SET - 1

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

•  (A)  I will not leave the place until the minister does not meet me.
•  (B)  I will not leave the place until the minister doesn’t meet me.
•  (C)  I will not leave the place until the minister meet me.
•  (D)  I will not leave the place until the minister meets me.

A rewording of something written or spoken is a ______________.

•  (A)  paraphrase
•  (B)  paradox
•  (C)  paradigm
•  (D)  paraffin

•  (A)  figurative
•  (B)  collateral
•  (C)  literal
•  (D)  figurine

•  (A)  zentaga
•  (B)  tagafer
•  (C)  tagazen
•  (D)  relffer

•  (A)  56
•  (B)  64
•  (C)  72
•  (D)  96

•  (A)  Elegance
•  (B)  Executive
•  (C)  Smooth
•  (D)  Soft

Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is.

Which of the following can be logically inferred from the above sentences?

•  (A)  India is a country of exactly seventeen languages.
•  (B)  Linguistic pluralism is the only indicator of a nation’s diversity.
•  (C)  Indian currency notes have sufficient space for all the Indian languages.
•  (D)  Linguistic pluralism is strong evidence of India’s diversity.

Consider the following statements relating to the level of poker play of four players P, Q, R and S.

I. P always beats Q

II. R always beats S

III. S loses to P only sometimes

IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players

(ii) S is the absolute worst player in the set

•  (A)  (i) only
•  (B)  (ii) only
•  (C)  (i) and (ii)
•  (D)  neither (i) nor (ii)

If $ \mathrm f\left(x\right)=2x^7+3x-5 $, which of the following is a factor of $\mathrm{f}\left(x\right)$ ?

•  (A)  $\left(x^3+8\right)$
•  (B)  $\left(x-1\right)$
•  (C)  $\left(2x-5\right)$
•  (D)  $\left(x+1\right)$

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

•  (A)  40.00
•  (B)  46.02
•  (C)  60.01
•  (D)  92.02

Newton-Raphson method is to be used to find root of equation $3x-e^x+\sin x=0$ If the initial trial value for the root is taken as 0.333, the next approximation for the root would be _________

(note: answer up to three decimal)

The type of partial differential equation $\frac{{\partial }^{2}P}{\partial x^2}+\frac{{\partial }^{2}P}{\partial y^2}+3\frac{{\partial }^{2}P}{\partial x\partial y}+2\frac{\partial P}{\partial x}-\frac{\partial P}{\partial y}=0$ is

•  (A)  elliptic
•  (B)  parabolic
•  (C)  hyperbolic
•  (D)  none of these

If the entries in each column of a square matrix ${\rm M}$ add up to 1, then an eigenvalue of ${\rm M}$ is

•  (A)  4
•  (B)  3
•  (C)  2
•  (D)  1

Type II error in hypothesis testing is

•  (A)  acceptance of the null hypothesis when it is false and should be rejected
•  (B)  rejection of the null hypothesis when it is true and should be accepted
•  (C)  rejection of the null hypothesis when it is false and should be rejected
•  (D)  acceptance of the null hypothesis when it is true and should be accepted

The solution of the partial differential equation $\frac{\partial u}{\partial t}=\alpha \frac{{\partial }^{2}u}{\partial x^2}$ is of the form

•  (A)  $\style{font-family:'Times New Roman'}{C\cos\left(kt\right)\left\lfloor C_1e^{\left(\sqrt{k/\alpha}\right)x}+C_2e^{-\left(\sqrt{k/\alpha}\right)x}\right\rfloor}$
•  (B)  $\style{font-family:'Times New Roman'}{Ce^{kt}\left\lfloor C_1e^{\left(\sqrt{k/\alpha}\right)x}+C_2e^{-\left(\sqrt{k/\alpha}\right)x}\right\rfloor}$
•  (C)  $\style{font-family:'Times New Roman'}{Ce^{kt}\left\lfloor C_1\cos\left(\sqrt{k/\alpha}\right)x+C_2\sin\left(-\sqrt{k/\alpha}\right)x\right\rfloor}$
•  (D)  $C\sin\left(kt\right)\left\lfloor c_1\cos\left(\sqrt{k/\alpha}\right)x+C_2\sin\left(-\sqrt{k/\alpha}\right)x\right\rfloor$

Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions at the joint B be H_B and V_B, respectively and V_C be the vertical reaction at the joint C.

Which one of the following sets gives the correct values of V_B, H_B and V_C?

•  (A)  ${\mathrm V}_\mathrm B=0;{\mathrm H}_\mathrm B=0;{\mathrm V}_\mathrm C=\mathrm P$
•  (B)  ${\mathrm V}_\mathrm B=\mathrm P/2;{\mathrm H}_\mathrm B=0;\;{\mathrm V}_\mathrm C=\mathrm P/2$
•  (C)  ${\mathrm V}_\mathrm B=\mathrm P/2;{\mathrm H}_\mathrm B=\mathrm P\left(\sin\;60^\circ\right);\;{\mathrm V}_\mathrm C=\mathrm P/2$
•  (D)  ${\mathrm V}_\mathrm B=\mathrm P;{\mathrm H}_\mathrm B=\mathrm P\left(\cos\;60^\circ\right);{\mathrm V}_\mathrm C=0$

In shear design of an RC beam, other than the allowable shear strength of concrete $ \style{font-family:'Times New Roman'}{\left(\tau_c\right)} $ , there is also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear stress $ \style{font-family:'Times New Roman'}{\left(\tau_{c\;\max}\right)} $ . The check for  $ \style{font-family:'Times New Roman'}{\tau_{c\;\max}} $ is required to take care of

•  (A) additional shear resistance from reinforcing steel
•  (B) additional shear stress that comes from accidental loading
•  (C) possibility of failure of concrete by diagonal tension
•  (D) possibility of crushing of concrete by diagonal compression

The semi-compact section of a laterally unsupported steel beam has an elastic section modulus, plastic section modulus and design bending compressive stress of $500\mathrm{cm}^3$ ,$650\mathrm{cm}^3$ and, $200\;\mathrm{MPa}$ respectively. The design flexural capacity (expressed in kNm) of the section is _________

Bull's trench kiln is used in the manufacturing of

•  (A)  lime
•  (B)  cement
•  (C)  bricks
•  (D)  none of these

The compound which is largely responsible for initial setting and early strength gain of Ordinary Portland Cement is

•  (A)  C₃A
•  (B)  C₃S
•  (C)  C₂S
•  (D)  C₄AF