Mathematics Test

Result

Mathematics Test - 7

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Question 1
1 / -0

Equation of tangent to the parabola $y^{2} = 16 x$ at $P (3, 6)$ is

A

B

C

D
None of these

Solution

As the point lies inside the parabola, it is not possible to draw any tangent from this point.

Main Concept :

Tangent to a ParabolaEquations of tangent in different forms
Question 2
1 / -0

Let for i = 1,2,3, pi(x) be a polynomial of degree 2 in x,b and be the first and second order derivatives of respectively. Let,

A
is a polynomial of degree 3 in x.

B
is a polynomial of degree 6 in x.

C
is a polynomial of degree 3 in x.

D
does not depend on x.

Solution

Main Concept :

Properties of Determinant P - 1: The value of determinant remains unchanged, if the rows and the columns are interchanged.

Since the determinant remains unchanged when rows and columns are interchanged, it is obvious that any theorem which is true for 'rows' must also be true for 'columns.'

P - 2: If any two rows (or columns) of a determinant be interchanged, the determinant is unaltered in numerical value but is changed in sign only.

P - 3: If a determinant has two rows (or columns) identical, then its value is zero.

P - 4: If all the elements of any two (or column) be multiplied by the same number, then the value of determinant is multiplied by that number.

P - 5: If each element of any row (or column) can be expressed as a sum of two terms, then the determinant can be expressed as the sum of the determinants.
Question 3
1 / -0

The area of the smaller segment made by the circle $x^{2} + y^{2} = 9 and x = 1$ is

A
$\frac{1}{2} (9 {sec}^{- 1} 3 - \sqrt{8}) sq unit$

B
$(9 {sec}^{- 1} 3 - \sqrt{8}) sq unit$

C
$(\sqrt{8} - 9 {sec}^{- 1} 3) sq unit$

D
None of the above

Solution
Question 4
1 / -0

A

B

C

D
None of these

Solution

All the laws of ordinary algebra hold for the addition or subtraction of matrices and their multiplication by scalars.
Question 5
1 / -0

A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their statements about an incident do not match is

A
7/20

B
3/20

C
2/7

D
5/7

Solution
Question 6
1 / -0

The vector equation of the straight line $\frac{1 - x}{3} = \frac{y + 1}{- 2} = \frac{3 - z}{- 1} i s$

A
$\vec{r} = (\hat{i} - \hat{j} + 3 \hat{k}) + λ (3 \hat{i} + 2 \hat{j} - \hat{k})$

B
$\vec{r} = (\hat{i} - \hat{j} + 3 \hat{k}) + λ (3 \hat{i} - 2 \hat{j} - \hat{k})$

C
$\vec{r} = (\hat{i} - \hat{j} - 3 \hat{k}) + λ (3 \hat{i} - 2 \hat{j} + \hat{k})$

D
$\vec{r} = (\hat{i} + \hat{j} - 3 \hat{k}) + λ (3 \hat{i} - 2 \hat{j} + \hat{k})$

Solution
Question 7
1 / -0

A
$x < y = z$

B
$x \leq y < z$

C
$x < y > z$

D
$x = y > z$

Solution
Question 8
1 / -0

A
$u^{2} + v^{2} + w^{2} - 2 u v w$

B
$u^{3} + v^{3} + w^{3} - 3 u v w$

C
0

D
none of these

Solution
Question 9
1 / -0

A

B

C

D

Solution
Question 10
1 / -0

A
(13, 23, 0)

B

C
(-13, 23, 0)

D

Solution