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- Total number of questions : 20
- Time allotted : 30:00 Minutes:Seconds.
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Quantitative Aptitude [ Question No: 1 To 17 ] :
At 40 past 4 in the evening, the smaller angle between the hour and minute hands of a clock is :
A ladder reaches a window that is 8 m above the ground on one side of the street. Keeping its foot on the same point, the ladder is twined to the other side of the street to reach a window 12 m high. Find the width of the street if the ladder is 13 m.
A retailer buys 40 pens at the market price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
Given below are two statements:
Statement I : If the side of a square is doubled, its area also doubles.
Statement II : The perimeter of a square increases linearly with the length of its side.
In the light of the above statements,choose the Correct answer from the options given below:
The sum of the greatest and smallest six digit numbers that can be formed from the digits 5, 9, 0, 2, 8 and 6 (without repetition) is :
Which of the following has/have only two lines of symmetry?
A. Equilateral triangle
B. Rectangle
C. Rhombus
D. Isosceles triangle
Choose the correct option.
The area of a rectangle whose sides are 176 cm and 56 cm is equal to the area of a circle. What is the circumference (in cm) of the circle ? (Take \(\pi = \dfrac{22}{7}\))
If we have to make numbers 8, 12, 16 and 22 in proportion, what number must be added to each number?
The total runs scored by four cricketers P, Q, R, and S in years 2009 and 2010 are given in the following table:
| Player | 2009 | 2010 |
|---|---|---|
| P | 802 | 1008 |
| Q | 765 | 912 |
| R | 429 | 619 |
| S | 501 | 701 |
The player with the lowest percentage increase in total runs is
The sum of four consecutive odd numbers is 112. The smallest number is:
What is the unit digit of \(32^{32}\)?
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
A bill for ₹3,000 due 6 months hence is discounted at 8% per annum. What is the banker’s discount?
Gurpreet went to a shop and bought a sofa, on which she got a 20% discount. Had she been given a 25% discount she would have saved Rs. 1000 more. What was the marked price of the sofa?
A circle is inscribed in a square. If the difference between area of the square and circle is 262.5 cm², then find the area of the rectangle whose perimeter is same as that of circle while length of rectangle is 20% more than the breadth of rectangle (in cm²).
The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is
If \(3\sqrt{5} + \sqrt{125}= 17.88\) , then what will be the value of\(\sqrt{80} + 16\sqrt{5}\) ?
Organic Chemistry [ Question No: 18 To 19 ] :
Which of the following will produce chiral product on treatment with :
(i) O3, MeOH; (ii) H2O2; (iii) Heat (-CO2)
The major product of the following reaction is :
Physical Chemistry [ Question No: 20 To 20 ] :
4 g of NaOH were dissolved in 1 litre of a solution containing 1 mole of CH3COOH and 1 mole of CH3COONa. The [H+] in the resultant solution is
(Given: Ka (CH3COOH) = 1.1×10-5)
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 17 ] :
At 40 past 4 in the evening, the smaller angle between the hour and minute hands of a clock is :
Your Answer : (Not Answered)
Correct Answer : D
The smaller angle is 100°.
The angle between the hands at H hours M minutes is \(|30H - 5.5M|\):
\[ \begin{aligned} |30 \times 4 - 5.5 \times 40| &= |120 - 220| \\ &= 100^\circ \end{aligned} \]
At 4:40 the minute hand points at 8 (240°) and the hour hand has moved two-thirds of the way from 4 to 5 (140°), so they are 100° apart. Forgetting the hour hand's movement gives 120°, which is not offered.
A ladder reaches a window that is 8 m above the ground on one side of the street. Keeping its foot on the same point, the ladder is twined to the other side of the street to reach a window 12 m high. Find the width of the street if the ladder is 13 m.
Your Answer : (Not Answered)
Correct Answer : A
The street is about 15.2 m wide.
The ladder's foot stays at one point, so the street's width is the sum of the two horizontal distances from the foot to each wall:
\[ \begin{aligned} \text{side 1} &= \sqrt{13^2 - 8^2} \\ &= \sqrt{105} \approx 10.25 \\ \text{side 2} &= \sqrt{13^2 - 12^2} = 5 \\ \text{width} &\approx 15.25 \text{ m} \end{aligned} \]
The paper's 15·2 m is this value cut to one decimal. 14 m and 14·6 m are both shorter than 10.25 + 5, and 12 m is the height of the second window, not a width.
A retailer buys 40 pens at the market price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
Your Answer : (Not Answered)
Correct Answer : B
The profit is 10%.
Take the market price of one pen as 1. The retailer pays the price of 36 pens for 40, and sells each at 1% below the market price:
\[ \begin{aligned} CP &= 36/40 = 0.90 \\ SP &= 0.99 \\ \text{profit} &= 0.09/0.90 = 10\% \end{aligned} \]
11% is the profit without the discount (4/36), and 9% comes from dividing the gain by the selling price instead of the cost.
Given below are two statements:
Statement I : If the side of a square is doubled, its area also doubles.
Statement II : The perimeter of a square increases linearly with the length of its side.
In the light of the above statements,choose the Correct answer from the options given below:
Your Answer : (Not Answered)
Correct Answer : D
Statement I is false but Statement II is true.
Area grows with the square of the side. Doubling a side of length a gives
\[ (2a)^2 = 4a^2 \]
so the area becomes four times as large, not twice. Statement I is false.
The perimeter is \(4a\), a straight-line (linear) function of a: doubling the side doubles the perimeter. Statement II is true. The options calling Statement I true confuse the perimeter's behaviour with the area's.
The sum of the greatest and smallest six digit numbers that can be formed from the digits 5, 9, 0, 2, 8 and 6 (without repetition) is :
Your Answer : (Not Answered)
Correct Answer : B
The sum is 1192209.
The greatest six-digit number from 5, 9, 0, 2, 8, 6 puts the digits in descending order: 986520.
The smallest puts them in ascending order, but a six-digit number cannot start with 0, so the smallest non-zero digit, 2, goes first and 0 second: 205689.
\[ 986520 + 205689 = 1192209 \]
Option A, 1192290, comes from a slip in the units digits, and the options starting 1292 come from adding 100000 too much. Starting the smallest number with 0 would give only a five-digit number, which is the trap the question sets.
Which of the following has/have only two lines of symmetry?
A. Equilateral triangle
B. Rectangle
C. Rhombus
D. Isosceles triangle
Choose the correct option.
Your Answer : (Not Answered)
Correct Answer : C
The answer is B and C: the rectangle and the rhombus.
A rectangle (that is not a square) has exactly two lines of symmetry, joining the midpoints of opposite sides. A rhombus (that is not a square) also has exactly two, along its diagonals.
An equilateral triangle has three lines of symmetry and an isosceles triangle has only one, so any option containing A or D is wrong, and 'Only B' leaves out the rhombus.
The area of a rectangle whose sides are 176 cm and 56 cm is equal to the area of a circle. What is the circumference (in cm) of the circle ? (Take \(\pi = \dfrac{22}{7}\))
Your Answer : (Not Answered)
Correct Answer : B
The circumference is 352 cm.
\[ \begin{aligned} \pi r^{2} &= 176 \times 56 = 9856 \\ r^{2} &= 9856 \times \frac{7}{22} = 3136 \\ r &= 56\ \text{cm} \\ C &= 2 \times \frac{22}{7} \times 56 = 352\ \text{cm} \end{aligned} \]
396 cm would need a radius of 63 cm, 440 cm a radius of 70 cm and 308 cm a radius of 49 cm; none of these gives an area equal to the rectangle's 9856 square cm.
If we have to make numbers 8, 12, 16 and 22 in proportion, what number must be added to each number?
Your Answer : (Not Answered)
Correct Answer : B
Four numbers a, b, c and d are in proportion when \(a : b = c : d\), that is, \(a \times d = b \times c\). Let x be added to each of 8, 12, 16 and 22.
\[ (8 + x)(22 + x) = (12 + x)(16 + x) \]
\[ 176 + 30x + x^2 = 192 + 28x + x^2 \] \[ 2x = 16 \Rightarrow x = 8 \]
Check: 16, 20, 24 and 30 have 16 : 20 = 24 : 30 = 4 : 5. The values 7, 9 and 10 do not make the products equal. The answer is 8, option B.
The total runs scored by four cricketers P, Q, R, and S in years 2009 and 2010 are given in the following table:
| Player | 2009 | 2010 |
|---|---|---|
| P | 802 | 1008 |
| Q | 765 | 912 |
| R | 429 | 619 |
| S | 501 | 701 |
The player with the lowest percentage increase in total runs is
Your Answer : (Not Answered)
Correct Answer : B
The lowest percentage increase belongs to Q.
Percentage increase = (2010 runs - 2009 runs) / 2009 runs x 100:
\[ \begin{aligned} P &: 206/802 = 25.7\% \\ Q &: 147/765 = 19.2\% \\ R &: 190/429 = 44.3\% \\ S &: 200/501 = 39.9\% \end{aligned} \]
Q has the smallest increase, both in runs (147) and as a percentage. P has the highest totals and might look slowest-growing at a glance, but its increase is 25.7%. R and S, starting from lower bases, grew fastest.
The sum of four consecutive odd numbers is 112. The smallest number is:
Your Answer : (Not Answered)
Correct Answer : A
Four consecutive odd numbers are symmetric about their average.
\[ \frac{112}{4} = 28 \]
The four numbers straddle 28 in steps of 2:
\[ 25,\ 27,\ 29,\ 31 \]
So the smallest is 25. Setting up \( x + (x+2) + (x+4) + (x+6) = 112 \) gives \( 4x + 12 = 112 \) and the same answer.
What is the unit digit of \(32^{32}\)?
Your Answer : (Not Answered)
Correct Answer : C
To find the unit digit of \(32^{32}\), we only need to consider the unit digit of the base, which is 2. So the problem is to find the unit digit of \(2^{32}\). The power cycle for 2 is (2, 4, 8, 6), with a length of 4. We need to find the remainder of the power \(32\) when divided by 4. Since 32 is a multiple of 4, the remainder is 0. A remainder of 0 corresponds to the last digit in the cycle, which is 6.
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Your Answer : (Not Answered)
Correct Answer : B
The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
A bill for ₹3,000 due 6 months hence is discounted at 8% per annum. What is the banker’s discount?
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: ₹120
The banker’s discount is simple interest on the face value for the unexpired period: \[ \text{BD} = \frac{3000 \times 8 \times \tfrac{1}{2}}{100} = \frac{12000}{100} = 120. \] The banker hands over \( 3000 - 120 = 2880 \), which is the discounted value of the bill, and collects the full 3,000 at maturity. The mathematically fair charge would be the true discount, \[ \text{TD} = \frac{3000 \times 4}{104} \approx 115.38, \] which is the second option - and the difference of about 4.62 is the banker’s gain, the banker’s profit on the transaction. That gap is the whole point of the topic: a banker charges interest on the amount that will be received rather than on the amount actually advanced, and so always gains a little.
Gurpreet went to a shop and bought a sofa, on which she got a 20% discount. Had she been given a 25% discount she would have saved Rs. 1000 more. What was the marked price of the sofa?
Your Answer : (Not Answered)
Correct Answer : C
The extra saving comes from the extra 5 percentage points of discount, and that difference is measured on the marked price.
\[ (25\% - 20\%) \times \text{MP} = 1000 \]
\[ 0.05 \times \text{MP} = 1000 \quad\Longrightarrow\quad \text{MP} = \frac{1000}{0.05} = \text{Rs. } 20{,}000 \]
As a check, a 20% discount leaves Rs. 16,000 and a 25% discount leaves Rs. 15,000 - a difference of exactly Rs. 1000. Only the gap between the two discount rates matters, never either rate on its own.
A circle is inscribed in a square. If the difference between area of the square and circle is 262.5 cm², then find the area of the rectangle whose perimeter is same as that of circle while length of rectangle is 20% more than the breadth of rectangle (in cm²).
Your Answer : (Not Answered)
Correct Answer : D
Let the side of square be 2a.
So, the diameter of circle = 2a
Radius of circle = a
WKT, Area of square = 4a
Area of circle = π r²
Perimeter of circle = 2π r
Area of rectangle = l x b
Perimeter of rectangle = 2(l + b)
Given that difference between area of the square and circle is 262.5 cm².
Area of square - Area of circle = 262.5
4a² - (22/7)a² = 262.5
28a² - 22a² = 1837.5
6a² = 1837.5
a² = 306.25
a = 17.5 cm
Perimeter of circle = 2πa = 2 x (22/7) x 17.5 = 110 cm
Also given length of rectangle is 20% more than the breadth of rectangle.
Let the breadth of rectangle be X.
So, length of rectangle = (120/100)X = 1.2X
As per the question,
Perimeter of rectangle = Perimeter of circle
2(1.2X + X) = 110
2.4X + 2X = 110
4.4X = 110
X = 25 cm
Breadth of rectangle = 25 cm
Length of rectangle = 1.2(25) = 30 cm
Area of rectangle = 25 x 30 = 750 cm².
The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is
Your Answer : (Not Answered)
Correct Answer : B
For a frustum the slant height spans the difference of the radii horizontally and the height vertically.
\[ l = \sqrt{h^{2} + (R - r)^{2}} \]
\[ l = \sqrt{4^{2} + (5-2)^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ cm} \]
It is the difference of the radii, not their sum, that forms the horizontal leg - using \( 5+2 \) would give \( \sqrt{65} \), the third option.
If \(3\sqrt{5} + \sqrt{125}= 17.88\) , then what will be the value of\(\sqrt{80} + 16\sqrt{5}\) ?
Your Answer : (Not Answered)
Correct Answer : D
\(3\sqrt{5} + \sqrt{125}= 17.88\\ \Rightarrow 3\sqrt{5} + \sqrt{25 \times 5}= 17.88\\ \Rightarrow 3\sqrt{5} + 5\sqrt{5}= 17.88\\ \Rightarrow 8\sqrt{5}= 17.88\\ \Rightarrow \sqrt{5}= \dfrac{17.88}{8} = 2.235\\\\ \therefore \sqrt{80} + 16\sqrt{5}\\= \sqrt{16 \times 5} + 16\sqrt{5} \\ 4\sqrt{5} + 16\sqrt{5}\\= 20\sqrt{5}\\ = 20 \times 2.235\\ = 44.7\)
Organic Chemistry [ Question No: 18 To 19 ] :
Which of the following will produce chiral product on treatment with :
(i) O3, MeOH; (ii) H2O2; (iii) Heat (-CO2)
Your Answer : (Not Answered)
Correct Answer : D
Only (D), norbornen-2-one, gives a chiral product.
Ozonolysis with oxidative work-up (H2O2) cleaves the C=C to two COOH groups on a cyclopentane ring. Heating then removes CO2 from any COOH that is β to a ketone (a β-keto acid).
- (A) norbornene: gives cis-cyclopentane-1,3-dicarboxylic acid, a meso compound, with no ketone to lose CO2.
- (B) the 7-ketone: both COOH groups are β to it, both are lost, leaving cyclopentanone, achiral.
- (C) the 2,7-dione: again both COOH groups are lost, leaving cyclopentane-1,3-dione, achiral.
- (D) the 2-ketone: only one COOH is β to the ketone and is lost; the other remains, giving 3-oxocyclopentanecarboxylic acid, whose ring carbon bearing COOH is a stereocentre.
So only (D) gives a chiral product (formed as a racemate).
The major product of the following reaction is :
Your Answer : (Not Answered)
Correct Answer : D
The major product is (D), 2-bromobutanoic acid formed with retention of configuration.
Diazotisation of an α-amino acid with NaNO2 and HBr converts NH2 into the diazonium group. The neighbouring carboxylate attacks the carbon from the back, expelling N2 with inversion and forming a strained α-lactone. Bromide then opens the α-lactone at the same carbon, again with inversion. Two inversions give overall retention, so Br takes the place of NH2 with H and Et unchanged.
Structure (D) matches the starting material with Br in the position of NH2. (A) shows the inverted configuration, (C) a racemic product and (B) an elimination product, none of which this neighbouring-group mechanism gives.
Physical Chemistry [ Question No: 20 To 20 ] :
4 g of NaOH were dissolved in 1 litre of a solution containing 1 mole of CH3COOH and 1 mole of CH3COONa. The [H+] in the resultant solution is
(Given: Ka (CH3COOH) = 1.1×10-5)
Your Answer : (Not Answered)
Correct Answer : E
The hydrogen ion concentration is \(0.9 \times 10^{-5}\) M.
4 g of NaOH is 0.1 mol. It neutralises 0.1 mol of the acetic acid, forming 0.1 mol more acetate, so the buffer now holds 0.9 mol acid and 1.1 mol salt in 1 L. For an acidic buffer:
\[ \begin{aligned} [\mathrm{H^{+}}] &= K_{a} \times \frac{[\text{acid}]}{[\text{salt}]} \\ &= 1.1 \times 10^{-5} \times \frac{0.9}{1.1} = 0.9 \times 10^{-5}\ \text{M} \end{aligned} \]
The added base lowers \([\mathrm{H^{+}}]\) only slightly from \(1.1 \times 10^{-5}\) M, which is the buffer action. Every other option is above \(1.1 \times 10^{-5}\) M, which would mean adding a base made the solution more acidic.
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20