cbse 11th mathematics | Online Objective Test

# Statistics # CBSE 11th Mathematics Prepare / Learn

Q1. If the angle between two lines of regression is

90^{0}

, then it represents

A. None of these

B. no linear correlation

C. perfect negative correlation

D. perfect positive correlation

Answer : Option B
Explaination / Solution:

$[r = \tan (\frac{π}{2} - θ)]$

here $[θ = \frac{π}{2}]$

hence r = 0, therefore there is no linear correlation.

# Straight Lines # CBSE 11th Mathematics Prepare / Learn

Q2. Slope of a line is not defined if the line is

A. parallel to the line x – y

B. parallel to X axis

C. parallel to Y axis

D. parallel to the line x+y

Answer : Option C
Explaination / Solution:

Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

# Mathematical Reasoning # CBSE 11th Mathematics Prepare / Learn

Q3. Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p ∧q is

A. I just sleep throughout the day if and only if I play cricket during the holidays

B. I play cricket during the holidays or I just sleep throughout the day

C. If I play cricket during the holidays , I just sleep throughout the day

D. I play cricket during the holidays and just sleep throughout the day

Answer : Option D
Explaination / Solution:

∧ is replaced by and in verbal form

# Principle of Mathematical Induction # CBSE 11th Mathematics Prepare / Learn

Q4. If P ( n ) = 2+4+6+………………..+2n , n

\in

N , then P ( k ) = k ( k + 1 ) + 2

\Rightarrow

P ( k + 1 ) = ( k + 1 ) ( k +2 ) + 2 for all k

\in

N . So we can conclude that P ( n ) = n ( n + 1 ) +2 for

A. n >1

B. nothing can be said

C. all n ∈ N

D. n > 2

Answer : Option B
Explaination / Solution:

Because the statement is incomplete without the conclusion/ RHS

# Conic Sections # CBSE 11th Mathematics Prepare / Learn

Q5.

The equation $x^{2} + y^{2} = 0$ represents

A. pairs of straight line.

B. an ellipse.

C. a degenerate circle.

D. an equilateral hyperbola.

Answer : Option C
Explaination / Solution:

The above circle can be written as

Here the center is (0,0) and radius is also 0 units.

So it is a degenerate circle as degenerate circle is a circle( a point) where radius is zero units.

# Permutations and Combinations # CBSE 11th Mathematics Prepare / Learn

Q6. Number of ways in which 10 different things can be divided into two groups containing 6 and 4 things respectively is

A. C(10 , 4)

B. P(10,6)

C. P(10,2)

D. P(10,4)

Answer : Option A
Explaination / Solution:

If there are 10 things and we have to make them in to two groups containing 6 things and 4 things respectively , you have to select 6 to form first group , then automatically another group would have formed of 4 remaining things.

Now 6 things can be selected from 10 things in $^{10} C_{6}$ different ways

Also we have $^{10} C_{6} =^{10} C_{4}$ $[∵^{n} C_{r} =^{n} C_{n - r}]$

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q7. There exists a triangle ABC satisfying the conditions

A. b sin A = a, a >> b

B. b sin A << a, a = b, A=π/2

C. bsinAπ/2

D. bsinA=a,A<π/2

Answer : Option D
Explaination / Solution:

$U s i n g s i n e r u l e w e h a v e \frac{a}{s i n A} = \frac{b}{s i n B} = k$

when k=1 we have

$b s i n A = a s i n B w h e n B = \frac{π}{2}, w e g e t b s i n A = a$

But we have in a triangle the sum of the three angles is 180 degrees ,so if B=90 degrees then $A < \frac{π}{2}$

# Introduction to Three Dimensional Geometry # CBSE 11th Mathematics Prepare / Learn

Q8. The direction cosines of any normal to the XY plane are

A. < 1 , 0 , 0 >

B. < 1 , 1 , 0 >

C. < 0 , 1 , 0 >

D. < 0 , 0 , 1 >

Answer : Option D
Explaination / Solution:

Concept used - Parellel lines have same direction cosines

Explanation We know Z axis is perpendicular to XY plane and direction cosines of Z axis are <0,0,1>

and as any normal to XY plane will be parallel to Z axis and parellel lines have same direction cosines so answer is <0,0,1>

# Maths Sets # CBSE 11th Mathematics Prepare / Learn

Q9. If A and B be any two sets , then (A∪BA∪B)′ is equal to

A. A′∪B′

B. A∩B

C. A∪B

D. A′∩B′

Answer : Option D
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q10.

2 \sqrt{- 9} \sqrt{- 16,}

is equals to

A. 48

B. -48

C. -24

D. 24

Answer : Option C
Explaination / Solution:

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