Mathematics I 2021 - Objective

1. If \( n_2 = 12 \), then value of n is

1. 4
2. 3
3. 2
4. 1

2. If A=(-2,2) and B=(1,5), the difference B-A is

1. (2,5)
2. (2,5)
3. (2,5)
4. [2,5]

3. Sum of the series \( 1 + \frac{1}{3} + \frac{1}{9} + \cdots \) is

1. 2/3
2. 3/2
3. 5/2
4. 7/2

4. The value of \( \log_a x \) is

1. \( a^x \)
2. \( x^a \)
3. \( x \)
4. \( a \)

5. If a matrix \( \begin{pmatrix} a & 2 & -3 \\ b & c & 5 \\ d & e & f \end{pmatrix} \) is shew symmetric, then the sum of a,b,c,d,e,f is

1. 1
2. 0
3. -4
4. ∅

6. The conic section become parabola if

1. a=0
2. e=1
3. c=−1
4. e=1

7. If \( \vec{a} \) is a non-zero vector, then unit vector in the direction of \( \vec{a} \) is

1. \( \vec{a} \)
2. \( \vec{a}/|\vec{a}| \)
3. \( \vec{a}|\vec{a}| \)
4. \( \vec{a}/|\vec{a}| \)

8. Equation of directrix for the parabola \( x^2 = 4ay \) is

1. x=-a
2. y=-a
3. x=-4a
4. y=-4a

9. The imaginary part of the complex number \( \frac{4+5i}{3-4} \) is

1. 30/25
2. 31/25
3. 30/25
4. 31/25

10. If f(x)=\( \sqrt{x} \) and g=x+1 then go f is equal to

1. \( \sqrt{x+1} \)
2. \( \sqrt{x+1} \)
3. x+\( \sqrt{x} \)
4. x\( \sqrt{x+1} \)