At how many points will the curves  and  intersect in the real  plane?

If, for non-zero real variables , and real parameter ,        

then, the ratio  is

Which one of the following options represents the given graph?

The price of an item is  cheaper in an online store  compared to the price at another online store M. Store S charges Rs. 150 for delivery. There are no delivery charges for orders from the store . A person bought the item from the store  and saved Rs. 100. What is the price of the item at the online store  (in Rs.) if there are no other charges than what is described above?

An ant is at the bottom-left corner of a grid (point. P) as shown below in the figure. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

Seven cars  and  are parked in a row not necessarily in that order. The cars  and  should be parked next to each other. The cars S and  also should be parked next to each other, whereas  and  cannot be parked next to each other.  and  must be parked next to each other.  is parked to the immediate right of .  is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

Consider five people – Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1. Lakshmi is taller than Rekha

2. Rekha is shorter than Mita

3. Rekha is taller than Sana

4. Sana is shorter than Ganga

Functions F(a, b) and G(a, b) are defined as follows:

and, where represents the absolute value of x. What would be the value of?

The three roots of the equation are . What are the three values of x for which?

The expression  is equal to

The number of roots of in the range [–5, 5] is

In a quadratic function, the value of the product of the roots  is 4. Find the value of

Choose the correct expression for  given in the graph.

If , then  is ______________.

Consider a function   on. The value of x at which the function attains a maximum, and the maximum value of the function are:

If the letters P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence?

(I) 2P, 2R, 2S, 2T, 2U

(II) P-3, R-3, S-3, T-3, U-3

(III)

If , compute .

The roots of  are real and positive. A, b and c are real. Then  has                

If x is real and , then possible values of  include

Consider the equation; , where  stands for X to the base N. Find Y.

The set values of p for which the roots of the equation are of opposite sign is

If  and , then

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is

Three friends, R, S and T shared toffee from a bowl. R took  of the toffees, but returned four to the bowl. S took  of what was left but returned three toffees to the bowl. T took half of the reminder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees were originally there in the bowl?

Given that  and q is any non-zero real number, the value of  is

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on  January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following factors:

(i) Hari’s age + Gita’s age > Irfan’s age + Saira’s age.

(ii) The age difference between Gita and Saira is 1 year. However Gita is not the oldest and saira is not the youngest.

(iii) There are no twins.

In what order were they born (oldest first)?