CBSE 11TH MATHEMATICS - Online Test

Answer : Option D
Explaination / Solution:

Answer : Option D
Explaination / Solution:

if byx>1, then 0<bxy<1,

Answer : Option C
Explaination / Solution:

Expanding the given equation

px+2qx+py-3qy = p-q

px+py+2qx-3qy = p-q

p(x+y) -q(-2x+3y) = p-q

Equating the coeffiecients of like terms

x+y=1 and -2x+3y=1

On solving both the equations we get,

x = 2/5 and y = 3/5

Hence the line passes through the fixed point (2/5.3/5)

Answer : Option A
Explaination / Solution:

Equations of the lines are

x≥0, y≥0, then x+y=1

x≤0, y≤0, then x+y=-1

x≥0, y≤0, then x-y = 2

x≤0 , y≥0, then x-y=-2

Clearly these lines form a square, whose coordinates are (1,1),(1,-1),(-1,-1),(-1,1)

Hence its area is 4 x [1/2]1 x 1= 2 sq units

Answer : Option C
Explaination / Solution:

it is a statement which is F.Hence it is a proposition.Other options are open sentences which are not propositions

Answer : Option B
Explaination / Solution:

y=4at

Squaring both sides,we get

y2=16a2t2

Putting the value of at2 i.e. at2=y216a in  x = at2 we get,

16ax=y2

or y2=4(4a)x

which is nothing but equation of parabola.

Answer : Option B
Explaination / Solution:

If n = 1 we get 7. n = 2 we get 63 which is divisible by 7........

Answer : Option B
Explaination / Solution:
No Explaination.

Answer : Option C
Explaination / Solution:

first degree equation in x, y, z can be written in the form Ax+By+Cz+d=0 Which represent a plane Where A,B and C are the direction ratios of normal to the plane

Answer : Option D
Explaination / Solution:

First we will find the number of four digit numbers that can be formed using the digits 0,1,2,3,4,5,6,7,8,9  with repetition .

The first place can be filled by any of the 9 digits other than 0, and the second, third and the fourth places each  can be filled by any of the ten digits

Hence the total number of ways of forming a four digit number = 9×10×10×10=9000

Now we will find the number of four digit numbers in which nall the digits are distinct 

The first place can be filled by any of the 9 digits other than 0, and the second, can be filled by any of the remaining 9 digits since repetition is not possible

Similarly  third and the fourth places each  can be filled by 8 and 7 digits respectively

Hence the total number of ways of forming a four digit number  with distinct digits b= 9×9×8×7=4536

The total number of numbers from 1000 to 9999 (both inclusive) that do not have 4 different digits=9000−4536=4464