Mathematics Test 160

Result

Mathematics Test 160

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Question 1
4 / -1

Two tangents on a parabola are x – y = 0 and x + y = 0. If (2, 3) is focus of the parabola then the equation of tangent at vertex is

A
4x – 6y + 5 = 0

B
4x – 6y + 3 = 0

C
4x – 6y + 1 = 0

D

Solution

Equation of AS :

(y – 3) = –1(x – 2)

y – 3 = –x + 2

x + y = 5

For point 'A' solve

x + y = 5

y = x

2x = 5
Question 2
4 / -1

If (6, 13) and (25, 8) are the foci of a hyperbola passing through the point (1, 1) then the eccentricity of the hyperbola is

A

B

C

D

Solution
Question 3
4 / -1

The number of points of non-differentiability of function f(x) = max {sgnx, 2^–x, x²},

A
4

B
3

C
2

D
1

Solution

From graph clearly '4' points of non-differentiability.
Question 4
4 / -1

If f is a differentiable function satisfying then the value of f(7776), is

A
3

B
4

C
5

D
6

Solution
Question 5
4 / -1

denotes scalar triple product) is

A
2

B
3

C
7

D
None of these

Solution
Question 6
4 / -1

The standard deviation of 35 numbers is 50. If each number is increased by 10, then new standard deviation will be :-

A
40

B
50

C
60

D
500

Solution

There will be no effect due to addition of constant in variables.
Question 7
4 / -1

The number of skew symmetric matrix with distinct elements except principal diagonal formed by the elements taking any number of elements at a time is

A
48

B
54

C
106

D
102

Solution
Question 8
4 / -1

A
0

B
m

C
m²

D
m² + sin²m

Solution

So Row 1 and Row 3 is same so value of determinant is zero.
Question 9
4 / -1

The number of integral values of 'b' for which origin and the point (1,1,1) lie on the opposite side of the plane 2x + a²y + abz – 1 = 0, for all a ∈ R – {0} is

A
3

B
2

C
1

D
0

Solution

Putting (0, 0, 0) expression is – 1 and putting (1, 1, 1) expression is 2 + a² + ab – 1

Both should have opposite sign so

2 + a² + ab – 1 > 0

a² + ab + 1 > 0

its discriminant is negative

D = b² – 4 < 0 = – 2 < b < 2

No. of integral value of 'b' is {–1, 0, 1}
Question 10
4 / -1

The is logically equivalent to

A
~p

B
p

C
q

D
~q

Solution