Official Entrance Archive
101 Solved Questions
CCS HAU Mathematics (เคเคฃเคฟเคค) Solved Questions
Explore all verified entrance examination questions in card view. Click "Solve & Solution" on any card to view the complete solution, KaTeX rationale, and interactive answer testing.
4-Yr B.Sc
Q.1
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dict...
4-Yr B.Sc
Q.2
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes remain empt...
4-Yr B.Sc
Q.3
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of arrangements of the letters of the word BANANA in which the two Nโs do not appear adjacently is...
4-Yr B.Sc
Q.4
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Number of divisors of the form 4n+2 (n> 0) of the integer 240 is...
4-Yr B.Sc
Q.5
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
6 men and 4 women are to be seated in a row so that no two women sit together. The number of ways they can be ...
4-Yr B.Sc
Q.6
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the cube roots of unity are 1,ษท, ษท 3, then the roots of the equation (x-1)3 + 8 =0 are...
4-Yr B.Sc
Q.7
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If z 1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg (z1) โ arg (z2) is ...
4-Yr B.Sc
Q.8
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If arg (z) < 0, then arg (-z) โ arg (z) =...
4-Yr B.Sc
Q.9
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If ษท is an imaginary cube root of unity, then (1+ษท-ษท 2)7 equals...
4-Yr B.Sc
Q.10
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only ...
4-Yr B.Sc
Q.11
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Let R = {(3,3) (6,6) (9,9) (12,12), (6,12) (3,9) (3,12), (3,6)}be in a relation on the set A= {3, 6, 9, 12}. T...
4-Yr B.Sc
Q.12
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If a real valued function f (x) satisfies the functional equation f (xโy) = f (x) f (y) โ f (aโx) f (a+y), whe...
4-Yr B.Sc
Q.13
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the graph of the function f (x) is symmetrical about the line x=2, then...
4-Yr B.Sc
Q.14
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The function f : R โ R defined by f (x) = sin x is...
4-Yr B.Sc
Q.15
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The...
4-Yr B.Sc
Q.16
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of a for which the sum of the squares of the roots of the equation x 2 โ (a โ 2) xโ a โ1=0 assume th...
4-Yr B.Sc
Q.17
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the roots of the equation x 2 โ bx + c = 0 be two consecutive integers, then b2 โ 4c equals...
4-Yr B.Sc
Q.18
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If (1-p) is a root of quadratic equation x 2 + px + (1โ p) = 0, then the roots are...
4-Yr B.Sc
Q.19
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of real solutions of the equation x 2 -3|x| + 2 =0 is/are...
4-Yr B.Sc
Q.20
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If x 2 + 2ax + 10 โ 3a > 0 for every real value of x, then...
4-Yr B.Sc
Q.21
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The angle between two diagonals of a cube is...
4-Yr B.Sc
Q.22
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the angle between two vectors โ + โ โ โ โ + โ is ฯ/3, then the value of a is...
4-Yr B.Sc
Q.23
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The scalar โ. โ+ โ ร ( โ + โ+ โ) equals...
4-Yr B.Sc
Q.24
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The points with position vectors 60 ฬ + 3 ฬ, 40 ฬ โ 8 ฬ, ฬ โ 52 ฬ are collinear if...
4-Yr B.Sc
Q.25
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of vectors of unit length perpendicular to vectors โ = (0 1, 1) and โ = (1 1, 0) is...
4-Yr B.Sc
Q.26
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The angle between the lines 2x = 3y = โ z and 6x = โ y = โ 4z is...
4-Yr B.Sc
Q.27
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is...
4-Yr B.Sc
Q.28
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The method of least squares dictates that we choose regression line where the sum of the square of deviations ...
4-Yr B.Sc
Q.29
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the value of any regression coefficient is zero, then two variables are:...
4-Yr B.Sc
Q.30
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
A process by which we estimate the value of dependent variable on the basis of one or more independent variabl...
4-Yr B.Sc
Q.31
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If A = 1 โ1 1 1 , then A3=...
4-Yr B.Sc
Q.32
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of 1 + 1 1 1 1 + 1 1 1 1 + is equal to...
4-Yr B.Sc
Q.33
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If A 2โ A + I = 0, then the inverse of A is...
4-Yr B.Sc
Q.34
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of bijective functions from a set A to itself when A contains 106 elements is...
4-Yr B.Sc
Q.35
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of 11 12 13 12 13 14 13 14 15 is...
4-Yr B.Sc
Q.36
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is...
4-Yr B.Sc
Q.37
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is...
4-Yr B.Sc
Q.38
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the obse...
4-Yr B.Sc
Q.39
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respec...
4-Yr B.Sc
Q.40
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the v...
4-Yr B.Sc
Q.41
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
For a linear programming equations, convex set of equations is included in the region of...
4-Yr B.Sc
Q.42
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Infeasibility means that the number of solutions to the linear programming models that satisfies all constrain...
4-Yr B.Sc
Q.43
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
A constraint that does not affect the feasible region is a...
4-Yr B.Sc
Q.44
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
For linear inequalities, solution set for a group of inequalities is classified as...
4-Yr B.Sc
Q.45
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Which of the following is unary operations?...
4-Yr B.Sc
Q.46
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If * is a binary operation in A then...
4-Yr B.Sc
Q.47
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Which of the following statements is not correct ?...
4-Yr B.Sc
Q.48
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If log (a/b) + log (b/a) = log (a+b), then...
4-Yr B.Sc
Q.49
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of e is...
4-Yr B.Sc
Q.50
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
1+ sin x + sin2x + โฆ. up to โ = 4 +2โ3, 0 < x < ฮ and x โ then x =...
4-Yr B.Sc
Q.51
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it ...
4-Yr B.Sc
Q.52
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
( ) = | | , โฅ 0, ( ) =...
4-Yr B.Sc
Q.53
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The total of number of terms in the expansion of (x + y) 100 + (xโy)100 after simplification is...
4-Yr B.Sc
Q.54
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ log (2, โ) ...
4-Yr B.Sc
Q.55
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ 1 2 โ 5 + 1 5 โ 8+ 1 8 โ 11+ โฆ โฆ ...
4-Yr B.Sc
Q.56
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
lim โ tan( โ 1) โ 1 ...
4-Yr B.Sc
Q.57
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= ( + ) โ ...
4-Yr B.Sc
Q.58
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= ( ) = ...
4-Yr B.Sc
Q.59
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ 1 โ 1 1 + 1 + 2 1 + 2 + 1 + 2 + 3 1 + 2 + 3 + โฆ,...
4-Yr B.Sc
Q.60
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ tan 8 ...
4-Yr B.Sc
Q.61
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ โ + = 0 ...
4-Yr B.Sc
Q.62
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
. = 1 3 , . = 1 4 , ( โช ) = 5 12 , โ ( โ ) =...
4-Yr B.Sc
Q.63
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
( โ 2) + 9 = 4 โ โ ...
4-Yr B.Sc
Q.64
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= 55, โ โ ...
4-Yr B.Sc
Q.65
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ 11 + 1 โ ...
4-Yr B.Sc
Q.66
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
+ ...
4-Yr B.Sc
Q.67
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
...
4-Yr B.Sc
Q.68
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
sec sec + tan ...
4-Yr B.Sc
Q.69
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
( ) + + , โ "(0) =...
4-Yr B.Sc
Q.70
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ โ โ โ 4 + 3 + 3 + 1 = 0 ...
4-Yr B.Sc
Q.71
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ tan โ5 4 ...
4-Yr B.Sc
Q.72
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= , โ = 0 ...
4-Yr B.Sc
Q.73
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= sin(2 ), โ โ ...
4-Yr B.Sc
Q.74
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ 2 1 + 1 โ + 1 โ 1 + ...
4-Yr B.Sc
Q.75
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The equation of the circle which touches the x-axis and whose centre is (1,2), is...
4-Yr B.Sc
Q.76
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ + = ...
4-Yr B.Sc
Q.77
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by, x+ 80t...
4-Yr B.Sc
Q.78
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ โ = 2 โ โ โ ...
4-Yr B.Sc
Q.79
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
( ) = 2 โ , โ < < 3 โ 2 , โค then which of the following is true...
4-Yr B.Sc
Q.80
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
A die is tossed thrice. If getting an even number is considered as success, the variance of the probability di...
4-Yr B.Sc
Q.81
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The coordinates of the foot of the perpendicular drawn from the point (3,4) on the line 2x +y โ 7 = 0 is...
4-Yr B.Sc
Q.82
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The point (5, โ7) lies outside the circle...
4-Yr B.Sc
Q.83
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If tan 15o = 2 โ โ3, then 2 tan 1095o + cot 975o + tan (โ195o) =...
4-Yr B.Sc
Q.84
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The number of circles touching the lines x = 0, y = a and y = b is...
4-Yr B.Sc
Q.85
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The order and degree of the differential equation 1 + = are respectively,...
4-Yr B.Sc
Q.86
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
x 2n โ y2n is divisible by...
4-Yr B.Sc
Q.87
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Mr. X has a 75% chance of attending the annual meet. Miss Y has an 80% chance, if Mr. X also attends. Otherwis...
4-Yr B.Sc
Q.88
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
โ4 โ โ +โ4 โ ...
4-Yr B.Sc
Q.89
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
lim โ โ 1 โ 1...
4-Yr B.Sc
Q.90
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of + + + โฆ โฆ . โ , , โฆ โฆ are the binomial coefficients of order n, is...
4-Yr B.Sc
Q.91
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The value of + 2 . โ 1 + โ 2 , โ denotes the binomial coefficient of order n, is...
4-Yr B.Sc
Q.92
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Which one of the following is possible?...
4-Yr B.Sc
Q.93
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
In the expansion of โ the term independent of x is...
4-Yr B.Sc
Q.94
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
= โฏ , > 0, โ ...
4-Yr B.Sc
Q.95
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
1 + sin 1 + cos ...
4-Yr B.Sc
Q.96
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
The function f (x) = [x], where [x] denotes greatest integer function is continuous at...
4-Yr B.Sc
Q.97
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
If the arithmetic mean of two positive numbers a and b (a>b) is twice their G.M., then a:b is...
4-Yr B.Sc
Q.98
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
lim โ sin / ...
4-Yr B.Sc
Q.99
MCQ
0.5M
Mathematics โข Calculus, Algebra & Geometry (HAU PYQ)
Differential coefficient of โ log ...
4-Yr B.Sc
Q.100
MCQ
0.5M
Mathematics โข Calculus - Integration
What is the value of the definite integral โซ from 0 to ฯ/2 of (sin x) / (sin x + cos x) dx?...
4-Yr B.Sc
Q.101
MCQ
0.5M
Mathematics โข Vectors - Dot & Cross Product
If two non-zero vectors a and b satisfy |a ยท b| = |a ร b|, the angle between vectors a and b is:...