Mathematics Test

Result

Mathematics Test - 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
3 / -1

The number of surjections from A = {1,2, ...n), n > 2 onto B = (a,b) is

A
ⁿP₂

B
2ⁿ- 2

C
2ⁿ + 1

D
None of these

Solution

Solution
Question 2
3 / -1

The number of bijective functions from set A to itself when A contains 106 elements is

A
106

B
106)²

C
106!

D
2¹⁰⁶

Solution

Solution

Total number of bijection from set of n elements to itself = n!
Question 3
3 / -1

A
Straight line

B
A circle

C
An ellipise

D
A hyperbola

Solution

Solution
Question 4
3 / -1

If a₁ a₂, a₃ are in G.P. with common ratio r, then value of a₃ > 4a₂ - 3a₁holds if

A
1 < r < 3

B
-3 < r < -1

C
r > 3 or r < 1

D
none

Solution

Solution

Let a = br and c = ar²

∴ 4b = a + 3c

⇒ 4ar = a + 3ar²

⇒ (3r —1) (r— 1) = 0

∴ r = 1/3
Question 5
3 / -1

If a∈ z, ( x - a ) (x - 10) + 1 = 0 has integral roots, then values of a are

A
10, 8

B
12,10

C
12,8

D
none

Solution

Solution

(x - a) (x - 10) + 1 = 0

∴ (x - a) (x - 10) = -1

∴ x - a = 1

and x - 1 0 = - 1 ,

or x - a = 1 and x - 10 = 1

∴ a = 8 ora = 12
Question 6
3 / -1

The value of a for which (1 - 2a) x² - 6ax - 1 = 0 and ax² -x + 1 = 0 have atleast one root, in common are

A

B

C

D

Solution

Solution
Question 7
3 / -1

The number of ways in which one or more balls can be selected out of 10 white, 9 green and 7 blues balls, is

A
892

B
881

C
891

D
879

Solution

Solution

Number of ways = (10 + 1) (9 + 1) (7 + 1) -1
= 879
Question 8
3 / -1

If sum of coefficient of (a + b)ⁿ is 4096, then greatest coefficient is

A
924

B
792

C
1594

D
None of these

Solution

Solution

Sum of coefficient = (a + b)ⁿ = (2)ⁿ

= 4096 = 2¹²

n = 12
Question 9
3 / -1

If A is singular, then A adj A is matrix

A
Identify

B
Null

C
Scalar

D
None of these

Solution

Solution

A(adj A) = IAII_n

Since, A is triangular, therefore IAI = 0

∴ A (adj) A is null.
Question 10
3 / -1

A
1

B
-1

C
2

D
-2

Solution

Solution

Degree of the determinant is

n + (n + 2) + (n + 3) = 3n + 5

and on R .H.S., degree = 2

3n + 5 = 2

⇒ n = -1