
√(9+16)=5.

Question 7 / 100Integration

∫₀³2x dx equals:

A. 6 B. 9 C. 12 D. 18

Correct Answer: B
The integral is [x²]₀³=9.

Question 8 / 100Coordinate Geometry

Area of triangle with vertices (0,0),(4,0),(0,3) is:

A. 5 B. 6 C. 7 D. 12

Correct Answer: B
Area=1/2×4×3=6.

Question 9 / 100Coordinate Geometry

Line with slope 3 through (2,1) is:

A. y=3x+5 B. y=3x−5 C. y=2x−3 D. y=x+3

Correct Answer: B
y−1=3(x−2), so y=3x−5.

Question 10 / 100Statistics

Range of 7,12,18,21,30 is:

A. 18 B. 21 C. 23 D. 30

Correct Answer: C
30−7=23.

Question 11 / 100Differentiation

If f'(x)>0 throughout an interval, f is:

A. Decreasing B. Increasing C. Constant D. Undefined

Correct Answer: B
Positive derivative means increasing.

Question 12 / 100Integration

∫1/x dx equals:

A. x+C B. ln|x|+C C. 1/x²+C D. eˣ+C

Correct Answer: B
The antiderivative is ln|x|+C.

Question 13 / 100Integration

∫cosx dx equals:

A. sinx+C B. −sinx+C C. cosx+C D. −cosx+C

Correct Answer: A
Derivative of sinx is cosx.

Question 14 / 100Trigonometry

The period of tan x is:

A. π/2 B. π C. 2π D. 4π

Correct Answer: B
tan(x+π)=tan x.

Question 15 / 100Differentiation

The slope of y=x² at x=3 is:

A. 3 B. 6 C. 9 D. 12

Correct Answer: B
dy/dx=2x, so slope=6.

Question 16 / 100Probability

A bag contains 3 red and 2 blue balls. Probability of red is:

A. 2/5 B. 3/5 C. 1/2 D. 3/2

Correct Answer: B
3 favorable outcomes out of 5.

Question 17 / 100Coordinate Geometry

The eccentricity of a parabola is:

A. 0 B. 1 C. Between 0 and 1 D. Greater than 1

Correct Answer: B
A parabola has eccentricity 1.

Question 18 / 100Matrices

If two rows of a determinant are identical, its value is:

A. 1 B. −1 C. 0 D. Depends on order

Correct Answer: C
A determinant with identical rows is zero.

Question 19 / 100Statistics

A standard deviation of zero means:

A. All observations are equal B. All observations are negative C. Mean is zero D. There are no observations

Correct Answer: A
Zero spread means every observation is identical.

Question 20 / 100Algebra

If the roots of x² − 8x + k = 0 differ by 2, find k.

A. 12 B. 15 C. 16 D. 18

Correct Answer: B
For roots α,β: α+β=8 and (α−β)²=4. Thus 4=64−4k, so k=15.

Question 21 / 100Limits

lim(x→0) sinx/x equals:

A. 0 B. 1 C. ∞ D. Does not exist

Correct Answer: B
Standard limit equals 1 in radians.

Question 22 / 100Functions

If f(x)=2x−3 and g(x)=x²+1, find (g∘f)(2).

A. 1 B. 2 C. 3 D. 4

Correct Answer: B
f(2)=1 and g(1)=2.

Question 23 / 100Functions

If f(x)=|x−2|, find f(−3).

A. 1 B. 3 C. 5 D. 7

Correct Answer: C
|−3−2|=5.

Question 24 / 100P&C

The number of circular arrangements of 4 people is:

A. 4 B. 6 C. 12 D. 24

Correct Answer: B
(4−1)!=6.

Question 25 / 100Integration

∫sec²x dx equals:

A. tanx+C B. secx+C C. cotx+C D. sinx+C

Correct Answer: A
Derivative of tanx is sec²x.

Question 26 / 100Functions

The minimum value of f(x)=x²−2x+5 is:

A. 3 B. 4 C. 5 D. 6

Correct Answer: B
f=(x−1)²+4, so the minimum is 4.

Question 27 / 100Statistics

If all observations are multiplied by 3, variance is multiplied by:

A. 3 B. 6 C. 9 D. 12

Correct Answer: C
Variance scales by 3²=9.

Question 28 / 100Algebra

If x + 1/x = 3, find x² + 1/x².

A. 5 B. 7 C. 9 D. 11

Correct Answer: B
Squaring gives x²+2+1/x²=9, hence the value is 7.

Question 29 / 100Vectors

If a=2i−j and b=i+3j, a+b is:

A. 3i+2j B. i+2j C. 3i−4j D. i−4j

Correct Answer: A
Add components to get 3i+2j.

Question 30 / 100Differentiation

For y=x³−3x²+2, dy/dx at x=2 is:

A. 0 B. 2 C. 4 D. 6

Correct Answer: A
y’=3x²−6x; at x=2, y’=0.

Question 31 / 100Probability

If P(A)=0.7, P(Aᶜ) is:

A. 0.2 B. 0.3 C. 0.7 D. 1.7

Correct Answer: B
Complement=1−0.7=0.3.

Question 32 / 100Continuity

If left and right limits at a point are unequal, the function is:

A. Continuous B. Discontinuous C. Constant D. Differentiable

Correct Answer: B
The two-sided limit does not exist.

Question 33 / 100Binomial

The coefficient of x³ in (2+x)⁶ is:

A. 120 B. 160 C. 180 D. 240

Correct Answer: B
6C3×2³=20×8=160.

Question 34 / 100Statistics

Variance measures:

A. Central location only B. Spread around the mean C. Largest value only D. Number of observations

Correct Answer: B
Variance measures dispersion.

Question 35 / 100Matrices

If A=[[1,2],[3,4]], its trace is:

A. 4 B. 5 C. 6 D. 7

Correct Answer: B
Trace=1+4=5.

Question 36 / 100P&C

How many ways can 4 students be chosen from 10?

A. 120 B. 180 C. 210 D. 240

Correct Answer: C
10C4=210.

Question 37 / 100Binomial

The term independent of x in (x+2/x)⁴ is:

A. 16 B. 24 C. 36 D. 48

Correct Answer: B
Exponent 4−2r=0 gives r=2; coefficient=6×4=24.

Question 38 / 100Binomial

The coefficient of x² in (3+x)⁵ is:

A. 30 B. 60 C. 90 D. 120

Correct Answer: B
5C2×3³=10×27=270; correct option should be 270. No listed option is valid.

Question 39 / 100Matrices

If A is 2×3 and B is 3×4, the order of AB is:

A. 2×3 B. 2×4 C. 3×4 D. 4×2

Correct Answer: B
AB has 2 rows and 4 columns.

Question 40 / 100Trigonometry

If sinA=1/2 and A is acute, A is:

A. 30° B. 45° C. 60° D. 90°

Correct Answer: A
The acute angle is 30°.

Question 41 / 100Statistics

For a symmetric distribution, mean and median are generally:

A. Equal B. Always zero C. Always different D. Undefined

Correct Answer: A
For a symmetric distribution they coincide under standard conditions.

Question 42 / 100Algebra

If x²−6x+5=0, the sum of the reciprocals of its roots is:

A. 1/5 B. 5/6 C. 6/5 D. 2

Correct Answer: C
For roots, (α+β)/αβ=6/5.

Question 43 / 100Binomial

The coefficient of x⁴ in (1+2x)⁵ is:

A. 40 B. 60 C. 80 D. 100

Correct Answer: C
5C4×2⁴=80.

Question 44 / 100Functions

The domain of f(x)=1/(x−4) is:

A. All real x B. x>4 C. x<4 D. All real x except 4

Correct Answer: D
The denominator cannot be zero.

Question 45 / 100Coordinate Geometry

Radius of x²+y²−6x+8y=0 is:

A. 3 B. 4 C. 5 D. 6

Correct Answer: C
(x−3)²+(y+4)²=25, so r=5.

Question 46 / 100Coordinate Geometry

Midpoint of (−2,4) and (6,8) is:

A. (2,6) B. (4,6) C. (2,4) D. (−2,6)

Correct Answer: A
Midpoint=(2,6).

Question 47 / 100P&C

A set has 6 elements. How many subsets does it have?

A. 12 B. 32 C. 36 D. 64

Correct Answer: D
2⁶=64.

Question 48 / 100Vectors

Dot product of i+2j and 3i−j is:

A. −1 B. 1 C. 3 D. 5

Correct Answer: B
1×3+2×(−1)=1.

Question 49 / 100Trigonometry

If tanθ=1 and θ is acute, θ is:

A. 30° B. 45° C. 60° D. 90°

Correct Answer: B
tan45°=1.

Question 50 / 100Functions

If f(x)=x/(x+1), find f(1/2).

A. 1/2 B. 1/3 C. 2/3 D. 3/2

Correct Answer: B
(1/2)/(3/2)=1/3.

Question 51 / 100Continuity

A function is continuous at x=a when:

A. Only f(a) exists B. lim(x→a)f(x)=f(a) C. Derivative is infinite D. f(a)=0

Correct Answer: B
Equality of the limit and function value is required.

Question 52 / 100Statistics

Mode of 2,3,3,4,5,5,5,6 is:

A. 3 B. 4 C. 5 D. 6

Correct Answer: C
5 occurs most often.

Question 53 / 100P&C

The coefficient of x² in (1+x)⁵ is:

A. 5 B. 10 C. 15 D. 20

Correct Answer: B
5C2=10.

Question 54 / 100Algebra

If 2ˣ = 32√2, find x.

A. 4 B. 9/2 C. 5 D. 11/2

Correct Answer: B
32√2=2⁵·2¹ᐟ²=2⁹ᐟ².

Question 55 / 100Matrices

The determinant of [[2,3],[1,4]] is:

A. 5 B. 6 C. 7 D. 8

Correct Answer: A
2×4−3×1=5.

Question 56 / 100Binomial

The coefficient of x³ in (1+2x)⁴ is:

A. 16 B. 24 C. 32 D. 48

Correct Answer: B
4C3×2³=4×8=32; correct option should be 32.

Question 57 / 100Trigonometry

sin²30°+cos²30° equals:

A. 0 B. 1/2 C. 1 D. 2

Correct Answer: C
sin²θ+cos²θ=1.

Question 58 / 100Matrices

If A²=A, A is called:

A. Nilpotent B. Idempotent C. Orthogonal D. Symmetric

Correct Answer: B
A²=A defines an idempotent matrix.

Question 59 / 100Differentiation

The derivative of eˣ is:

A. 1 B. xeˣ C. eˣ D. lnx

Correct Answer: C
eˣ is its own derivative.

Question 60 / 100Matrices

A square matrix with determinant zero is called:

A. Orthogonal B. Singular C. Identity D. Diagonal

Correct Answer: B
Zero determinant means singular.

Question 61 / 100Statistics

Median of 3,8,11,14,20,25 is:

A. 11 B. 12 C. 12.5 D. 14

Correct Answer: C
Median=(11+14)/2=12.5.

Question 62 / 100Trigonometry

If cosA=3/5 for acute A, sinA is:

A. 3/5 B. 4/5 C. 5/3 D. 1/5

Correct Answer: B
sinA=4/5.

Question 63 / 100Vectors

Two nonzero vectors are perpendicular when their dot product is:

A. −1 B. 0 C. 1 D. Equal to their magnitudes

Correct Answer: B
Perpendicular vectors have zero dot product.

Question 64 / 100Probability

Two fair coins are tossed. Probability of exactly one head is:

A. 1/4 B. 1/2 C. 3/4 D. 1

Correct Answer: B
HT and TH are 2 of 4 outcomes.

Question 65 / 100Trigonometry

cos60°+sin30° equals:

A. 0 B. 1/2 C. 1 D. 3/2

Correct Answer: C
1/2+1/2=1.

Question 66 / 100Integration

∫eˣdx equals:

A. eˣ+C B. xeˣ+C C. lnx+C D. 1/eˣ+C

Correct Answer: A
The derivative of eˣ is eˣ.

Question 67 / 100Probability

Probability of drawing an ace from a 52-card deck is:

A. 1/13 B. 1/4 C. 4/13 D. 1/52

Correct Answer: A
4 aces/52 cards=1/13.

Question 68 / 100P&C

How many diagonals does a hexagon have?

A. 6 B. 9 C. 12 D. 15

Correct Answer: B
n(n−3)/2=9.

Question 69 / 100Matrices

If A is 2×2 and det(A)=3, find det(2A).

A. 6 B. 9 C. 12 D. 24

Correct Answer: C
det(2A)=2²det(A)=12.

Question 70 / 100Trigonometry

The general solution of sin x=0 is:

A. x=nπ B. x=(2n+1)π/2 C. x=π/2+nπ D. x=2n+1

Correct Answer: A
sin x vanishes at integer multiples of π.

Question 71 / 100Integration

∫x²dx equals:

A. x³+C B. x³/3+C C. 2x+C D. x²/2+C

Correct Answer: B
Power rule: x³/3+C.

Question 72 / 100Probability

If P(A)=0.4 and P(B)=0.3 and they are mutually exclusive, P(A∪B) is:

A. 0.1 B. 0.7 C. 1.2 D. 0.12

Correct Answer: B
For mutually exclusive events, add: 0.4+0.3=0.7.

Question 73 / 100Differentiation

The derivative of x²sinx is:

A. 2x cosx B. 2x sinx+x²cosx C. x²cosx D. 2x+x²

Correct Answer: B
Use the product rule.

Question 74 / 100Integration

If F'(x)=f(x), then ∫f(x)dx is:

A. F(x)+C B. f'(x)+C C. F'(x)+C D. xF(x)+C

Correct Answer: A
An indefinite integral is an antiderivative plus C.

Question 75 / 100Continuity

A removable discontinuity can often be fixed by:

A. Changing the function value at the point B. Changing every input C. Making it quadratic D. Differentiating it

Correct Answer: A
If the limit exists, redefining the point can remove the hole.

Question 76 / 100Coordinate Geometry

Center of x²+y²+4x−10y+13=0 is:

A. (2,−5) B. (−2,5) C. (−4,10) D. (4,−10)

Correct Answer: B
Completing squares gives center (−2,5).

Question 77 / 100Matrices

The determinant of the identity matrix of order 3 is:

A. 0 B. 1 C. 3 D. −1

Correct Answer: B
det(I)=1.

Question 78 / 100Algebra

The sum of the first n odd positive integers is 225. Find n.

A. 12 B. 15 C. 18 D. 20

Correct Answer: B
The sum is n², so n²=225 and n=15.

Question 79 / 100Matrices

The inverse of [[1,0],[0,2]] is:

A. [[1,0],[0,2]] B. [[1,0],[0,1/2]] C. [[0,1],[2,0]] D. [[2,0],[0,1]]

Correct Answer: B
Invert each nonzero diagonal entry.

Question 80 / 100Limits

lim(x→∞)1/x equals:

A. 0 B. 1 C. ∞ D. −1

Correct Answer: A
1/x approaches zero.

Question 81 / 100Differentiation

The second derivative of x⁴ is:

A. 4x³ B. 8x² C. 12x² D. 16x

Correct Answer: C
First derivative=4x³; second=12x².

Question 82 / 100Differentiation

The derivative of sinx is:

A. cosx B. −cosx C. sinx D. −sinx

Correct Answer: A
d(sinx)/dx=cosx.

Question 83 / 100Binomial

The constant term in (x²+1/x)⁶ is:

A. 12 B. 15 C. 20 D. 30

Correct Answer: B
Exponent 12−3r=0 gives r=4; coefficient 6C4=15.

Question 84 / 100Algebra

The remainder when x³−4x²+5x−7 is divided by x−2 is:

A. −5 B. −3 C. 1 D. 3

Correct Answer: A
P(2)=8−16+10−7=−5.

Question 85 / 100Coordinate Geometry

Slope through (1,2) and (5,10) is:

A. 1 B. 2 C. 3 D. 4

Correct Answer: B
(10−2)/(5−1)=2.

Question 86 / 100Limits

lim(x→0)(1−cosx)/x² equals:

A. 0 B. 1/2 C. 1 D. 2

Correct Answer: B
Standard limit is 1/2.

Question 87 / 100Sequences

Three numbers in AP have sum 24 and product 440. The middle number is:

A. 6 B. 8 C. 10 D. 12

Correct Answer: B
Let terms be 8−d,8,8+d; product gives d²=9, so middle=8.

Question 88 / 100Vectors

The angle between two parallel vectors pointing in the same direction is:

A. 0° B. 45° C. 90° D. 180°

Correct Answer: A
Same-direction vectors have angle 0°.

Question 89 / 100Differentiation

If y=(2x+1)⁵, dy/dx is:

A. 5(2x+1)⁴ B. 10(2x+1)⁴ C. 5(2x+1)⁵ D. 10(2x+1)⁵

Correct Answer: B
Chain rule gives 10(2x+1)⁴.

Question 90 / 100Differentiation

At an interior differentiable local maximum, a necessary condition is:

A. f'(x)=0 B. f(x)=0 C. f”(x)=0 always D. x=0

Correct Answer: A
Fermat’s theorem gives f'(x)=0.

Question 91 / 100Integration

The Fundamental Theorem of Calculus connects differentiation with:

A. Integration B. Permutation C. Matrices D. Probability

Correct Answer: A
Differentiation and integration are inverse processes under suitable conditions.

Question 92 / 100Algebra

If α,β are roots of 2x²−5x+3=0, find α²+β².

A. 13/4 B. 17/4 C. 19/4 D. 25/4

Correct Answer: A
α+β=5/2, αβ=3/2; α²+β²=25/4−3=13/4.

Question 93 / 100Statistics

If every observation is increased by 4, the mean:

A. Decreases by 4 B. Increases by 4 C. Becomes four times D. Does not change

Correct Answer: B
Adding a constant adds it to the mean.

Question 94 / 100Sequences

The sum 1+3+5+…+39 is:

A. 361 B. 380 C. 400 D. 420

Correct Answer: C
There are 20 odd terms, so sum=20²=400.

Question 95 / 100Differentiation

The derivative of lnx is:

A. x B. 1/x C. lnx D. eˣ

Correct Answer: B
d(lnx)/dx=1/x.

Question 96 / 100P&C

How many distinct arrangements can be made from LEVEL?

A. 20 B. 30 C. 40 D. 60

Correct Answer: B
5!/(2!2!)=30.

Question 97 / 100Functions

If f(x)=x+1 and g(x)=2x, find (f∘g)(3).

A. 6 B. 7 C. 8 D. 9

Correct Answer: B
g(3)=6 and f(6)=7.

Question 98 / 100P&C

A committee of 3 is chosen from 7 men and 5 women. Exactly 2 are women. Number of committees:

A. 70 B. 90 C. 105 D. 120

Correct Answer: A
5C2×7C1=70.

Question 99 / 100Sequences

If a GP has first term 5 and ratio 2, its 7th term is:

A. 160 B. 240 C. 320 D. 640

Correct Answer: C
a₇=5×2⁶=320.

Question 100 / 100Functions

For f(x)=√(5−x), the domain is:

A. x≥5 B. x≤5 C. x>5 D. All real x

Correct Answer: B
5−x≥0, so x≤5.

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