BCA Entrance Group B Mathematics Questions with Answers

If $n(A)=30$, $n(B)=50$, $n(U)=60$ and $n(A\cup B)=55$, then the sum of $n(A-B)$ and $n(B-A)$ is equal to

Answer: $30$

The sum of natural numbers from 1 to 20 is

Answer: $\frac{20\times21}{2}$

If $n(A)=26$ and $n(B)=32$ then the maximum value of $n(A\cap B)$ is

Answer: $26$

For some integer $n$, which of the following forms is always an odd integer?

Answer: $2n+1$

The range of the function $f(x)=\sqrt{x-1}$ is

Answer: $[0,\infty)$

For the infinite sum of a geometric series to exist, its ratio should be

Answer: between $1$ and $-1$

If the quadratic equation is $x^2+x+1=0$ then $x=$

Answer: $\frac{-1\pm i\sqrt3}{2}$

A function is defined as $f(x)=\frac{3x+1}{4}$. Its inverse is

Answer: $\frac{4x-1}{3}$

One factor of the polynomial $x^3-4x^2+x+6$ is $(x-2)$. The two other factors are

Answer: $(x+1)(x-3)$

The sum of the infinite series $1+\frac12+\frac14+\frac18+\cdots$ is

Answer: $2$

The sum of cubes of the first 6 natural numbers is

Answer: $441$

Marked price of an article is Rs. 8500. If a discount of 10% is allowed, the selling price is

Answer: $7650$

If 7 pounds = 11 US dollars and 2 US dollars = Rs. 213, how many pounds can be exchanged for Rs. 117150?

Answer: $700$

A mobile is sold for Rs. 11000 with a profit of Rs. 1000. The percentage profit is

Answer: $10\%$

If 12 girls or 8 boys can do a piece of work in 3 days, how many days are required for 4 boys and 6 girls to do the same work?

Answer: $3$

If $f(x)=4x$, $g(x)=x+1$ and $fog(x)=20$ then $x=$

Answer: $4$

The sum of 15 terms of an A.P. is 435 and the common difference is 4. The first term is

Answer: $1$

Which one is the same as $\log 8$?

Answer: $\log4+\log2$

If $A=\begin{pmatrix}2&3\-4&-5\end{pmatrix}$ and $B=\begin{pmatrix}0&-3\2&5\end{pmatrix}$ then $(AB)^T=$

Answer: $\begin{pmatrix}6&-10\9&-13\end{pmatrix}$

The harmonic mean between two numbers $a$ and $b$ is

Answer: $\frac{2ab}{a+b}$

The sum of the first 10 odd numbers is

Answer: $100$

The solution of the equation $x^2+1=0$ in the complex number system is

Answer: $\pm i$

The next term of the sequence $1,2,4,7,11,\ldots$ is

Answer: $16$

If $f(x)=x^2-3x+1$ and $f(2a)=2f(a)$ then $a=$

Answer: $\frac1{\sqrt2}$ or $-\frac1{\sqrt2}$

If $x<0$, then $|x|$ is equal to

Answer: $-x$

If $2x^3-7x^2+x+10=(x-1)Q(x)+R(x)$ then the remainder $R(x)$ is

Answer: $6$

If $5^{x+3}=(25)^x$ then $x=$

Answer: $3$

If $x+y=3$ and $x^2+y^2=5$ then $xy=$

Answer: $2$

The value of $0!$ is

Answer: $1$

A matrix $A$ has order $3\times4$ and $B$ has order $4\times3$. The order of $AB$ is

Answer: $3\times3$

If the transpose of a matrix $A$ is $A$ itself, then $A$ is called

Answer: symmetric

The sum $1^3+2^3+3^3+\cdots+n^3$ is

Answer: $\left(\frac{n(n+1)}{2}\right)^2$

The fifth term of the sequence $\frac12,\frac45,\frac78,\ldots$ is

Answer: $\frac{13}{14}$

The radius of a cylinder is 7 cm and its height is 3 cm. Its volume is

Answer: $462\ cm^3$

If $b^2-4ac=0$ then the roots of $ax^2+bx+c=0$ are

Answer: real and equal

A single equation represented by the two straight lines $x=2y$ and $2x=y$ is

Answer: $2x^2-5xy+2y^2=0$

Two angles subtended by an arc, one at the center and the other at the circumference, are related as

Answer: The angle at the center is double the angle at the circumference.

The two lines $3x+2y=5$ and $9x+6y=14$ have

Answer: no solution

A point $(3,4)$ is rotated $90^\circ$ anticlockwise and then translated by $(5,-2)$. The resulting point is

Answer: $(1,1)$

If $m_1$ and $m_2$ are the slopes of the pair of lines $ax^2+2hxy+by^2=0$ then $m_1m_2$ is

Answer: $\frac ab$

In the general equation of a circle $x^2+y^2+2gx+2fy+c=0$ the centre of the circle is

Answer: $(-g,-f)$

The complement of an angle is $20^\circ$ less than 4 times the angle. Then the angle is

Answer: $22$

A pole at a distance of 25 m from the observer makes an angle of $60^\circ$ at its top. Then the height of the pole is

Answer: $25\sqrt3$

The value of $\tan75^\circ$ is

Answer: $2+\sqrt3$

If two children are born in a family, find the probability that both are girls.

Answer: $\frac14$

A die is thrown. The probability of getting an odd number is

Answer: $\frac12$

If $\vec a=(0,3,4)$ and $\vec b=(2,-2,0)$, the cosine of the angle between them is

Answer: $-\frac{3}{5\sqrt2}$

A point in three-dimensional space has coordinates $(1,2,-2)$. Its distance from the origin is

Answer: $3$

The derivative of $\tan x$ with respect to $x$ is

Answer: $\sec^2x$