Mix Test 12...

‘a’ and ‘b’ are two positive integers such that the least prime factor of ‘a’ is 3 and the least prime factor of ‘b’ is 5. Then the least prime factor of (a + b) is

If \(\alpha,\) \(\beta\) are the zeros of the polynomial f(x) = \(\mathrm{x^2 - 5x + k}\) such that \(\alpha - \beta = 1\). Then the value of k is

We have a rectangle whose length and breadth is l m and b m respectively. The length of a rectangle is increased by 20% and breadth is decreases by 20%.

The original area of rectangle is: (in \(m^2\))

We have a rectangle whose length and breadth is \(l\) m and b m respectively. The length of a rectangle is increased by 20% and breadth is decreases by 20%.

The new length is:

We have a rectangle whose length and breadth is \(l \) m and b m respectively. The length of a rectangle is increased by 20% and breadth is decreases by 20%.

The new breadth is:

We have a rectangle whose length and breadth is \(l\) m and b m respectively. The length of a rectangle is increased by 20% and breadth is decreases by 20%.

The new area of rectangle is: (in \(m^2\))

We have a rectangle whose length and breadth is \(l\) m and b m respectively. The length of a rectangle is increased by 20% and breadth is decreases by 20%.

Percentage change in area will be:

The median of first 8 prime numbers is

A family is having 3 children. Then the probability of having at least one boy is

If the points A(4, 3) and B(x, 5) lie on the circle with center O(2,3). Then the value of x is

The \(4^{th}\) term of an A.P is 11 The sum of the \(5^{th}\) and \(7^{th}\) terms of this AP is 34.

\(T_4\) = 11, then we can say that; 

The \(4^{th}\) term of an AP is 11. The sum of the \(5^{th}\) and \(7^{th}\) terms of this AP is 34.

Given that \(T_5 + T_7 = 34\), signifies

The \(4^{th}\) term of an AP is 11. The sum of the \(5^{th}\) and \(7^{th}\) terms of this AP is 34.

The value of \(1^{st}\) term ‘a’ is:

The \(4^{th}\) term of an AP is 11. The sum of the \(5^{th}\) and \(7^{th}\) terms of this AP is 34.

Common difference of AP is:

The \(4^{th}\) term of an AP is 11. The sum of the \(5^{th}\) and \(7^{th}\) terms of this AP is 34.

\(T_{50}\) = ?

The difference between two numbers is 5 and the difference between their squares is 65. Then the numbers are

If 3x = cosecθ and \(\frac{3}{\mathrm x}\) = cotθ. Then the value of \(\mathrm{3\left(x^2-\frac{1}{x^2}\right)} \) is

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. The speed of the stream is 2 km/hour and speed of boat in still water is 10 km/hour.

Speed downstream is equal to:

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. The speed of the stream is 2 km/hour and speed of boat in still water is 10 km/hour.

Speed upstream is equal to:

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. The speed of the stream is 2 km/hour and speed of boat in still water is 10 km/hour.

Time taken to cover 8 km downstream will be:

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. The speed of the stream is 2 km/hour and speed of boat in still water is 10 km/hour.

Time taken to cover 8 km upstream is:

If the speed of boat in still water is x km/hr, other parameter remaining the same, then, we have \(\mathrm{\frac{8}{x+2}+\frac{8}{x-2} = \frac{5}{3}}\), which reduces to:

If one zero of the polynomial \(\mathrm{(a^2+9)x^2 + 13x + 6a}\) is reciprocal of the other. Then the value of a is