Which of the following options is correct? (1) Every integer and fraction is a rational number. (2) A rational number \[\frac{p}{q}\] is positive if p and q are either both positive or both negative. (3) A rational number \[\frac{p}{q}\] is negative if one of p and q is positive and other is negative. (4) If there are two rational numbers with same denominator, then the one with the larger numerator is larger than the other.

In the given figure (not drawn to scale), ABCD is a rhombus, FHI is an equilateral triangle and CEFG is a trapezium with EC parallel to FG. DCF/, BCG and GFH are straight lines. Find \[x+y+z\].

In the given figure, the ratio of the area of the shaded portion to the area of total figure is ____.

The difference between \[{{\left( \frac{\text{3}}{\text{5}} \right)}^{\text{th}}}\] of \[{{\left( \frac{\text{2}}{\text{3}} \right)}^{\text{rd}}}\]of a number and \[{{\left( \frac{\text{2}}{5} \right)}^{\text{th}}}\]of \[{{\left( \frac{1}{4} \right)}^{\text{th}}}\] of the same number is 288. What is the number?

Which greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively?

A student was asked to divide a number by 3. But, instead of dividing it, he multiplied it by 3 and got 29.7. What was the correct answer?

P, Q and R start at the same time and in the same direction to run around a circular stadium. P completes a round in 252 seconds, Q in 308 seconds and R in 198 seconds, ail starting at the same point. After what time will they meet again at the starting point?

At Shimla, on Tuesday the temperature was\[\text{-8 }\!\!{}^\circ\!\!\text{ C}\]. It then dipped by \[\text{4 }\!\!{}^\circ\!\!\text{ C}\] on Wednesday. On Thursday, it rose by x. if the temperature on Thursday is\[\text{-7 }\!\!{}^\circ\!\!\text{ C}\], then find the value of x.

The number of trees in different parks of a city are 33, 38, 48, 33. 34, 34, 33 and 24. The mode of this data is

In the given diagram, the triangle stands for graduates, square stands for membership of professional organisations and the circle stands for membership of social organisations. The number of graduates who has membership in professional organisations only is

The value of\[({{2}^{3}}+{{2}^{2}}+{{2}^{-2}}+{{2}^{-3}})\] is equal to_____.

In an examination, 65% of the total examinees passed. If the number of failures is 420, the total number of examinees is _______.

Dalbergia is a large genus of small to medium- sized trees, shrubs and lianas in the pea family. With which of the following is Dalbergia associated?

Saffron is a spice derived from the plant of saffron crocus. It gives food a golden yellow colour and is the world's most expensive spice. Which part of saffron plant is used to obtain the spice saffron?

Match column I with column II and select the correct option from the given codes. Column I Column II 1. Tallest perennial grass (a) Spruce 2. Evergreen tree (b) Gulmohar 3. Flame tree (c) Sequoia 4. General Sherman (d) Bamboo