# Mathematics (Test 5)

## 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
Variance of first 20 natural numbers is
A. 32.25
B. 44.25
C. 33.25
D. 30
Explaination / Solution:

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Q.2
A purse contains 10 notes of ₹2000, 15 notes of ₹500, and 25 notes of ₹200. One note is drawn at random. What is the probability that the note is either a ₹500 note or ₹200 note?
A. 1/5
B. 3/10
C. 2/3
D. 4/5
Explaination / Solution:

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Q.3
A frustum of a right circular cone is of height 16cm with radii of its ends as 8cm and 20cm. Then, the volume of the frustum is
A. 3328π cm3
B. 3228π cm3
C. 3240π cm3
D. 3340π cm3
Explaination / Solution:

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Q.4
If 5x = sec θ and 5/x = tan θ, then x2 – (1/ x2) is equal to
A. 25
B. 1/25
C. 5
D. 1
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Q.5
The angle of elevation of a cloud from a point h metres above a lake is β. The angle of depression of its reflection in the lake is 45° . The height of location of the cloud from the lake is
A.
B.
C. h tan(45° − β)
D. none of these
Explaination / Solution:

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Q.6
The equation of a line passing through the origin and perpendicular to the line 7x − 3y + 4 = 0 is
A. 7x − 3y + 4 = 0
B. 3x − 7y + 4 = 0
C. 3x + 7y = 0
D. 7x − 3y = 0
Explaination / Solution:

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Q.7
The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is
A. 6(2/3) cm
B. 10√6 /3 cm
C. 66(2/3) cm
D. 15 cm
Explaination / Solution:

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Q.8
In figure if PR is tangent to the circle at P and O is the centre of the circle, then POQ is

A. 120°
B. 100°
C. 110°
D. 90°
Explaination / Solution:

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Q.9
The values of a and b if 4x 4 − 24x 3 + 76x 2 + ax +b is a perfect square are
A. 100,120
B. 10,12
C. -120 ,100
D. 12,10
Explaination / Solution:

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Q.10
If . Which of the following statements are correct?

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