# Mathematics (Test 4)

## Under Graduate Entrance Exams : Iit Jee Ieee Entrance Exam

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Mathematics
| Maths Sets | | Relations and Functions | | Trigonometric Functions | | Principle of Mathematical Induction | | Complex Numbers and Quadratic Equations | | Linear Inequalities | | Permutations and Combinations | | Binomial Theorem | | Sequences and Series | | Straight Lines | | Conic Sections | | Introduction to Three Dimensional Geometry | | Limits and Derivatives | | Mathematical Reasoning | | Statistics | | Probability | | Inverse Trigonometric Functions | | Matrices | | Determinants | | Continuity and Differentiability | | Application of Derivatives | | Integrals | | Application of Integrals | | Differential Equations | | Vector Algebra | | Three Dimensional Geometry | | Linear Programming | | Chapter 1: Sets, Relations and Functions | | Chapter 2: Basic Algebra | | Chapter 3: Trigonometry | | Chapter 4: Combinatorics and Mathematical Induction | | Chapter 5: Binomial Theorem, Sequences And Series | | Chapter 6: Two Dimensional Analytical Geometry | | Chapter 8: Iteration and recursion | | Chapter 7: Matrices and Determinants | | Chapter 8: Vector Algebra I | | Chapter 9: Differential Calculus Limits and Continuity | | Chapter 11: Integral Calculus | | Chapter 12: Introduction to probability theory | | Chapter 1: Applications of Matrices and Determinants | | Chapter 2: Complex Numbers | | Chapter 3: Theory of Equations | | Chapter 4: Inverse Trigonometric Functions | | Chapter 5: Two Dimensional Analytical Geometry II | | Chapter 6: Applications of Vector Algebra | | Chapter 1: Relation and Function | | Chapter 2: Numbers and Sequences | | Chapter 3: Algebra | | Chapter 4: Geometry | | Chapter 5: Coordinate Geometry | | Chapter 6: Trigonometry | | Chapter 7: Mensuration | | Chapter 8: Statistics And Probability |
Q.1
The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is
A. 40000
B. 160900
C. 160000
D. 30000
Explaination / Solution:

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Q.2
If a letter is chosen at random from the English alphabets {a,b,...,z}, then the probability that the letter chosen precedes x
A. 12/13
B. 1/13
C. 23/26
D. 3/26
Explaination / Solution:

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Q.3
A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is
A. 3x cm
B. x cm
C. 4x cm
D. 2x cm
Explaination / Solution:

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Q.4
If sin θ + cos θ = a and sec θ + cosecθ = b , then the value of b(a 2 -1) is equal to
A. 2a
B. 3a
C. 0
D. 2ab
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Q.5
Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is
A. √2 x
B. x / 2√2
C. x / √2
D. 2x
Explaination / Solution:

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Q.6
If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is
A. 8x + 5y = 40
B. 8x − 5y = 40
C. x = 8
D. y = 5
Explaination / Solution:

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Q.7

In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of ΔPQR to the area of ΔPST is

A. 25: 4
B. 25: 7
C. 25: 11
D. 25: 13
Explaination / Solution:

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Q.8

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

A. 6 cm
B. 5 cm
C. 8 cm
D. 4 cm
Explaination / Solution:

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Q.9
The solution of  2x − 12  = 9 is equal to
A. -1
B. 2
C. –1, 2
D. None of these
Explaination / Solution:

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Q.10

Which of the following can be calculated from the given matrices

, (i) A2 (ii) B2 (iii) AB (iv) BA

A. (i) and (ii) only
B. (ii) and (iii) only
C. (ii) and (iv) only
D. all of these