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Question 1041
StructuredStandard6 marks
CBSE Class 11 Physics · Laws of Motion · Newton's laws and free-body diagrams

Explain four observations using Newton's laws:

(a)
a horse-cart cannot accelerate in empty space
(b)
riders lurch forward when a bus stops
(c)
pulling a mower is easier than pushing
(d)
a fielder draws the hands backward while catching.
Question 1042
StructuredStandard5 marks
CBSE Class 11 Mathematics · Probability · Probability of events

If P(E′∪F′)=0.25, decide whether E and F are mutually exclusive.

Question 1043
StructuredStandard5 marks
CBSE Class 11 Mathematics · Statistics · Grouped data

Eight observations have mean 9 and variance 9.25. Six are 6,7,10,12,12,13. Find the remaining two.

Question 1044
StructuredStandard5 marks
CBSE Class 11 Mathematics · Limits and Derivatives · Algebraic limits

For f(x)=2x+3 when x≤0 and f(x)=3(x+1) when x>0, find the limits at x=0 and x=1.

Question 1045
StructuredStandard5 marks
CBSE Class 11 Mathematics · Conic Sections · Parabolas

Find the parabola with focus (0,−3) and directrix y=3.

Question 1046
StructuredStandard5 marks
CBSE Class 11 Mathematics · Straight Lines · Forms of a straight line

A line through (2,2) has axis intercepts whose sum is 9. Find every possible equation.

Question 1047
StructuredStandard5 marks
CBSE Class 11 Mathematics · Sequences and Series · Geometric progressions

Find the sum through n terms of 1, −a, a², −a³, …, where a≠−1.

Question 1048
StructuredStandard4 marks
CBSE Class 11 Mathematics · Permutations and Combinations · Combinations

Given {n\choose8}={n\choose2}, determine {n\choose2}.

Question 1049
StructuredStandard4 marks
CBSE Class 11 Mathematics · Complex Numbers and Quadratic Equations · Conjugate and modulus

Calculate the modulus of (1+i)/(1−i)−(1−i)/(1+i).

Question 1050
StructuredStandard4 marks
CBSE Class 11 Mathematics · Trigonometric Functions · Trigonometric functions

Complete every requested part of exercise 3.2, question 16: tan 2x = 2 if 2 x ≠ n π + , where n is an integer 1 – tan x 2 We know that tan x + tan y tan (x + y) = 1 – tan x tan y 2 tan x Replacing y by x , we get tan 2 x = 1− tan 2 x