‘Prince of Pilgrims’ was the name attributed to
The Lahore Conspiracy Case was registered against whom?
Which one of the following battles led to the foundation of the Mughal rule at Delhi?
Arbind spends 75% of his income and saves the rest. His income is Increased by 20% and he increases his expenditure by 10%. Then the increase in savings in percentage is

Solution
Let Arbind's income be Rs 100
∴ Expenditure = Rs 75 and savings = Rs 25
Again,
New income = Rs 120, Expenditure = 75 + 7.5 = Rs 82.5 and Savings = 120  82.5 = Rs 37.5
∴ Required percentage
= \(frac{37.5  25}{25} times 100 = 50%\)
Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3?

Solution
If \(\frac{\left ( x – \sqrt{24} \right )\left ( \sqrt{75} + \sqrt{50}\right )}{\sqrt{75} – \sqrt{50}} = 1\) then the value of x is

Solution
\(frac{left ( x  sqrt{24} right )left ( sqrt{75} + sqrt{50}right )}{sqrt{75}  sqrt{50}} = 1\)
⇒ \(frac{left ( x  2sqrt{6} right )left ( 5sqrt{3} + 5sqrt{5}right )}{5sqrt{3}  5sqrt{2}} = 1\)
⇒ \(frac{left ( x  2sqrt{6} right )left ( sqrt{3} + sqrt{2}right )}{sqrt{3}  sqrt{2}} = 1\)
⇒ \(x  2sqrt{6} = frac{sqrt{3}  sqrt{2}}{sqrt{3} + sqrt{2}}\)
⇒ \(x  2sqrt{6} = frac{left (sqrt{3}  sqrt{2} right )^{2}}{left (sqrt{3} + sqrt{2} right )left (sqrt{3}  sqrt{2} right )} = 3 + 2  2sqrt{6}\)
⇒ \(x  2sqrt{6} = 5  2sqrt{6} Leftrightarrow x = 5\)
The value of \(3\frac{1}{2} – \left[2\frac{1}{4} \div \left \{ 1\frac{1}{4} – \frac{1}{2}\left(1\frac{1}{2} – \frac{1}{3} – \frac{1}{6} \right)\right \}\right]\) is

Solution
In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 36, then the dividend is

Solution
Divisor = 5 X remainder = 5 × 36 = 180
∴ Again, Divisor = 12 × quotient
∴ 180 = 12 × quotient
∴ Quotient = \(frac{180}{12} = 15\)
∴ Dividend = Divisor × Quotient + Remainder
= 180 × 15 + 36 = 2700 + 36 = 2736
In how many years shall ₹ 2500, invested at the rate of 8% simple interest per annum, amount to ₹ 3300?

Solution
Let the required number of years be T years
Now, according to the question,3300 2500 =\(=frac{2500times 8 times T}{100}\)
\(∴T=frac{800}{200}= 4 years\)
The ratio of father’s age to his son’s age is 7 : 3. The product of their ages is 756. The ratio of their ages after 6 years will be

Solution
Let the father's age and his son's age be 7x years and 3x years respectively.
Now, according to the question,
7x × 3x= 756\(⇒x^{2}=frac{756}{21}=36=(6)^{2}\)
\(⇒x=6\)
∴ Ratio of their ages after 6 years
\(=frac{7 times 6+6}{3 times 6 + 6}=frac{48}{24}=2:1\)
Ashok’s mother was 3 times as old as Ashok 5 years ago. After 5 years she will be twice as old as Ashok. How old is Ashok today?

Solution
Let the present age of Ashok be x years.
⇒ The present age of Ashok's mother
= 3(x  5) + 5 years
Now, according to the question,
⇒ 3(×  5) + 5 + 5 = (× + 5) × 2
⇒ 3×  15 + 10 = 2x+ 10 ⇔×= 15 years
Which one number is wrong in the given series?
126,98,70,41,14

Solution
126  28 = 98
9828 = 70
7028 = 42 ≠ 41
4228 = 14
Find out a set of numbers amongst the four sets of numbers given in the alternatives, which is the most similar to the numbers given in the question.
Given: (6, 30, 90)

Solution
Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
a_b_a__ n_bb_abbn

Solution
a b b n / a b b n / a b b n / a b b n
Out of the numbers 0.3, 0.03, 0.9, 0.09 the number that is nearest to the value of \(\sqrt{0.9}\) is

Solution
The total number of prime factors in 4^{10} × 7^{3} × 16^{2} × 11 × 10^{2} is

Solution
4^{10} × 7^{3} × 16^{2} × 11 × 10^{2}
= (2^{2})^{10} × (7)^{3} × (2^{4})^{2} × 11 x (2 x 5)^{2}
= 2^{20} × 7^{3} × 2^{8} × 11 × 2^{2} × 5^{2}
= (2)^{20 + 8 + 2} × 5^{2} × 7^{3} × 11^{1}
= (2)^{30} × 5^{2} × 7^{3} × 11^{1}
∴ Total number of prime factors
= 30 + 2 + 3 + 1 = 36
The base of right prism is a triangle whose perimeter is 28 em and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is

Solution
Volume of prism = Area of base × height
⇒ 366 = ^{1}⁄_{2} × 4 × 28 × h ⇔ h = ^{366}⁄_{56} = 6.53 cm
In a twodigit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is

Solution
Let the digit at the ten's place be x.
∴ unit's digit = 2x  1
∴ original number = 10x + (2x  1) = 12x  1
New number = 10 (2x  1) + x
= 20x  10 + x = 21x  l0
∴ 21x  10  12x + 1 = 12x  1  20
⇒ 9x  9 = 12x  21
⇒ 3x = 12 ⇔ x = 4
∴ original number = 12x  1 = 12 × 4  1 = 47
If a + b + C = 9 (where a, b, c are real numbers), then the minimum value of a^{2} + b^{2} + c^{2} is

Solution
a + b + c = 9
a^{2} + b^{2} + c^{2} = (a + b + c)^{2}  2 (ab + bc + ca)
ab + bc + ca will be maximum if a = b  c
a^{2} + b^{2} + c^{2} = 9^{2}  2 × 27 = 81  54 = 27
Find the next two letters in the given series BCEHL??

Solution