List of practice Questions

The sets $ P_n $ are defined as $ \{ n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8 \} $, where $ n = 1, 2, 3, \ldots, 520 $. How many of these sets contain a multiple of 17?

In an examination of 12600 students, the ratio of the number of boys to the number of girls is 3:4. The ratio of the number of students who passed the exam to those who failed the exam is in the ratio of 11:3. Among the girls, the ratio of the number of students who passed to those who failed the exam is in ratio 11:4. Find the difference between the number of boys who passed and failed the exam.

Solution P contains three liquids A, B, and C in the ratio 2:3:5 respectively. Another solution Q contains A, B, and C in the ratio 5:3:2 respectively. Solutions P and Q are mixed in the ratio 7:3 to obtain another solution R. Now 50% volume of R is replaced with another solution having A and B in the ratio 7:3. The resulting solution is Z. Find the percentage amount of B in solution Z.

Perimeter of $\Delta ABC$ is 32 m. If AB = BC and altitude BD measures 8 m, find area of triangle ABC.

In a bag there are 100 coins. The coins in the bag are of denomination Rs.1 or Rs.2 or Rs.5. There are at least 10 coins and at most 60 coins of each denomination. Urvashi takes out 40 coins, which consist at least one coin of each denomination from the bag and finds that total worth of coins that she has taken out is Rs.148. The total worth of coins that are still in the bag is Rs.212. Which of the following can be the total number of coins of denomination Rs.1 that are still in the bag?

If 150! is converted to base 7, how many consecutive zeros would be there at the end of it?

All natural numbers that give remainders 1 and 2 when divided by 6 and 5, respectively, are written in ascending order, side by side, from left to right. What is the 99th digit from the left of the number thus formed?

Find the sum of the digits of $ 100^{100} - 10 $.

Let R1 and R2 respectively denote the maximum and the minimum possible remainders when 276$^n$ is divided by 91 for any natural number n, n ≥ 144. Find R1 + R2.

How would you describe the character and temperament of Sophie’s father?

Integrate the function: $\frac {1}{\sqrt {(x-a)(x-b)}}$

Find:
(i) 2.7 ÷ 100
(ii) 0.3 ÷ 100
(iii) 0.78 ÷ 100
(iv) 432.6 ÷ 100
(v) 23.6 ÷ 100
(vi) 98.53 ÷ 100

The ionisation potential is lowest for the

Draw the structures of all isomeric alcohols of molecular formula C₅H₁₂O and give their IUPAC names. (ii)Classify the isomers of alcohols in question 11.3(i)as primary, secondary and tertiary alcohols.

Evaluate $ \int_1^3 [x - 1] \, dx $

Draw:

1) a leaf

2) a taproot and

3) a flower,

you have studied for Table 4.3

‘Some leaders are dishonest. Satyapriya is a leader.’ Which of the following inferences definitely follows from these statements ?

Give four rational numbers equivalent to:
(i)$\frac{-2}{7}$
(ii) $\frac{5}{-3}$
(iii) $\frac{4}{9}$

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

The current drawn by the primary of a transformer, which steps down $200\,V$ to $20\,V$ to operate a device of resistance $20\,\Omega $. is (Assume the efficiency of the transformer to be $80\, \%$)

$ {{(C{{H}_{3}})}_{3}}CMgCl $ on reaction with $ {{D}_{2}}O $ produces

What incidents during the Everest expedition show Santosh’s concern for her team-mates?

Let the domains of the functions $ f(x) = \log_4 \log_3 \log_7 (8 - \log_2(x^2 + 4x + 5)) $ and $ g(x) = \sin^{-1} \left( \frac{7x + 10}{x - 2} \right)$ be $ (\alpha, \beta) $ and $ [\gamma, \delta] $, respectively. Then $ \alpha^2 + \beta^2 + \gamma^2 + \delta^2 $ is equal to:

In a group of 100 people, 70 like coffee, 60 like tea, and 45 like both coffee and tea. How many people like neither coffee nor tea?

Find the number of digits in the square root of each of the following numbers (without any calculation).

64
144
4489
27225
390625