Maharashtra AAC Common Entrance Test
With a MHT CET score of 150, you may have a chance to get into various colleges in Maharashtra, especially government colleges and some private institutions. However, top-tier colleges like COEP Pune, VJTI Mumbai, and MIT Pune might be challenging unless you belong to a reserved category or meet additional
Question : The value of $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$ is:
Option 1: 3
Option 2: 4
Option 3: –1
Option 4: –2
Correct Answer: –2
Solution : $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$ $= \frac{3\left(\operatorname{sec}^2 64^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\operatorname{cosec} ^2 42^{\circ}\right)}{\tan \left(68^{\circ}+\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\cot ^2\left(62^{\circ}+\theta\right)}$ $= \frac{3\left(1\right)+\left(\cot ^2 42^{\circ}-1-\cot ^2 42^{\circ}\right)}{-(\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\cot ^2\left(62^{\circ}+\theta\right))}$ $= \frac{3-1}{-1}$ $= -2$ Hence, the correct answer is –2.
Question : Directions: Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. AEI, EIO, IOU, ?
Option 1: UAE
Option 2: AEI
Option 3: OUA
Option 4: All
Correct Answer: OUA
Solution : Given: AEI, EIO, IOU, ?
Vowels are replaced with immediate next vowels according to the English alphabetical series and the order is – A, E, I, O, U AEI → The immediate next vowel of A is E, the Immediate next vowel of E is
Question : Case Study 72
OPQ Corporation is a conglomerate planning to trade its shares on a stock exchange. The company's management is reviewing the roles of stockbrokers.
Question :
What type of broker offers advice to clients and executes orders on their behalf?
Option 1: Full-service broker
Option 2: Discount broker
Option 3: Floor broker
Option 4: Specialist broker
Correct Answer: Full-service broker
Solution : The correct answer is (a) Full-service broker
A full-service broker is a type of broker that offers a wide range of services to clients, including investment advice, research, financial planning, and execution of orders on behalf of their clients. They provide personalized assistance and
Question : Three metallic spheres of radii 10 cm, 8 cm, and 6 cm, respectively are melted to form a single solid cone of radius 12 cm. Find the curved surface area of the cone, correct to two places of decimal. (Take $\pi=3.14$)
Option 1: $1664.50 \text{ cm}^2$
Option 2: $1669.86 \text{ cm}^2$
Option 3: $1876.79 \text{ cm}^2$
Option 4: $1864.41 \text{ cm}^2$
Correct Answer: $1864.41 \text{ cm}^2$
Solution : The volume of a sphere, where $r$ is the radius. $V = \frac{4}{3}\pi r^3$ The volume of a cone, where $r$ is the radius and $h$ is the height. $V = \frac{1}{3}\pi r^2 h$ The volume of the three spheres is equal to
Question : Direction: Some equation have been solved on the basis of certain system. Find out the correct answer for the unsolved equation on that basis.
9 x 7 x 4 = 794
3 x 4 x 6 = 436
4 x 2 x 7 = ?
Option 1: 742
Option 2: 247
Option 3: 724
Option 4: 472
Correct Answer: 247
Solution : Here, the given equations follows a pattern in which the first number and the middle number in LHS becomes the tens place digit and the hundreds place digit in the answer part in RHS respectively.
⇒ 9 x 7 x 4 = 794
⇒ 3
Question : Who among the following Mauryan kings turned to Buddhism and its tenet of nonviolence after the Kalinga war?
Option 1: Chandragupta Maurya
Option 2: Bindusara
Option 3: Ashoka
Option 4: Dasharatha
Correct Answer: Ashoka
Solution : The correct answer is Ashoka.
The last significant ruler of India's Mauryan dynasty was Ashoka. Following his victorious conquest of the Kalinga, he turned to Buddhism, gave up violent conquest and embraced a strategy he called "conquer by dharma," realising the carnage of the
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