**Set 2 :** **Maths Questions **

**Q.1:** A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?

(A) 1.9

(B) 2.7

(C) 2.5

(D) 2.1

###### Show Answer

**Q.2:** If $latex cos\theta =\frac{4x}{1+4x^2}$, then what is the value of $latex sin\theta$ ?

(A) $latex \frac{1+4x^2}{1-4x^2}$

(B) $latex \frac{1+4x^2}{4x^2}$

(C) $latex \frac{1-4x^2}{1+4x^2}$

(D) $latex \frac{1-4x^2}{4x}$

###### Show Answer

**Q.3:** In a triangle ABC, $latex \angle\text{BAC}=90^o$ and AD is perpendicular to BC. If AD = 8.4 cm and BD = 4.8 cm, then the length of BC is:

(A) 19.5 cm

(B) 15 cm

(C) 18 cm

(D) 18.5 cm

###### Show Answer

**Q.4:** Tap P can fill a cistern in 6 hours and tap Q can empty the full cistern in 10 hours. If both taps P and Q are kept open simultaneously, then in how many hours will the empty cistern be completely full ?

(A) 15

(B) 18

(C) 16

(D) 12

###### Show Answer

**Q.5:** One dozen notebooks quoted at ₹125 are available at 20% discount. How many notebooks can be bought for ₹75 ?

(A) 10

(B) 6

(C) 9

(D) 8

###### Show Answer

**Q.6:** A man invests ₹7,000 at 8% per annum simple interest for 2 years and ₹10,000 at compound interest at the sane rate for the same period, compounded annually. What will be the total interest and the total interest and the total amount (in ₹) respectively, on maturity ?

(A) 19,748 and 2,874

(B) 2,748 and 19,784

(C) 19,784 and 2,784

(D) 2,784 and 19,784

###### Show Answer

**Q.7:** If (sin A-cos A) =0, then what is the value of cot A ?

(A) $latex \frac\pi6$

(B) 0

(C) 1

(D) $latex \frac\pi4$

###### Show Answer

**Q.8:** A boat can travel with a speed of 19 km/h in still water. If the speed of the stream is 3 km/h, then what will be the total time ( in hours) taken by the boat to go 88 km downstream and 24 km upstream ?

(A) 4.5

(B) 5

(C) 4

(D) 5.5

###### Show Answer

**Q.9:** A is 150% of B and B is 40% of C. If A+B+C=20, then the value of 2B+3C-4A is equal to:

(A) 16

(B) 14

(C) 20

(D) 15

###### Show Answer

**Q.10:** The following histogram represents the distribution of household expenditure (in ₹) of 200 manual workers in a city.

(A) 3 : 5

(B) 2 : 5

(C) 4 : 5

(D) 3 : 4

###### Show Answer

**Q.11:** Using algebraic identities, simplify the following expression.**$latex \frac{(x^4+x^2+1)}{x^2+x+1)}$**

(A) (x^{2} – 2x + 1)

(B) (x^{2} + x + 1)

(C) (x^{2} + 2x + 1)

(D) (x^{2} – x + 1)

###### Show Answer

^{2}– x + 1)

**Q.12:** Students of Primary, Middle, Secondary and Sr. Secondary classes collected donation for a Relief Fund as shown in the pie chart. If the donation collected from Middle classes was ₹6,750 then how much money was collected by the Primary classes ?

(A) ₹4,050

(B) ₹4,005

(C) ₹4,500

(D) ₹3,960

###### Show Answer

**Q.13:** One quarter of a circular pizza of diameter 28 cm was removed from the whole pizza. What is the perimeter (in cm) of the remaining pizza ? (take $latex \pi=\frac{22}{7})$

(A) 88

(B) 94

(C) 80

(D) 66

###### Show Answer

**Q.14:** The inner and outer radii of two concentric circles are 6.7 cm and 9.5 cm, respectively. What is the difference between their circumferences (in cm) ? Take $latex \pi=\frac{22}{7}$

(A) 20.5

(B) 10.5

(C) 6.5

(D) 17.6

###### Show Answer

**Q.15:** Study the given graph and answer the question that follows.

(A) 2016

(B) 2018

(C) 2017

(D) 2019

###### Show Answer

**Q.16:** What is the perimeter (in cm) of an equilateral triangle whose height is 3.46 cm? take $latex \sqrt3=1.73$.

(A) 10.4

(B) 9

(C) 6

(D) 12

###### Show Answer

**Q.17:** The value of $latex [(232\div29 of 2)+ 77\times10\div18] -\frac{18\times8\div4 of 3-4}{2\times(8-6)+1-2\times3\div4 of\frac12}$ is:

(A) 39

(B) 44

(C) 33

(D) 47

###### Show Answer

**Q.18:** The string of a kite is 158 m long and it makes an angle of 30^{o} with the horizontal. What is height (in m) of the kite? Assume there is no slack in the string.

(A) 100

(B) 99

(C) 79

(D) 80

###### Show Answer

**Q.19:** If $latex (x+\frac1x)^3=27$, then what is the value of $latex (x^2+\frac{1}{x^2})$? Given that x is real.

(A) 11

(B) 25

(C) 7

(D) 9

###### Show Answer

**Q.20:** What is the area (in cm^{2}, correct to one decimal place) of a triangle whose base is 214 cm and height is 15.5 cm?

(A) 165.9

(B) 156.6

(C) 165.6

(D) 156.9

###### Show Answer

**Q.21:** One-fifth of a journey is covered at a speed of km/h, one-fourth of the journey at a speed of 25 km/h and the rest at 60 km/h. What is the average speed (in km/h, correct to one decimal place) for the whole journey?

(A) 38.7

(B) 30.6

(C) 40.5

(D) 25.4

###### Show Answer

**Q.22:** If a + b = p, ab = q, then (a^{4} + b^{4}) is equal to:

(A) p^{4} – 2p^{2}q^{2} + q^{2}

(B) p^{4} – 4p^{2}q^{2} + 2q^{2}

(C) p^{4} – 4p^{2}q + q^{2}

(D) p^{4} – 4p^{2}q + 2q^{2}

###### Show Answer

^{4}– 4p

^{2}q + 2q

^{2}

**Q.23:** What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21 and 5 ?

(A) 92680

(B) 99120

(C) 95760

(D) 98320

###### Show Answer

**Q.24:** By selling an article for 1,170, Elisa suffers as much loss as she would have gained by selling it at a profit of 22%. If she sells it for 1,450, then her profit/loss per cent (correct up to one decimal place) is:

(A) Profit, 3.3

(B) Loss, 3.3

(C) Loss, 26.2

(D) Profit, 26.2

###### Show Answer

**Q.25:** If A : B = 11 : 7 and B : C = 5 : 19, then what is A : B : C ?

(A) 55 : 35 : 133

(B) 35 : 55 : 133

(C) 35 : 133 : 55

(D) 55 : 133 : 35

###### Show Answer

Maths Questions for SSC CHSL