Mathematics Test 111

Result

Mathematics Test 111

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D

Solution
Question 2
4 / -1

Given ƒ (g(x)) = 1 + x – 2x² + 5x³ and ƒ (x) = 1 + 3x ∀ x ∈ R, then the value of 3g(1) is equal to

A
5

B
6

C
4

D
8

Solution
Question 3
4 / -1

The number of points where f(x) is continuous is-

A
1

B
2

C
3

D
4

Solution

f(x) is continuous when x³ + 3x = 3x² + 1

⇒ x = 1

Hence (A)
Question 4
4 / -1

(Where sgn(x) represents signum function)

A
π

B
2π

C
3π

D
0

Solution
Question 5
4 / -1

By using all the letters of the word 'AAIPEEAL' words are formed. If N denotes the number of such words in which no 'E' comes before 'A' and do not contain the word 'IPL' , then N/55 is

A
5

B
6

C
4

D
8

Solution

AAAEE, IPL

ways = total – IPL together

N = (⁸C₅.1)3! – (⁶C₁.1)

N = 330
Question 6
4 / -1

g(x) = x² + 1 ∀ x ∈ R

Range of ƒ(g(x)) is -

A
[0,6]

B
[1,6]

C
(0,6]

D
(1,6]

Solution
Question 7
4 / -1

If 60 is expressed as sum of two numbers such that the product of one number and square of other number is maximum, then what will be the ratio of smaller to larger number ?

A
2 : 3

B
1 : 3

C
2 : 5

D
1 : 2

Solution

Let 60 be divided in two parts x and 60 - x

such that f(x) = (60 - x) x² is maximum

f(x) = 60x² - x³

for maximum value of f(x)

f'(x) = 0 and f " (x) < 0

120 x - 3x² = 0

x = 0 or x = 40 f" (40) < 0

⇒ f(x) is maximum when x = 40

x = 40, 60 - x = 20

Required ratio 60-x / x = 20/40 = 1:2
Question 8
4 / -1

Direction ratios of normal to the plane through the line x + y + z + 3 = 0 = 3x + y – z and parallel to the line x-2 / 1 = y+3 / 2 = z-5 / 3 will be :

A
4 : 1 : –2

B
4 : 1 : 2

C
4 : –1 : 2

D
–4 : 1 : 2

Solution

Any plane through the line x + y + z + 3 = 0

3x + y - z will be

3x + y - z + λ (x + y + z + 3) = 0

(3 + λ) x + (1 + λ) y + (λ – 1) z + 3λ = 0 .....(1)

this plane is parallel to the line

8x + 2y - 4z – 1 = 0

Direction ratios of normal to this plane

8 : 2 : -4 = 4 : 1 : -2
Question 9
4 / -1

Which of the following statement is logically equivalent to the statement "If India wins the toss, then Rohit will make century"

A
If Rohit make century, then India wins toss.

B
If India does not win toss, then Rohit will not make century.

C
If Rohit does not make century, then India will not win the toss.

D
India win the toss and Rohit will not make century.

Solution

p = India wins the toss

q = Rohit will make century

Given statement is p → q

and it is logically equivalent o

~q →~p (contrapositive)

=> correct ans is

If rohit does not make century, then India will not win.
Question 10
4 / -1

General solution of differential equation

(where c is an arbitrary constant)

A
y = ƒ(x) + ce^–x

B
y = –ƒ(x) + ce^xƒ(x)

C
y = –ƒ(x) + ce^x

D
y = ƒ(x) + e^x + c

Solution