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TS NMMS 2023 Previous Year Question Paper with Answers | NMMS Telangana Key & Solutions

PART-2
MENTAL ABILITY TEST
TS NMMS 2023
SAT (Scholastic Test)
Mathematics

NMMS Mock Test

126) The value of $\frac{2^{2021}+2^{2019}}{2^{2020}-2^{2018}}$ is…….

A) 2020
B) $\frac{10}3$
C) $2^{1000}+1$
D) 10

View Answer

D) 10

127) The cost of $7\frac23$ meters of rope is $₹12\frac34$ then the cost of rope of 1 meter is……

A) $₹2\frac{30}{47}$
B) $₹3\frac{18}{25}$
C) $₹1\frac{61}{92}$
D) $₹6\frac{16}{90}$

View Answer

C) $₹1\frac{61}{92}$

Problem: $7\tfrac{2}{3}=\dfrac{23}{3}$ metres of rope cost ₹ $12\tfrac{3}{4}=\dfrac{51}{4}$ . Find cost of 1 m.
Solution:
Cost per metre $= \dfrac{51/4}{23/3}=\dfrac{51}{4}\cdot\dfrac{3}{23}=\dfrac{153}{92}$ .
Write as mixed number: $\dfrac{153}{92}=1\;\dfrac{61}{92}$ .
Answer: ₹ $1\tfrac{61}{92}$ . (Option 3)

128) The sides of a triangle are in the ratio of $\frac12:\frac13:\frac14$ If it’s perimeter is 104 cm, then the length of the longest side (in cm) is ……

A) 48
B) 32
C) 26
D) 52

View Answer

A) 48

Explanation:Problem: Sides are proportional to $\tfrac12:\tfrac13:\tfrac14$ . Perimeter $=104$ . Find longest side.
Solution:
Multiply ratios by 12 to clear denominators: sides ∝ $6:4:3$ .
Sum = $6+4+3=13$ parts. One part $=104/13=8$ .
Longest side $=6\times8=48$ cm.
Answer: $48$ cm. (Option 1)

129) The capacity of a tank of dimensions 8m × 6m × 2.5m is ….

A) 120 liters
B) 1200 liters
C) 12000 liters
D) 120000 liters

View Answer

D) 120000 liters

Explanation:Problem: Tank dimensions $8\text{ m}\times6\text{ m}\times2.5\text{ m}$ . Find capacity in litres.
Solution:
Volume $=8\times6\times2.5=120$ cubic metres.
$1\ \text{m}^3=1000$ litres, so capacity $=120\times1000=120000$ litres.
Answer: $120000$ litres. (Option 4)

130) In the given figure, ∠PTQ = 30°, ∠TPQ=34° and ∠SRQ = 45°, then the value of x is……

A) 64°
B) 75°
C) 109°
D) 79°

View Answer

C) 109°

Explanation:Problem (angles): In triangle $\triangle PTQ$ , $\angle P=34^\circ,\ \angle TPQ=30^\circ$ . Point $S$ lies on segment $TQ$ . Ray $SR$ meets the baseline at $R$ so that $\angle SRQ=45^\circ$ . Find $x$ , the angle between $ST$ and $SR$ .
Solution:
First find $\angle PQT$ (angle at $Q$ of $\triangle PTQ$ ):
$\angle Q = 180^\circ - (34^\circ + 30^\circ)=116^\circ.$
The baseline is a straight line $P\!-\!Q\!-\!R$ . The angle between $TQ$ and the ray $QR$ equals
$\angle TQR = 180^\circ - \angle PQT = 180^\circ - 116^\circ = 64^\circ.$
In triangle $\triangle SRQ$ the angles are $\angle SQR=64^\circ$ and $\angle SRQ=45^\circ$ , so the angle at $S$ (between $SR$ and $SQ$ ) is
$\angle RSQ = 180^\circ - (64^\circ+45^\circ)=71^\circ.$
But $ST$ is opposite in direction to $SQ$ (since $S$ lies on segment $TQ$ ), so the required angle between $ST$ and $SR$ is the supplement:
$x = 180^\circ - 71^\circ = 109^\circ.$
Answer: $109^\circ$ . (Option 3)

131) The smallest natural number to be added to 803642 to get a number which is completely divisible by 9 is……

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

View Answer

D) 4

Explanation:Problem: Smallest natural number to add to $803642$ to make it divisible by $9$ .
Solution:
Sum of digits $=8+0+3+6+4+2=23$ . Nearest multiple of 9 greater than 23 is 27.
Needed addition $=27-23=4$ .
Answer: $4$ . (Option 4)

132) If $\frac x3-\frac{2x}5=\frac{2x}3-\frac{11}{30}$ , then the value of ‘x’ is……

A) $\frac12$
B) $-\frac43$
C) $\frac34$
D) $-\frac34$

View Answer

C) $\frac34$

133) Standard form of 0.00000000234 is……

A) $2.34\times10^{-8}$
B) $2.34\times10^{-9}$
C) $234\times10^{-10}$
D) $23.4\times10^{-11}$

View Answer

B) $2.34\times10^{-9}$

Explanation:Write $0.00000000234$ in standard form.
$0.000000001 = 10^{-9}$ . So $0.00000000234 = 2.34\times10^{-9}$ .
Answer: $2.34\times10^{-9}$ . (Option 2)

134) In Δ ABC, AB = BC and in ΔCDE, CD = DE. If ∠BCD = 72°, ∠DEF 124° and ACEF is a straight line, then the value of ‘y’ is……..

A) 52°
B) 58°
C) 68°
D) 76°

View Answer

A) 52°

135) The product of $\left(x^2\;-\;7y^2\right)$ and $\left(x^2\;+\;4y^2\right)$ is….

A) $x^4\;+\;3x^2y^2\;-\;28y^4$
B) $x^4\;-\;3x^2y^2\;-\;28y^4$
C) $x^4\;+\;3x^2y^2\;+\;28y^4$
D) $x^4\;-\;3x^2y^2\;+\;28y^4$

View Answer

B) $x^4\;-\;3x^2y^2\;-\;28y^4$

Explanation:Compute $(x^2-7y^2)(x^2+4y^2)$ .
Multiply: $x^2\cdot x^2 + x^2\cdot4y^2 -7y^2\cdot x^2 -7y^2\cdot4y^2$
$= x^4 +4x^2y^2 -7x^2y^2 -28y^4 = x^4 -3x^2y^2 -28y^4$ .
Answer: $x^4 -3x^2y^2 -28y^4$ . (Option 2)

136) A vertical stick 2 meter tall casts a shadow 5 meter long. At the same time, if a tree casts a shadow 55 meter long, then the height of the tree (in meters) is……

A) 137.5
B) 27.5
C) 22
D) 10

View Answer

C) 22

Explanation:Similar triangles: stick height $2$ m casts shadow $5$ m. Tree shadow $55$ m, so tree height $= \dfrac{2}{5}\times55 = 22$ m.
Answer: $22$ m. (Option 3)

137) If a number exceeds 20% of itself by 40, then the number is……

A) 50
B) 60
C) 80
D) 320

View Answer

A) 50

Explanation:Let number be $n$ . “Number exceeds $20\%$ of itself by $40$ ” means $n = 0.2n + 40$ .
So $0.8n = 40 \Rightarrow n = \dfrac{40}{0.8} = 50$ .
Answer: $50$ . (Option 1)

138) The value of $\sqrt{41+\sqrt{54+\sqrt{88+\sqrt{128+\sqrt{256}}}}}$ Is…….

A) 7
B) 6
C) 8
D) 10

View Answer

A) 7

Explanation:Evaluate nested radicals:
$\sqrt{41+\sqrt{54+\sqrt{88+\sqrt{128+\sqrt{256}}}}}$ .
Compute inside out:
$\sqrt{256}=16$ .
$\sqrt{128+16} = \sqrt{144}=12$ .
$\sqrt{88+12} = \sqrt{100}=10$ .
$\sqrt{54+10} = \sqrt{64}=8$ .
$\sqrt{41+8} = \sqrt{49}=7$ .
Answer: $7$ . (Option 1)

139) If two adjacent angles of a parallelogram are 2x°+25° and 3x° – 5°, then the value of ‘x’ is….

A) 28
B) 32
C) 36
D) 42

View Answer

B) 32

Explanation:Two adjacent angles of a parallelogram are $2x^\circ+25^\circ$ and $3x^\circ-5^\circ$ .
Adjacent angles in a parallelogram are supplementary, so
$(2x+25)+(3x-5)=180 \Rightarrow 5x+20=180 \Rightarrow 5x=160 \Rightarrow x=32.$
Answer: $32$ . (Option 2)

140) If $5^{x-1}+5^x+5^{x+1}=775$ , then the value of ‘x’ is……

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

View Answer

D) 4

141) Top view of the figure made up of Cubes joined together is……

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

View Answer

D) (4)

142) The value of $\left(1^3+2^3+3^3+4^3\right)^\frac{-3}2$ is…….

A) $\frac1{100}$
B) 100
C) $\frac1{1000}$
D) 1000

View Answer

B) 100

143) ABCD and DBEF are rectangles drawn as shown in the figure. If AB 4cm and AD = 3cm, then area of rectangle DBEF (in square cm) is…….

A) 10
B) 12
C) 14
D) 15

View Answer

D) 15

144) Marked price of an article is ₹ 675. If it is sold at a discount of 20%, then it’s selling price (in rupees) is….

A) 540
B) 525
C) 510
D) 500

View Answer

A) 540

Explanation:Marked price = ₹675, discount = $20\%$ . Selling price $= 0.8\times675$ .
$0.8\times675 = 540.$
Answer: ₹540. (Option 1)

145) The compound interest on ₹ 8000 at 5% per annum for 2 years compounded annually is……

A) ₹ 8280
B) ₹ 400
C) ₹ 8420
D) ₹ 820

View Answer

D) ₹ 820

Explanation:Compound interest on ₹8000 at $5\%$ p.a. for 2 years (compounded annually).
Amount $=8000(1+0.05)^2 =8000(1.05)^2 =8000(1.1025)=8820.$
Compound interest $=8820-8000=820.$
Answer: ₹820. (Option 4)

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PART-2 MENTAL ABILITY TEST TS NMMS 2023 SAT (Scholastic Test) Mathematics

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PART-2
MENTAL ABILITY TEST
TS NMMS 2023
SAT (Scholastic Test)
Mathematics