Staff Selection Commission Combined Graduate Level Exam
Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm, and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:
Option 1: 11.6
Option 2: 10.8
Option 3: 13.4
Option 4: 12.7
Correct Answer: 12.7
Solution : According to the question DE || BC using basic proportionality theorem ⇒ $\frac{AD}{DB}$ = $\frac{AE}{EC}$ ⇒ $\frac{5}{9}$ = $\frac{4}{EC}$ ⇒ EC = $\frac{36}{5}$ = 7.2 cm Now, since the two triangles ADE and ABC are similar ⇒ $\frac{AD}{AB}$ = $\frac{DE}{BC}$ ⇒ $\frac{5}{14}$ = $\frac{DE}{15.4}$ ⇒
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
The amount multiplies over a period of time.
(1) within
(2) in
(3) by
(4) No improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct answer is the fourth option.
Explanation: The original phrase "multiplies over" effectively conveys the idea that the amount increases or grows over a period of time.
The meanings of the other options are as follows:
'Within" suggests a time frame or limit, but
Question : If a nine-digit number 789x6378y is divisible by 72, then the value of xy is:
Option 1: 10
Option 2: 12
Option 3: 8
Option 4: 15
Correct Answer: 8
Solution : Given number = 789x6378y Since the number is divisible by 72 It means it is divisible by 8 and 9 both. For divisible by 8 ⇒ last 3 digits 78y is divisible by 8 when y = 4 Now, the number becomes 789x63784 For divisible
Question : Direction: In this question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. A can be represented by 02,14, 40, etc. and P can be represented by 56, 75, 87, etc. Similarly, you have to identify the set for the word TAKE.
Option 1: 23, 21, 85, 95
Option 2: 30, 33, 87, 88
Option 3: 04, 33, 66, 99
Option 4: 11, 21, 85, 86
Correct Answer: 23, 21, 85, 95
Solution : Given – TAKE
Option first: 23, 21, 85, 95
TAKE
The first set represents the word TAKE.
Option second: 30, 33, 87, 88
TAPE
Option third: 04, 33, 66, 99
TAKP
Option fourth: 11, 21, 85, 86
TAKS
Hence, first option is
Question : Directions: Which of the following letter clusters will replace the question mark (?) and complete the following letter cluster series? LE, OJ, UO, DT, (?)
Option 1: PZ
Option 2: QY
Option 3: PX
Option 4: PY
Correct Answer: PY
Solution : Given: LE, OJ, UO, DT, ?
Add multiples of 3 to the first letter of the series and add 5 to the second letter of the series. LE: L + 3 = O; E + 5 = J. OJ: O + 6 = U; J
Question : In 1979, who shared the Nobel Prize with Georg Wittig for their ‘development of the use of Boron- and Phosphorus-containing compounds, respectively, into important reagents in organic synthesis’?
Option 1: Herbert C. Brown
Option 2: Arne Tiselius
Option 3: Henry Taube
Option 4: Emil Fischer
Correct Answer: Herbert C. Brown
Solution : The correct answer is Herbert C. Brown.
Herbert C. Brown, along with Georg Wittig of the University of Heidelberg, was jointly awarded the Nobel Prize in Chemistry in 1979 for their independent contributions to organic synthesis. Purdue University commemorates his achievements
Question : Directions: Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given equation. 32 * 42 * 7 * 7 * 17 = 202
Option 1: ×, ÷, –, +
Option 2: ×, –, +, ÷
Option 3: +, ÷, ×, –
Option 4: +, ×, ÷, –
Correct Answer: ×, ÷, –, +
Solution : Given: 32 * 42 * 7 * 7 * 17 = 202
Let's check the given options – First option: ×, ÷, –, + ⇒ 32 × 42 ÷ 7 – 7 + 17 = 202 Solving the L.H.S. of the equation
Question : Directions: If A – B means that A is the mother of B, A + B means that A is the father of B, and A ÷ B means that A is the sister of B, then which of the following expressions shows that P is the aunt of Q?
Option 1: P + R ÷ Q
Option 2: Q ÷ R + P
Option 3: P ÷ R – Q
Option 4: R ÷ P – Q
Correct Answer: P ÷ R – Q
Solution : Given: A – B ⇒ A is the mother of B A + B ⇒ A is the father of B A ÷ B ⇒ A is the sister of B
Let's check each option – First option: P + R
Question : Direction: If the first and second letters in the word COMMUNICATIONS were interchanged, also the third and the fourth letters, the 5th and 6th letters, and so on, which letter would be the tenth letter counting from the right end?
Option 1: N
Option 2: U
Option 3: A
Option 4: T
Correct Answer: N
Solution : Assign the numbers consecutively to each letter individually of the given letter cluster as shown below –
Question : If $a+b=1$, then $a^4+b^4-a^3-b^3-2a^2b^2+ab$ is equal to:
Option 1: 1
Option 2: 2
Option 3: 4
Option 4: 0
Correct Answer: 0
Solution : Given: $a+b=1$ (equation 1) We know that the algebraic identities are $(a-b)^2=a^2+b^2-2ab$, $(a^3+b^3)=(a+b)(a^2-ab+b^2)$ and $(a^2-b^2)=(a+b)(a-b)$. So, $a^4+b^4-2a^2b^2-a^3-b^3+ab$ $=(a^2-b^2)^2-(a^3+b^3)+ab$ $=(a+b)^2(a-b)^2-(a+b)(a^2-ab+b^2)+ab$ Substituting the value from equation 1 in the above expression we get, $a^4+b^4-2a^2b^2-a^3-b^3+ab=(a-b)^2-a^2+ab-b^2+ab$ $=(a-b)^2-(a^2-2ab+b^2)$ $=(a-b)^2-(a-b)^2=0$ Hence, the correct answer is 0.
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