PGDBA 2022 Question Paper | PGDBA QA

PGDBA Question Paper | PGDBA Previous Year Paper

PGDBA 2022 Question Paper QA

The domain of the function \( f ( x ) = \sqrt { \frac { 1 - | x | } { 2 - | x | } } \) is
1. \( [ - 1,1 ] \cup ( - \infty , - 2 ) \cup ( 2 , \infty ) \)
2. \( ( - \infty , - 2 ) \cup ( 2 , \infty ) \)
3. \( \mathbb { R } \backslash \{ - 2,2 \} \)
4. \( ( - 1,1 ) \cup ( - \infty , - 2 ) \cup ( 2 , \infty ) \)
Choice A
\( [ - 1,1 ] \cup ( - \infty , - 2 ) \cup ( 2 , \infty ) \)
PGDBA 2022 Question Paper QA

Let \( P \) be a \( 19 \times 19 \) matrix whose entries in both the diagonals are all equal to 1 and all other entries are equal to 0 . Then, \( \operatorname { rank } ( P ) \) is equal to
1. \( 10 \)
2. \( 19 \)
3. \( 11 \)
4. \( 9 \)
Choice A
\( 10 \)
PGDBA 2022 Question Paper QA

If \( P \) and \( Q \) are two matrices such that \( P Q = Q \) and \( Q P = P \), then \( P ^ { 3 } + Q ^ { 3 } \) is equal to
1. \( P + Q \)
2. \( P ^ { 3 } Q ^ { 3 } \)
3. \( 3 P Q \)
4. \( 3 Q P \)
Choice A
\( P + Q \)
PGDBA 2022 Question Paper QA

If \( \alpha \) and \( \beta \) are the two roots of the quadratic equation \( x ^ { 2 } + x + 1 = 0 \), then the equation whose roots are \( \alpha ^ { 2022 } \) and \( \beta ^ { 2022 } \) is
1. \( x ^ { 2 } + x - 1 = 0 \)
2. \( x ^ { 2 } - 2 x + 1 = 0 \)
3. \( x ^ { 2 } + x + 1 = 0 \)
4. \( x ^ { 2 } + 2 x - 1 = 0 \)
Choice B
\( x ^ { 2 } - 2 x + 1 = 0 \)
PGDBA 2022 Question Paper QA

In how many ways can the 26 letters of the English alphabet be arranged such that no two vowels are next to each other in the arrangement?
1. \( 26 ! - 5 \times 25 ! \)
2. \( { } ^ { 22 } C _ { 5 } \times 21 ! \times 5 ! \)
3. \( { } ^ { 21 } P _ { 5 } \times 21 ! \)
4. \( 26 ! - 5 \times 21 ! \)
Choice B
\( { } ^ { 22 } C _ { 5 } \times 21 ! \times 5 ! \)
PGDBA 2022 Question Paper QA

If a circle passes through the points of intersection of the coordinate axes with the lines \( x - \lambda y + 1 = 0 \) and \( x - 2 y + 3 = 0 \), then \( \lambda \) equals
1. \( \frac { 4 } { 3 } \quad \) or \( \quad \frac { 1 } { 3 } \)
2. \( \frac { 3 } { 4 } \) or \( \quad \frac { 1 } { 3 } \)
3. \( \frac { 2 } { 3 } \quad \) or \( \quad \frac { 1 } { 2 } \)
4. \( \frac { 3 } { 2 } \quad \) or \( \quad \frac { 1 } { 2 } \)
Choice C
\( \frac { 2 } { 3 } \quad \) or \( \quad \frac { 1 } { 2 } \)
PGDBA 2022 Question Paper QA

Let \(P, Q, R\) be any three sets. Consider the following two statements:
(I) \(\quad P-(Q-R)=(P-Q) \cup R\)
(II) \(\quad P-(Q \cup R)=(P-Q)-R\)
Which of the following is TRUE?
1. Both (I) and (II) are always correct
2. (II) is always correct and (I) is correct if and only if \( P \subset R \)
3. (II) is always correct and (I) is correct if and only if \( R \subset P \)
4. Both (I) and (II) are always incorrect
Choice C
(II) is always correct and (I) is correct if and only if \( R \subset P \)
PGDBA 2022 Question Paper QA

An airplane is observed to be approaching a point that is at a distance of \( 20 \mathrm {~km} \) from the point of observation such that the angle of elevation is \( 60 ^ { \circ } \). Then the height of the airplane above the ground is
1. \( 10 \sqrt { 3 } \mathrm {~km} \)
2. \( 40 \sqrt { 3 } \mathrm {~km} \)
3. \( \sqrt { 30 } \mathrm {~km} \)
4. \( 20 \mathrm {~km} \)
Choice A
\( 10 \sqrt { 3 } \mathrm {~km} \)
PGDBA 2022 Question Paper QA

Let \( a _ { 1 } , a _ { 2 } \in \mathbb { R } \) be such that \( \left| a _ { 1 } - a _ { 2 } \right| = 10 \). Consider \[ f ( x ) = \left| \begin{array} { c c c } 1 & a _ { 2 } & a _ { 1 } \\ 1 & a _ { 2 } & 2 a _ { 1 } - x \\ 1 & 2 a _ { 2 } - x & a _ { 1 } \end{array} \right| \] Then, the largest value of \( f ( x ) \) is
1. \( 25 \)
2. \( 30 \)
3. \( 20 \)
4. \( 15 \)
Choice A
\( 25 \)
PGDBA 2022 Question Paper QA

Consider a function \( f ( x ) = x ^ { 2 } + p x + q \) such that the roots of \( f ( x ) = 0 \) are positive and distinct. Let the arithmetic mean, the geometric mean and the harmonic mean of the two roots be \( a , b \) and \( c \), respectively. Then, which of the following statements is TRUE?
1. \( f ( a ) < f ( c ) < f ( b ) \)
2. \( f ( a ) > f ( c ) > f ( b ) \)
3. \( f ( a ) < f ( b ) < f ( c ) \)
4. \( f ( a ) > f ( b ) > f ( c ) \)
Choice C
\( f ( a ) < f ( b ) < f ( c ) \)
PGDBA 2022 Question Paper QA

Suppose \( E _ { 1 } \) and \( E _ { 2 } \) are two independent events, each having probability \( p \). If \( P \left( E _ { 1 } \cup E _ { 2 } \right) = \frac { 5 } { 9 } \), what is the value of \( p \) ?
1. \( \frac { 1 } { 9 } \)
2. \( \frac { 1 } { 3 } \)
3. \( \frac { 5 } { 18 } \)
4. \( \frac { 2 } { 9 } \)
Choice B
\( \frac { 1 } { 3 } \)
PGDBA 2022 Question Paper QA

Let \( a _ { 1 } , a _ { 2 } , a _ { 3 } , a _ { 4 } , a _ { 5 } \) be the distinct fifth roots of 1 . Then the value of \( a _ { 1 } ^ { 2022 } + a _ { 2 } ^ { 2022 } + a _ { 3 } ^ { 2022 } + a _ { 4 } ^ { 2022 } + a _ { 5 } ^ { 2022 } \) is
1. \( 5 \)
2. \( 7 \)
3. \( 0 \)
4. \( 10 \)
Choice C
\( 0 \)
PGDBA 2022 Question Paper QA

A straight line segment \( A B \) of length \( p \) moves with its ends on the axes. Let \( C \) be a point on \( A B \) such that \( A C : B C = 1 : 3 \). Then the equation of the locus of \( C \) is
1. \( 16 \left( 9 x ^ { 2 } + y ^ { 2 } \right) = p ^ { 2 } \)
2. \( 16 \left( x ^ { 2 } + 9 y ^ { 2 } \right) = 9 p ^ { 2 } \)
3. \( 16 \left( x ^ { 2 } + y ^ { 2 } \right) = 9 p ^ { 2 } \)
4. \( 16 \left( 9 x ^ { 2 } + y ^ { 2 } \right) = 9 p ^ { 2 } \)
Choice D
\( 16 \left( 9 x ^ { 2 } + y ^ { 2 } \right) = 9 p ^ { 2 } \)
PGDBA 2022 Question Paper QA

Suppose \( 2 \sin \theta - 5 \cos \theta = \sqrt { 13 } \). Then the expression \( ( 2 \cos \theta + 5 \sin \theta ) \) equals
1. \( \pm 5 \)
2. \( \pm 13 \)
3. \( \pm 4 \)
4. \( 0 \)
Choice C
\( \pm 4 \)
PGDBA 2022 Question Paper QA

Consider the function \( f : \mathbb { R } \rightarrow \mathbb { R } \) defined by \[ f ( x ) = \max \left\{ x , x ^ { 2 } \right\} - \min \left\{ x , x ^ { 2 } \right\} \] Then \( f \) is differentiable
1. everywhere except \( x = 0 \)
2. everywhere except \( x = 0 \) and \( x = - 1 \)
3. everywhere except \( x = 0 \) and \( x = 1 \)
4. everywhere except \( x = 0 , x = 1 \) and \( x = - 1 \)
Choice C
everywhere except \( x = 0 \) and \( x = 1 \)
PGDBA 2022 Question Paper QA

The area of the region bounded by the curves \( y ^ { 2 } = 4 x \) and \( y = 2 x \) is
1. \( \frac { 1 } { 5 } \)
2. \( \frac { 1 } { 8 } \)
3. \( \frac { 1 } { 10 } \)
4. \( \frac { 1 } { 3 } \)
Choice D
\( \frac { 1 } { 3 } \)
PGDBA 2022 Question Paper QA

For which values of \(\lambda \in R\) will the system of linear equations
\(x+y+z=2\)
\(x+2y+z=-2\)
\(x+y+( \lambda - 5)z = \lambda\)
have a unique solution?
1. \( \lambda = 6 \)
2. \( \lambda \neq 3 \)
3. \( \lambda \neq 6 \)
4. \( \lambda = 2 \)
Choice C
\( \lambda \neq 6 \)
PGDBA 2022 Question Paper QA

The number of terms in the expansion of \( ( 1 - x ) ^ { 51 } \left( 1 + x + x ^ { 2 } + x ^ { 3 } + x ^ { 4 } \right) ^ { 50 } \) is
1. \( 101 \)
2. \( 102 \)
3. \( 100 \)
4. \( 112 \)
Choice B
\( 102 \)
PGDBA 2022 Question Paper QA

Which of the following equations will have positive integer solutions?
1. \( x ^ { 2 } + y ^ { 2 } = 2025 \)
2. \( x ^ { 2 } + y ^ { 2 } = 2023 \)
3. \( x y ( x - y ) = 2021 \)
4. \( x ^ { 2 } - y ^ { 2 } = 2022 \)
Choice A
\( x ^ { 2 } + y ^ { 2 } = 2025 \)
PGDBA 2022 Question Paper QA

For what value of \( m \) will the equation \[ \frac { x ^ { 2 } - b x } { a x - c } = \frac { m - 1 } { m + 1 } \] have roots equal in magnitude but opposite in sign?
1. \( \frac { a + b } { a - b } \)
2. \( \frac { a - b } { a + b } \)
3. \( \frac { a - c } { a + c } \)
4. \( \frac { b - c } { b + c } \)
Choice B
\( \frac { a - b } { a + b } \)
PGDBA 2022 Question Paper QA

The highest power of 7 that divides 2022 ! is
1. \( 337 \)
2. \( 334 \)
3. \( 323 \)
4. \( 345 \)
Choice B
\( 334 \)
PGDBA 2022 Question Paper QA

For any real number \( x \), let \( [ x ] \) denote the greatest integer \( m \) such that \( m \leq x \). Then the value of \( \int _ { 0 } ^ { \pi } [ 2 \sin x ] d x \) is
1. \( \frac { \pi } { 6 } \)
2. \( \frac { \pi } { 3 } \)
3. \( \frac { 2 \pi } { 3 } \)
4. \( \frac { \pi } { 2 } \)
Choice C
\( \frac { 2 \pi } { 3 } \)
PGDBA 2022 Question Paper QA

If \( f ( x ) = \sin \left( \log _ { 10 } x \right) \) and \( h ( x ) = \cos \left( \log _ { 10 } x \right) \), then \[ \frac { 1 } { 2 } \left( h \left( \frac { x } { y } \right) + h ( x y ) \right) - f ( x ) f ( y ) \] equals
1. \( \sin \left( \log _ { 10 } \left( \frac { x } { y } \right) \right) \)
2. \( \cos \left( \log _ { 10 } ( x y ) \right) \)
3. \( \cos \left( \log _ { 10 } \left( \frac { x } { y } \right) \right) \)
4. \( \sin \left( \log _ { 10 } ( x y ) \right) \)
Choice B
\( \cos \left( \log _ { 10 } ( x y ) \right) \)
PGDBA 2022 Question Paper QA

If the line \( \frac { x } { a } + \frac { y } { b } = 1 \) is a tangent to the curve \( x ^ { \frac { 2 } { 3 } } + y ^ { \frac { 2 } { 3 } } = 1 \), then which of the following is TRUE?
1. \( a ^ { 2 } + b ^ { 2 } = \frac { 2 } { 3 } \)
2. \( a ^ { 2 } + b ^ { 2 } = 1 \)
3. \( a ^ { 2 } + b ^ { 2 } = 2 \)
4. \( \frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = 1 \)
Choice B
\( a ^ { 2 } + b ^ { 2 } = 1 \)
PGDBA 2022 Question Paper QA

The limit \[ \lim _ { x \rightarrow 0 } \left( \frac { \tan x } { x } \right) ^ { \frac { 1 } { x } } \]
1. is 0
2. is \( e \)
3. is 1
4. does not exist
Choice C
is 1