List of top Questions asked in CAT

Choose the correct phrasal usage of the given words:
[I.] Trace to
[II.] Sparing of
[III.] Replete with
[IV.] Wonder at \bigskip
Choose the correct sequence of sentences:
[I.] But she gained courage as she went on
[II.] She was a little nervous about it just at first
[III.] and opened their eyes and mouths so very wide
[IV.] the two creatures got so close to her, one on each side \bigskip
Choose the correct sequence of sentences:
[I.] It would perhaps be possible for him to be of some use to this brave girl
[II.] he said to himself, vaguely at first, that
[III.] without neglecting anything of what was due to his important mission.
[IV.] and this idea pleased him \bigskip
Match the dictionary definitions of the word "Catch" with its correct usage:
[A.] Capture
[B.] Grasp with senses or mind
[C.] Deception
[D.] Thing or person worth trapping Usage:
[E.] All her friends agreed that Prasad was a good catch.
[F.] The proposal sounds very good but where is the catch?
[G.] Hussain tries to catch the spirit of India in this painting.
[H.] Sorry, I couldn’t catch you. \bigskip
______ of different categories of problems often leads to design of improper solutions that fail to address the complexities of the problem. \bigskip
Choose the option that points out sentence(s) with grammatical error(s):
[I.] I love the man dancing on the table.
[II.] I love the man’s dancing on the table.
[III.] In 1986 Elie Wiesel was named the Nobel Peace Prize recipient, an honour established by Alfred Nobel.
[IV.] Neither of the recommendations works as well as we thought they would.
[V.] Either the Minister or the Minister’s wife will have to excuse themselves from the reception to speak to the caterer. \bigskip
During the heated discussion, the leader of the group ______ refuted all the claims brought by his opponents. Later everybody acknowledged that he survived by most ______ luck. \bigskip
Justice Minister Bola Ige, confronted with the general incivility of local police, placed a ______ on the cads. Said the Hon. Bola Ige, “I pray that God will make big holes in their pockets.” \bigskip
Match the dictionary definitions of the word "Infer" with its correct usage:
[A.] To derive by reasoning or implication
[B.] To surmise
[C.] To point out
[D.] To hint Usage:
[E.] We see smoke and infer fire
[F.] Given some utterance, a listener may infer from it all sorts of things which neither the utterance nor the utterer implied
[G.] I waited all day to meet him. From this you can infer my zeal to see him.
[H.] She did not take part in the debate except to ask a question inferring that she was not interested in the debate. \bigskip
If \( r, s, t \) are consecutive odd integers with \( r<s<t \), which of the following must be true?
Let \( S \) be the set of rational numbers with the following properties:
[I.] \( \frac{1}{2} \in S \)
[II.] If \( x \in S \), then both \( \frac{1}{x+1} \in S \) and \( \frac{x}{x+1} \in S \) Which of the following is true?
\( P, Q, R \) are three consecutive odd numbers in ascending order. If the value of three times \( P \) is three less than two times \( R \), find the value of \( R \).
Consider the following statements: When two straight lines intersect, then:
[I.] Adjacent angles are complementary
[II.] Adjacent angles are supplementary
[III.] Opposite angles are equal
[IV.] Opposite angles are supplementary Which of these statements are correct?
A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates \( A \) and \( B \) on the boundary is 7 metres. The distance of the pole from one of the gates is:
From a square piece of cardboard measuring \( 2a \) on each side, a box with no top is to be formed by cutting out from each corner a square with sides \( b \) and bending up the flaps. The value of \( b \) for which the box has the greatest volume is:
The sum of the areas of two circles which touch each other externally is \( 153\pi \). If the sum of their radii is 15, find the ratio of the larger to the smaller radius.
Consider the following statements:
[I.] If \( a^x = b^x = c^x = abc \), then \( xyz = 1 \)
[II.] If \( a^p = b^q = c^r \) and \( a^q b^r c^p = 1 \), then \( xyz = 1 \)
[III.] If \( x^a = y^b = z^c \) and \( ab + bc + ca = 0 \), then \( xyz = 1 \)
If \( a, b, c \) are three real numbers, then which of the following is not true?
Let \( S \) denote the infinite sum: \[ S = 2 + 5x + 9x^2 + 14x^3 + 20x^4 + \ldots \quad \text{where } |x|<1 \] and the coefficient of \( x^n \) is \( \frac{1}{2}n(n+3) \). Then \( S \) equals:
ABCD is a rectangle. Points \( P \) and \( Q \) lie on \( AD \) and \( AB \) respectively. If triangles \( PAQ, QBC, \) and \( PCD \) all have the same areas and \( BQ = 2 \), then \( AQ = \) ?

For what value of \( k \) does the following pair of equations yield a unique solution for \( x \), such that the solution is positive?

\(x^2 - 3y^2 = 0 \)
\(x^2 - 6y^2 + k = 0 \)

In an examination, the average marks obtained by students who passed was \( x\% \), while the average of those who failed was \( y\% \). The average marks of all students taking the exam was \( z\% \). Find in terms of \( x, y, z \), the percentage of students taking the exam who failed.
If \( a = \log 2, b = \log 3, c = \log 4 \), then the value of \( \log(abcd) \) would be:
If three positive real numbers \( a, b, c \) (with \( c>a \)) are in Harmonic Progression, then \( \log(a + c) + \log(a - 2b + c) \) is equal to:

Let \( f \) be an injective map with domain x, y, z and range 1, 2, 3 such that exactly one of the following statements is correct and the remaining are false.} 
[I.] \( f(x) = 1 \Rightarrow f(y) = 1, f(z) = 2 \) 
[II.] \( f(x) = 2 \Rightarrow f(y) = 1, f(z) = 1 \) 
[III.] \( f(x) = 1, f(y) = 1, f(z) = 2 \) Then the value of \( f(1) \) is: